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z`Inr|*^tvYKgj9Ux1kOA2IS`4{N4XGH&2_G_ih|o7uC-y8teNoqx~qGYi|@*#q?vo z$@63r3ZmA$4>fplm+f96>&*QZU|znHb#={dM-BKFZRRV+x+;_wEt?gQ)7vU*_@iI6 z*LMo;gN=-H{8BhU3fa==ZL3lv@1f~>^0fU%GRxc#U%k3LbxnKqt%!#ryH@X58ad#x z1!L&y!VLFEr>A!(o$xC8WI}N=rlcs}iQN!}#c_SqBi0@N7KXodHEak&j*;7Xou+o- zKxuv*PGVfGWjwjXXe2gT_c%hr?izQehJ%SNnnstWEi24v=S?7@SL()OcJi!8LB4$x N!wA80BQl^o{{oD0)GPo1 literal 0 HcmV?d00001 diff --git a/_posts/2020-08-02-prediction-of-medical-costs/prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/prediction-of-medical-costs.Rmd new file mode 100644 index 00000000..eba88cb0 --- /dev/null +++ b/_posts/2020-08-02-prediction-of-medical-costs/prediction-of-medical-costs.Rmd @@ -0,0 +1,617 @@ +--- +title: Prediction of Medical Costs +categories: + - regression + - visualization + - tuning +author: + - name: Charlotte Castell + - name: Veronika Kronseder + - name: Melissa Schmoll + - name: Eileen Wuest +date: 08-02-2020 +description: | + Use case illustrating data vizualization and tuning via mlr3 on the "Medical Costs" dataset. +output: + distill::distill_article: + self_contained: false + css: ../../custom.css +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + echo = TRUE, + R.options = list(width = 80), + warning = FALSE, + message = FALSE +) +lgr::get_logger("mlr3")$set_threshold("warn") +library(kableExtra) +``` + +```{r setup, include=FALSE} + +# get operating system information +os = Sys.info()[["sysname"]] + +# set corresponding installation type +itype = ifelse(os == "Linux", "source", "binary") + +# a bunch of required packages +# required packages +packages_required = c( + "mlr3", + "mlr3learners", + "mlr3viz", + "mlr3tuning", + "mlr3filters", + "mlr3misc", + "ggplot2", + "grid", + "gridExtra", + "dplyr", + "tidyr", + "data.table", + "ranger", + "paradox", + "RCurl" +) + +# check which ones are not installed +not_installed = packages_required[!packages_required %in% + installed.packages()[, "Package"]] + +# install them +if (length(not_installed) > 0) { + lapply( + not_installed, + install.packages, + repos = "http://cran.us.r-project.org", + dependencies = TRUE, + type = itype + ) +} + +# load them +lapply(packages_required, library, character.only = TRUE) +``` + + +## Introduction + +Our project "Prediction of Medical Costs" is an implementation of supervised learning. The algorithms used and the topic of supervised learning more generally were covered in the course "Introduction to Machine Learning" as a subfield of Machine Learning, which in turn is a subfield of Artificial Intelligence. The main task of supervised learning is to find a function explaining an outcome, given a specified set of objects, for which all features as well as the outcome are known. + +Myriad implementations of supervised learning algorithms can be found in a wide range of fields of science and business. This project serves as an example for an implementation in the actuarial sciences. It analyses insurance costs based on the following data set: "https://www.kaggle.com/mirichoi0218/insurance". Applying supervised machine learning methods, we want to investigate the following questions: + +1. Which learner qualifies best to explain insurance charges by means of the given covariates? +2. What is the unbiased generalisation error associated with the selected model? +3. Which tariffication criteria (= covariates) have the strongest impact on the charges? + +Firstly, we will introduce the data set. We will then apply nested resampling in order to explain and predict insurance charges. Lastly, we will investigate the feature importance emerging from our final model. + +## Descriptive Analysis of the Data + +Below the data are imported and a seed is set for reproducibility. + +```{r} +url = getURL("https://raw.githubusercontent.com/stedy/Machine-Learning-with-R-datasets/master/insurance.csv") +insurance = read.csv(text = url) +set.seed(246) +``` + +The data set consists of 1338 insurees and their respective information on age, sex, bmi, number of children, smoking behaviour and region. As mentioned above our defined target variable, the outcome, are insurance costs named charges. These shall be explained by the information given about each insuree. + +```{r, echo = FALSE} +head(insurance) +``` + +The target variable, charges, is continuous and its distribution is shown below. It has to be noted, that the variable has been logarithmised in order to avoid the problem of non-normality. + +```{r, echo = FALSE} +ggplot(insurance, aes(x = log(charges))) + + geom_histogram(col = "darkgray") + + theme_bw() + +insurance$charges = log(insurance$charges) +``` + +The following plots give a brief overview of the distribution of the independent variables: + +```{r, echo = FALSE} +age = ggplot(insurance, aes(x = age)) + + geom_histogram(col = "darkgray", size = 0.5) + + theme_bw() + +sex = ggplot(insurance, aes(sex)) + + geom_bar() + + theme_bw() + +bmi = ggplot(insurance, aes(x = bmi)) + + geom_histogram(col = "darkgray", size = 0.5) + + theme_bw() + +children = ggplot(insurance, aes(x = children)) + + geom_bar() + + theme_bw() + + scale_x_continuous(breaks = 0:6, labels = c("0", "1", "2", "3", "4", "5", "6")) + +smoker = ggplot(insurance, aes(x = smoker)) + + geom_bar() + + theme_bw() + +levels(insurance$region)[levels(insurance$region) == "northeast"] = "ne" +levels(insurance$region)[levels(insurance$region) == "northwest"] = "nw" +levels(insurance$region)[levels(insurance$region) == "southeast"] = "se" +levels(insurance$region)[levels(insurance$region) == "southwest"] = "sw" + +region = ggplot(insurance, aes(x = region)) + + geom_bar() + + theme_bw() + + theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1)) + +grid.arrange(age, sex, bmi, children, smoker, region, nrow = 2) +``` + +Before we resume in our analysis, all independent, metric variables will be standardised (i.e. each variable will be transformed to have a mean of 0 and standarad deviation of 1). This ensures commensurability of variables originally measured on differing metric scales and is particularly important for learners, which assess distances between individual observations. + + +```{r} +insurance[, c("age", "bmi", "children")] = + scale(insurance[, c("age", "bmi", "children")]) +``` + + + +Given the aforementioned continuity of our target variable, it is clear that we face a so-called *regression problem*. In regression problems a numeric output associated with the variables is predicted - opposed to a specific class as it is the case for so-called *classification problems*. First of all, we initiate our task which specifies the underlying data and the target variable: + +```{r} +ins_task = TaskRegr$new(id = "ins_task", backend = insurance, target = "charges") +``` + +The plots below give a brief overview of the conditional distribution of charges given each independent variable. It can, for example, be seen that charges seem to increase with age or that smokers seem to face higher charges than non-smokers. + +```{r echo = FALSE} +age = ggplot() + + geom_point(data = insurance, aes(x = age, y = charges), col = "grey30") + + ggtitle("age") + + xlab("age (standradised)") + + theme_bw() + + theme(plot.title = element_text(hjust = 0.5)) + +bmi = ggplot() + + geom_point(data = insurance, aes(x = bmi, y = charges), col = "grey30") + + ggtitle("bmi") + + xlab("bmi (standradised)") + + theme_bw() + + theme(plot.title = element_text(hjust = 0.5)) + +children = ggplot() + + geom_point(data = insurance, aes(x = children, y = charges), col = "grey30") + + ggtitle("children") + + xlab("children (standradised)") + + theme_bw() + + theme(plot.title = element_text(hjust = 0.5)) + +sex = ggplot() + + geom_histogram(data = insurance, aes(x = charges), col = "darkgray", size = 0.5) + + facet_wrap(~sex, ncol = 1) + + ggtitle("sex") + + theme_bw() + + theme(plot.title = element_text(hjust = 0.5)) + +smoker = ggplot() + + geom_histogram(data = insurance, aes(x = charges), col = "darkgray", size = 0.5) + + facet_wrap(~smoker, ncol = 1) + + ggtitle("smoker") + + theme_bw() + + theme(plot.title = element_text(hjust = 0.5)) + +region = ggplot() + + geom_histogram(data = insurance, aes(x = charges), col = "darkgray", size = 0.25) + + facet_wrap(~region, ncol = 2) + + ggtitle("region") + + theme_bw() + + theme(plot.title = element_text(hjust = 0.5)) + + +grid.arrange(age, sex, bmi, children, smoker, region, nrow = 2) +``` + + +Different learners are available to solve regression problems and each learner produces a mapping function (also called model) from the observed dataset and its features. + +The learners we use are Linear Model (LM), k-Nearest Neighbors (kNN), Decision Trees (CART) and Random Forest (Ranger). It may be interesting to note, that while the first learner is suitable for regression tasks only, the other ones are suitable for both, regression and classification tasks. Just like the task, the learners have to be initiated: + +```{r} +lrn_lm = lrn("regr.lm") +lrn_kknn = lrn("regr.kknn") +lrn_rpart = lrn("regr.rpart") +lrn_ranger = lrn("regr.ranger") +``` + + +## Model Optimization: Nested Resampling + +To evaluate the performance of these learners, several resampling strategies exist. The mlr3 package contains 6 predefined options: Cross-validation, Leave-one-out cross validation, Repeated cross-validation, Out-of-bag bootstrap and other variants, Monte-Carlo cross-validation and Holdout. + +Nested Resampling embedds all parts of model-building including hyperparameter tuning in the model-finding process. Some of the associated steps can require resampling themselves, which is done within the *inner loop*. To obtain unbiased performance estimates, all parts of the model-building should be based on training data. An untouched test set should be reserved for model evaluation in the *outer loop*, which again requires the application of resampling. The resampling strategies for the inner and the outer loop can be defined individually. We will, however, focus solely on "5-fold-cross-validation" as it has become one of the standard methods. + +## Inner Loop: Model and Hyperparameter Tuning + +Adressing the inner loop, we first specify the hyperparameters of each learning algorithm - if applicable. These hyperparameters can have a strong influence on the performance of the algorithm and it can be advantageous to try different settings before fitting the model on the training data. An example would be the specification of the number of neareast neighbours, $k$, for the kNN learner. This process is called *tuning* the model. + +Depending on the selected learner, various hyperparameters are obtained. Each of them impacts the performance of the learning algorithm. In order to evaluate this performance, we then need to choose a resampling strategy and a performance measure. + +Again, in regression tasks, there is a variety of potential measures of accuracy to compare the performance of each learner, such as Mean Squared Error (MSE), Mean Absolute Error (MAE) and $R^2$. We will calculate all three to check if they come to the same conclusions. + +```{r} +resampling_inner = rsmp("cv", folds = 5) +# measures = list(msr("regr.mse"), msr("regr.mae"), msr("regr.rsq")) +measures = mlr_measures$mget(c("regr.mse", "regr.mae", "regr.rsq")) +``` + +Before the actual tuning starts, we still need to select the way, in which the optimisation takes place. In other words, to find the optimal hyperparamters of a model, which result in the most accurate predictions, we need to choose an the parameter space as well as the class and termination criterion of our tuner. + +*Grid search* is a technique, which attempts all hyperparameter combinations on a multi-dimensional discretized grid, in arbitrary order. This means, grid search builds a model for every combination of hyperparameters sepecified and evaluates each model. It scales, however, badly as the combinatorial possibilities explode. + +A more efficient technique for hyperparamter tuning is *random search*, where random combinations of hyperparamters are tested to find the best solution instead of all possible combinations exhaustively. + +```{r} +tuner_rs = mlr3tuning::tnr("random_search") +``` + +To determine when to stop tuning a *terminator* is used. Here, we create a terminator which allows for 30 evaluations. + +```{r} +terminator = trm("evals", n_evals = 30) +``` + + +## Automating the Tuning of kNN, CART and Ranger + +K-Nearest Neighbors is a computationally complex procedure but very simple in terms of understanding as well as implementation. Furthermore, the resulting models often have a high degree of accuracy. As shown below, the parameter $k$, the number of neighbors, will be optimized as part of the model development. We specify that $k$-values between 10 and 40 shall be taken into account. + +```{r} +param_set_knn = ParamSet$new(params = list(ParamInt$new("k", lower = 10, upper = 40))) +``` + +For Classification Tree learners there are more options for hyperparameter optimisation. In our case we choose to optimise two hyperparameters: Firstly, the complexity parameter $cp$. It ensures that only splits that improve the overall fit by a factor of $cp$ are attempted. Secondly, the hyperparameter $minsplit$. It determines the minimal number of observations per leaf necessary for a split to be attempted. + +```{r} +param_set_rpart = + ParamSet$new(params = list( + ParamDbl$new("cp", lower = 0.001, upper = 0.5), + ParamInt$new("minsplit", lower = 1, upper = 50))) +``` + +Finally, for the Random Forest learner, the hyperparameters we choose to optimise are $mtry$, the number of randomly sampled features considered by each tree when splitting a node, and $min.node.size$, the minimum number of observations per node. An exemplary value of 20 means that no node with fewer than 20 cases will be split. + +```{r} +param_set_ranger = + ParamSet$new(params = list( + ParamInt$new("mtry", lower = 2, upper = 6), + ParamInt$new("min.node.size", lower = 1, upper = 50))) +``` + + +Automated hyperparameter tuning uses methods such as Gradient Decent, Bayesian Optimization or Evolutionary Algorithms to conduct a guided search for the best hyperparameters. +The *AutoTuner* from the mlr3 package adjusts itself by first tuning the hyperparameters of the respective learner on the training data, then setting the optimal parameters in the learner and finally fitting the model on the complete training dataset. + +```{r} +at_knn = AutoTuner$new( + learner = lrn_kknn, + resampling = resampling_inner, + measure = msr("regr.mse"), + search_space = param_set_knn, + terminator = terminator, + tuner = tuner_rs +) +at_rpart = AutoTuner$new( + learner = lrn_rpart, + resampling = resampling_inner, + measure = msr("regr.mse"), + search_space = param_set_rpart, + terminator = terminator, + tuner = tuner_rs +) +at_ranger = AutoTuner$new( + learner = lrn_ranger, + resampling = resampling_inner, + measure = msr("regr.mse"), + search_space = param_set_ranger, + terminator = terminator, + tuner = tuner_rs +) +``` + +```{r grid1, echo=FALSE, eval=FALSE} +# An dieser Stelle wird Code ausgeführt, aber noch nicht im Markdown angezeigt (wir interessieren uns an dieser Stelle nur für die Boxplots zu den Tuning-Ergebnissen) +resampling_outer = rsmp("cv", folds = 5) + +grid = benchmark_grid( + task = ins_task, + learner = list(lrn_lm, at_knn, at_rpart, at_ranger), + resampling = resampling_outer +) + +bmr = benchmark(grid, store_models = TRUE) + + +# Each fold of outer resampling computes tuning, i.e. there are different sets of tuned hyperparameters +# Extract optimal HP for each fold of outer resampling: + +knn = bmr$score()[learner_id == "regr.kknn.tuned"]$learner +hp_knn = data.frame( + iteration = seq(1:resampling_outer$iters), + k = NA) +for (i in 1:resampling_outer$iters) { + hp_knn$k[i] = knn[[i]]$tuning_result$params +} + +plot_hp_knn = ggplot(data = hp_knn) + + geom_boxplot(aes(x = 1, y = unlist(k))) + + ylim(c(10, 40)) + + geom_hline(yintercept = 10, col = "red", linetype = "dashed") + + geom_hline(yintercept = 40, col = "red", linetype = "dashed") + + labs(y = "k", x = "", subtitle = "Learner: kNN \nHP: k") + + theme_bw() + + theme(axis.text.x = element_blank()) + +rpart = bmr$score()[learner_id == "regr.rpart.tuned"]$learner +hp_rpart = data.frame( + iteration = seq(1:resampling_outer$iters), + cp = NA, + minsplit = NA) +for (i in 1:resampling_outer$iters) { + hp_rpart$cp[i] = rpart[[i]]$tuning_result$params$cp + hp_rpart$minsplit[i] = rpart[[i]]$tuning_result$params$minsplit +} + +plot_hp_rpart_1 = ggplot(data = hp_rpart) + + geom_boxplot(aes(x = 1, y = unlist(cp))) + + ylim(c(0.001, 0.5)) + + geom_hline(yintercept = 0.001, col = "red", linetype = "dashed") + + geom_hline(yintercept = 0.5, col = "red", linetype = "dashed") + + labs(y = "cp", x = "", subtitle = "Learner: Decision Trees \nHP: cp") + + theme_bw() + + theme(axis.text.x = element_blank()) + +plot_hp_rpart_2 = ggplot(data = hp_rpart) + + geom_boxplot(aes(x = 1, y = unlist(minsplit))) + + ylim(c(1, 50)) + + geom_hline(yintercept = 1, col = "red", linetype = "dashed") + + geom_hline(yintercept = 50, col = "red", linetype = "dashed") + + labs(y = "minsplit", x = "", subtitle = "Learner: Decision Trees \nHP: minsplit") + + theme_bw() + + theme(axis.text.x = element_blank()) + +ranger = bmr$score()[learner_id == "regr.ranger.tuned"]$learner +hp_ranger = data.frame( + iteration = seq(1:resampling_outer$iters), + # num.trees = NA, + mtry = NA, + min.node.size = NA +) +for (i in 1:resampling_outer$iters) { + hp_ranger$mtry[i] = ranger[[i]]$tuning_result$params$mtry + hp_ranger$min.node.size[i] = ranger[[i]]$tuning_result$params$min.node.size +} + + +plot_hp_ranger_1 = ggplot(data = hp_ranger) + + geom_boxplot(aes(x = 1, y = unlist(min.node.size))) + + ylim(c(1, 50)) + + geom_hline(yintercept = 1, col = "red", linetype = "dashed") + + geom_hline(yintercept = 50, col = "red", linetype = "dashed") + + labs(y = "min.node.size", x = "", subtitle = "Learner: Random Forest \nHP: min.node.size") + + theme_bw() + + theme(axis.text.x = element_blank()) + +plot_hp_ranger_2 = ggplot(data = hp_ranger) + + geom_boxplot(aes(x = 1, y = unlist(mtry))) + + ylim(c(2, 6)) + + geom_hline(yintercept = 2, col = "red", linetype = "dashed") + + geom_hline(yintercept = 6, col = "red", linetype = "dashed") + + labs(y = "mtry", x = "", subtitle = "Learner: Random Forest \nHP: mtry") + + theme_bw() + + theme(axis.text.x = element_blank()) + +grid.arrange(plot_hp_knn, plot_hp_rpart_1, plot_hp_rpart_2, plot_hp_ranger_1, plot_hp_ranger_2, + nrow = 2, + top = textGrob("Tuning Results: Hyperparameter Settings", gp = gpar(fontface = 2, fontsize = 14))) +``` + +```{r grid1rds, echo=FALSE} +# saveRDS(grid1, "grid1.rds") +plot(readRDS("grid1.rds")) +``` + + +These plots show the range of optimal hyperparameters obtained by the inner resampling loop. So, each boxplot is based on 5 values. The red lines (dashed) indicate the range, within which the hyperparameters were optimised. It can, for example, be seen that while various different $k$-values are deemed optimal for kNN, $mtry = 4$ is determined the optimal setting for the Ranger algorithm in every iteration. Also, the optimal $cp$ in CART seems to lie within a small range, while the best-performing $minsplit$-parameter is rather volatile. However, the illustration neglects the fact that in tuning we are looking at combinations of hyperparameters and the more dimensions we consider, the fewer of the hyperparameter space we are investigating with a fixed number of evaluations in the tuning. + + +## Outer Loop: Model Selection + +For the outer loop of our nested resampling, we also define a 5-fold cross validation as our resampling strategy. This means, we obtain five pairs of training and test sets. Each of those initiates the tuning process for the hyperparameter spaces specified earlier. It is possible - and depending on the individual case even likely - that the optimal hyperparameter settings derived from the five inner loops differ amongst each other. For each of the five iterations, the learner is fitted on the outer training set while its performance is evaluated on the outer test set. By averaging these five performance estimates of the outer loops, we get an unbiased performance estimate for the learner. + +As mentioned earlier, we aim to compare the performance of different learning algorithms on the prediction of insurance costs. By initiating a benchmarking process, we can combine all candidate models in one single nested resampling process. All we have to do is to define a grid with the regression task, the (tuned) learners and the outer resampling strategy. + +```{r benchmark, echo=TRUE, eval=FALSE} +resampling_outer = rsmp("cv", folds = 5) + +grid = benchmark_grid( + task = ins_task, + learner = list(lrn_lm, at_knn, at_rpart, at_ranger), + resampling = resampling_outer +) + +bmr = benchmark(grid, store_models = TRUE) +``` + +This part of the analysis can be computationally demanding. With our termination criterion of 30 evaluations in the tuning process, a 5-fold CV in the inner loop and another 5-fold CV in the outer loop, a total of 755 models is fitted for each learner that requires tuning and another 5 models for the Linear Model, which doesn't have hyperparamerters to optimize. Overall, in our example the benchmarking fits 2270 models, which in turn allow for us to make a decision on the best model and its generalisation error. + + +```{r echo=FALSE, eval=FALSE} +scores = bmr$score(measures) %>% + select(Learner = learner_id, Iteration = iteration, MSE = regr.mse) + +# Tabelle mit performance estimates, die den Boxplots zugrunde liegen: nicht in Markdown aufnehmen, aber vielleicht für Test nutzen? +# scores %>% kable() %>% +# kable_styling(full_width = F)%>% +# pack_rows("Linear Model", 1, 5) %>% +# pack_rows("KNN", 6, 10) %>% +# pack_rows("CART", 11, 15) %>% +# pack_rows("Random Forest", 16, 20) + +plot_bmr = autoplot(bmr) + + labs(x = "Learner", y = "MSE", title = "MSE-Score for each learner over the performance estimates") + + theme_bw() +plot_bmr +``` + +![Benchmarking Boxplot](bmr_plot.png) + +Benchmarking generates scores for each learner and each outer loop iteration. Drawing boxplots over the performance estimates - here the Mean Squared Error - shows that kNN seems to work fine but produces some variation in performance estimates. The Linear Model doesn't deliver satisfactory results and produces large MSEs compared to the other candidate learners. Random Forest appears to be the best model producing accurate predictions in terms of the MSE. Finally, Decision Trees produce performance estimates similar to those of kNN, with even smaller variability. + +One of our inintial questions was: Which learner qualifies best to predict insurance charges - that is, as accurately as possible? + +To come to answer this question, we do not necessarily have to study the boxplots - though it might be helpful. Instead, we can access the aggregated performance estimates for each learner, directly. In the graphic below the learners are ranked according to our three performance measures: MSE, MAE and $R^2$. The inverse value of $R^2$ has been computed and plotted to allow for easy comparison; improvements are indicated by lower values in each of the three plots. + +```{r, eval=FALSE, echo=FALSE} +tab = bmr$aggregate(measures) + +ranks = tab[, .(learner_id, regr.mse, rank_mse = rank(regr.mse), regr.mae, rank_mae = rank(regr.mae), inv_regr.rsq = 1 / regr.rsq, rank_rsq = rank(-regr.rsq))] +``` + +```{r tabrds, echo=FALSE} +# saveRDS(ranks, "ranks.rds") +ranks = readRDS("ranks.rds") +``` + + +```{r echo=FALSE, eval=TRUE} +# Table of aggregated results with ranking +# ranks[order(ranks$rank_mse),] %>% +# kable() %>% +# kable_styling(full_width = F) + +ranks = ranks %>% pivot_longer(c(regr.mse, regr.mae, inv_regr.rsq), names_to = "key", values_to = "value") +ranks$key = factor(ranks$key, levels = c("regr.mse", "regr.mae", "inv_regr.rsq")) + +# Visualization +ggplot(data = ranks) + + geom_point(aes(x = key, y = value, col = as.factor(learner_id)), size = 5) + + facet_wrap(~key, + scales = "free", + labeller = as_labeller(c("regr.mse" = "MSE", "regr.mae" = "MAE", "inv_regr.rsq" = "Inverse of R^2"))) + + theme_bw() + + theme(axis.text.x = element_blank(), axis.title = element_blank(), legend.position = "right") + + scale_color_discrete(labels = c( + "regr.kknn.tuned" = "kNN (tuned)", + "regr.lm" = "LM", + "regr.ranger.tuned" = "Ranger (tuned)", + "regr.rpart.tuned" = "CART (tuned)")) + + labs(col = "Learner") +``` + + +But what about the hyperparameters? We just learned that from nested resampling we obtain five different sets of optimal combinations: Which one of them shall we use for the final model? + +The answer is: none of them. Unlike before, the final model is fit on the whole dataset and includes its own tuning step and resampling. The major difference is that there is no outer loop. Based on the tuning results, the model is trained on the whole dataset. + + +```{r eval = FALSE} +lgr::get_logger("mlr3")$set_threshold("warn") +learner = lrn("regr.ranger", importance = "impurity") + +# Autotuning to find the optimal hyperparameter configuration +# based on the complete dataset: +at_ranger_final = AutoTuner$new( + learner = learner, + resampling = resampling_inner, + measure = msr("regr.mse"), + search_space = param_set_ranger, + terminator = terminator, + tuner = tuner_rs +) + +# Train the model: +at_ranger_final$store_tuning_instance = TRUE +at_ranger_final$train(ins_task) +``` + +```{r eval = FALSE, echo=FALSE} +tab_tuning = at_ranger_final$archive$data()[, c("batch_nr", "regr.mse", "min.node.size", "mtry")] + +# tab_tuning[regr.mse == min(tab_tuning$regr.mse),] + +# tab_tuning %>% +# kable() %>% +# kable_styling(full_width = F) %>% +# row_spec(10, bold = T, background = "lightpink") +``` + +```{r tabtuningrds, echo=FALSE} +# saveRDS(tab_tuning, file = "tab_tuning.rds") +tab_tuning = readRDS("tab_tuning.rds") +learner = lrn("regr.ranger", importance = "impurity") +``` + +From the tuning process of our final model, we conlude that the optimal hyperparameter setting is achieved through the combination of $min.node.size = 30$ and $mtry = 4$. The figure below illustrates the investigated parameter combinations via random search. The color intensity matches the value of the respective MSE and the hyperparameter combination with the best performance, which is used to train the model, is highlighted in red. + +```{r echo=FALSE, eval=TRUE} +ggplot() + + geom_point(aes(x = min.node.size, y = mtry, fill = regr.mse, col = regr.mse), data = tab_tuning, size = 5, shape = 21) + + geom_point(aes(x = min.node.size, y = mtry, fill = regr.mse), data = tab_tuning[regr.mse == min(tab_tuning$regr.mse), ], col = "red", size = 5, shape = 21, stroke = 2) + + annotate("text", + x = tab_tuning$min.node.size[tab_tuning$regr.mse == min(tab_tuning$regr.mse)], + y = tab_tuning$mtry[tab_tuning$regr.mse == min(tab_tuning$regr.mse)], col = "red", label = "min", vjust = -1) + + labs(title = "Visualization of Tuning Results", subtitle = "Random Search, Termination after 30 evaluations") + + theme_bw() + + labs(fill = "MSE", col = "MSE") +``` + + + +Eventually, we want to investigate how well the final model can explain the data observed. Overall, the model fit does not seem too bad: the majority of observations are close to the diagonal. There is, however, a considerable number of observations with charges higher than the ones predicted by the model. This could indicate that features are not considered with their true functionality or that the insurance company uses additional tariffication criteria outside the dataset. + +```{r echo = FALSE, eval=FALSE} +# Compare predicted values to true values: +autoplot(at_ranger_final$predict(ins_task)) + + theme_bw() +``` + +![Prediction autotuned ranger](prediction_at_ranger.png) + +## Feature Importance + +As a last step of our analysis, we want to shed some light onto the functionality of our final "black box" model. To get a better understanding of the predictions made, we investigate the importance of each individual covariate. This can be done with the help of filter methods, which assign an importance value to each feature, which will then be ranked. For the Ranger learning algorithm, we can make use of the filter methods embedded in the mlr3-package. + +```{r} +filter = flt("importance", learner = learner) +filter$calculate(ins_task) +``` + + +```{r echo = FALSE} +var = as.data.table(filter) +var$rank = 7 - rank(var$score) +var[order(var$rank), ] %>% + kable() %>% + kable_styling(full_width = F) + +ggplot(data = var, aes(x = feature, y = score)) + + geom_bar(stat = "identity") + + labs(x = "Features", y = "Feature Importance") + + theme_bw() +``` + + +When looking at *impurity* as a measure of importance, we can see that first and foremost, the smoking status determines the predicted value of insurance charges. This is followed by age. The bmi, on the other hand, doesn't seem to have a strong impact on the predicted charges and similarly, the remaining features (children, region and sex) lead to minor improvments in impurity only. Overall, these findings are supported by domain knowledge and are in line with the descriptive analysis mentioned above. + + +## Summary and Implications + +Our analysis solves the regression task of predicting insurance charges by computing a supervised machine learning model. Among a selection of candidate models, we identify Random Forest as the preferred learning algorithm. To determine the optimal hyperparameter configuration, we include a tuning step which is embedded in a nested resampling approach. This way, we obtain unbiased performance estimators without reducing our dataset, which the model is trained on. + +The scope of our project was limited by factors like time and computing power. To improve the analysis other learning algorithms, resampling strategies and tuning configurations could be tested. Moreover, advanced feature selection and feature engineering may improve the model's performance estimate. 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...dical-costs.Rmd => 2020-08-02-prediction-of-medical-costs.Rmd} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename _posts/2020-08-02-prediction-of-medical-costs/{prediction-of-medical-costs.Rmd => 2020-08-02-prediction-of-medical-costs.Rmd} (100%) diff --git a/_posts/2020-08-02-prediction-of-medical-costs/prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd similarity index 100% rename from _posts/2020-08-02-prediction-of-medical-costs/prediction-of-medical-costs.Rmd rename to _posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd From 79900346d779a82fb67e49676e826b6bdb47b30b Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Sun, 2 Aug 2020 15:32:30 +0200 Subject: [PATCH 03/17] update & tidy description --- DESCRIPTION | 17 ++++++++++++----- 1 file changed, 12 insertions(+), 5 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index c17bc1ea..e6b07aa7 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -11,23 +11,27 @@ Description: Case studies and examples for 'mlr3'. License: CC0 URL: https://github.com/mlr-org/mlr3gallery Imports: - DataExplorer, - GGally, - MASS, - OpenML, anytime, bbotk (>= 0.2.0), blogdown, caret, + data.table, + DataExplorer, distill, + dplyr, e1071, farff, + GGally, ggmap, + ggplot2, ggpubr, git2r, glmnet, + grid, + gridExtra, igraph, kknn, + MASS, mlbench, mlr3, mlr3book, @@ -41,19 +45,22 @@ Imports: mlr3proba, mlr3tuning, mlr3viz, + OpenML, paradox, praznik, precrec, ranger, rchallenge, + RCurl, skimr, smotefamily, stopwords, + tidyr, visNetwork, xgboost Remotes: - mlr-org/mlr3pipelines, mlr-org/mlr3book, + mlr-org/mlr3pipelines, mlr3learners/mlr3learners.randomforest Encoding: UTF-8 LazyData: true From 4d8af134ed6bc42a768ccd2815c23788e15efc43 Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Mon, 3 Aug 2020 13:33:20 +0200 Subject: [PATCH 04/17] add kableExtra to description --- DESCRIPTION | 1 + 1 file changed, 1 insertion(+) diff --git a/DESCRIPTION b/DESCRIPTION index e6b07aa7..e72cd671 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -30,6 +30,7 @@ Imports: grid, gridExtra, igraph, + kableExtra, kknn, MASS, mlbench, From 882d93e12a0982f6cda04969b8ef9469742549ac Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Mon, 3 Aug 2020 14:54:35 +0200 Subject: [PATCH 05/17] grid.arrange --- .../2020-08-02-prediction-of-medical-costs.Rmd | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index eba88cb0..78d261e6 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -421,13 +421,14 @@ grid.arrange(plot_hp_knn, plot_hp_rpart_1, plot_hp_rpart_2, plot_hp_ranger_1, pl top = textGrob("Tuning Results: Hyperparameter Settings", gp = gpar(fontface = 2, fontsize = 14))) ``` -```{r grid1rds, echo=FALSE} +```{r gridrds, echo=FALSE} # saveRDS(grid1, "grid1.rds") -plot(readRDS("grid1.rds")) +grid1 <- readRDS("grid1.rds") +grid.arrange(grid1) ``` -These plots show the range of optimal hyperparameters obtained by the inner resampling loop. So, each boxplot is based on 5 values. The red lines (dashed) indicate the range, within which the hyperparameters were optimised. It can, for example, be seen that while various different $k$-values are deemed optimal for kNN, $mtry = 4$ is determined the optimal setting for the Ranger algorithm in every iteration. Also, the optimal $cp$ in CART seems to lie within a small range, while the best-performing $minsplit$-parameter is rather volatile. However, the illustration neglects the fact that in tuning we are looking at combinations of hyperparameters and the more dimensions we consider, the fewer of the hyperparameter space we are investigating with a fixed number of evaluations in the tuning. +These plots show the range of optimal hyperparameters obtained by the inner resampling loop. So, each boxplot is based on 5 values. The red lines (dashed) indicate the range, within which the hyperparameters were optimized. It can, for example, be seen that while various different $k$-values are deemed optimal for kNN, $mtry = 4$ is determined the optimal setting for the Ranger algorithm in every iteration. Also, the optimal $cp$ in CART seems to lie within a small range, while the best-performing $minsplit$-parameter is rather volatile. However, the illustration neglects the fact that in tuning we are looking at combinations of hyperparameters and the more dimensions we consider, the fewer of the hyperparameter space we are investigating with a fixed number of evaluations in the tuning. ## Outer Loop: Model Selection From fc43ce4ab688d559838f86cfd50f68da189b4ec1 Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Wed, 2 Sep 2020 17:11:16 +0200 Subject: [PATCH 06/17] editing text --- ...2020-08-02-prediction-of-medical-costs.Rmd | 256 ++++++++---------- .../grid1.rds | Bin 21386 -> 0 bytes .../hyperparam_setting.png | Bin 0 -> 8146 bytes 3 files changed, 117 insertions(+), 139 deletions(-) delete mode 100644 _posts/2020-08-02-prediction-of-medical-costs/grid1.rds create mode 100644 _posts/2020-08-02-prediction-of-medical-costs/hyperparam_setting.png diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index 78d261e6..263d7ded 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -9,6 +9,8 @@ author: - name: Veronika Kronseder - name: Melissa Schmoll - name: Eileen Wuest +editor: + - name: Henri Funk date: 08-02-2020 description: | Use case illustrating data vizualization and tuning via mlr3 on the "Medical Costs" dataset. @@ -18,7 +20,7 @@ output: css: ../../custom.css --- -```{r, include = FALSE} +```{r, include=FALSE} knitr::opts_chunk$set( echo = TRUE, R.options = list(width = 80), @@ -30,65 +32,29 @@ library(kableExtra) ``` ```{r setup, include=FALSE} - -# get operating system information -os = Sys.info()[["sysname"]] - -# set corresponding installation type -itype = ifelse(os == "Linux", "source", "binary") - -# a bunch of required packages -# required packages -packages_required = c( - "mlr3", - "mlr3learners", - "mlr3viz", - "mlr3tuning", - "mlr3filters", - "mlr3misc", - "ggplot2", - "grid", - "gridExtra", - "dplyr", - "tidyr", - "data.table", - "ranger", - "paradox", - "RCurl" -) - -# check which ones are not installed -not_installed = packages_required[!packages_required %in% - installed.packages()[, "Package"]] - -# install them -if (length(not_installed) > 0) { - lapply( - not_installed, - install.packages, - repos = "http://cran.us.r-project.org", - dependencies = TRUE, - type = itype - ) -} - -# load them -lapply(packages_required, library, character.only = TRUE) +library(mlr3verse) +library(ggplot2) +library(grid) +library(gridExtra) +library(dplyr) +library(tidyr) +library(RCurl) + +longrun = FALSE ``` ## Introduction -Our project "Prediction of Medical Costs" is an implementation of supervised learning. The algorithms used and the topic of supervised learning more generally were covered in the course "Introduction to Machine Learning" as a subfield of Machine Learning, which in turn is a subfield of Artificial Intelligence. The main task of supervised learning is to find a function explaining an outcome, given a specified set of objects, for which all features as well as the outcome are known. - -Myriad implementations of supervised learning algorithms can be found in a wide range of fields of science and business. This project serves as an example for an implementation in the actuarial sciences. It analyses insurance costs based on the following data set: "https://www.kaggle.com/mirichoi0218/insurance". Applying supervised machine learning methods, we want to investigate the following questions: +Myriad implementations of supervised learning algorithms can be found in a wide range of fields of science and business. +This project serves as an example for an implementation in the actuarial sciences. +It analyses insurance costs based on the following data set: "https://www.kaggle.com/mirichoi0218/insurance". +Applying supervised machine learning methods, we want to investigate the following questions: 1. Which learner qualifies best to explain insurance charges by means of the given covariates? 2. What is the unbiased generalisation error associated with the selected model? 3. Which tariffication criteria (= covariates) have the strongest impact on the charges? -Firstly, we will introduce the data set. We will then apply nested resampling in order to explain and predict insurance charges. Lastly, we will investigate the feature importance emerging from our final model. - ## Descriptive Analysis of the Data Below the data are imported and a seed is set for reproducibility. @@ -99,13 +65,16 @@ insurance = read.csv(text = url) set.seed(246) ``` -The data set consists of 1338 insurees and their respective information on age, sex, bmi, number of children, smoking behaviour and region. As mentioned above our defined target variable, the outcome, are insurance costs named charges. These shall be explained by the information given about each insuree. +The data set consists of 1338 insurees and their respective information on age, sex, bmi, number of children, smoking behaviour and region. +As mentioned above our defined target variable, the outcome, are insurance costs named charges. +These shall be explained by the information given about each insuree. ```{r, echo = FALSE} head(insurance) ``` -The target variable, charges, is continuous and its distribution is shown below. It has to be noted, that the variable has been logarithmised in order to avoid the problem of non-normality. +The target variable, charges, is continuous and its distribution is shown below. +It has to be noted, that the variable has been logarithmised in order to avoid the problem of non-normality. ```{r, echo = FALSE} ggplot(insurance, aes(x = log(charges))) + @@ -114,10 +83,14 @@ ggplot(insurance, aes(x = log(charges))) + insurance$charges = log(insurance$charges) ``` +Note, that the same result can be achieved more easily by using `PipeOpTargetTrafo` from mlr3pipelines. +This PipeOp provides a smooth implementation to transform the target variable mlr3 tasks. The following plots give a brief overview of the distribution of the independent variables: ```{r, echo = FALSE} + + age = ggplot(insurance, aes(x = age)) + geom_histogram(col = "darkgray", size = 0.5) + theme_bw() @@ -152,23 +125,26 @@ region = ggplot(insurance, aes(x = region)) + grid.arrange(age, sex, bmi, children, smoker, region, nrow = 2) ``` -Before we resume in our analysis, all independent, metric variables will be standardised (i.e. each variable will be transformed to have a mean of 0 and standarad deviation of 1). This ensures commensurability of variables originally measured on differing metric scales and is particularly important for learners, which assess distances between individual observations. - +Before we resume in our analysis, all independent, metric variables will be standardized. +This ensures commensurability of variables originally measured on differing metric scales and is particularly important for learners, which assess distances between individual observations. +Therefore PipeOpScale from mlr3pipelines is used. ```{r} insurance[, c("age", "bmi", "children")] = - scale(insurance[, c("age", "bmi", "children")]) + scale(insurance[, c("age", "bmi", "children")]) ``` +Note, that the same result can be achieved more easily by using `PipeOpScale` from mlr3pipelines. +This PipeOp provides a smooth implementation to scale numeric features for mlr3 tasks. - -Given the aforementioned continuity of our target variable, it is clear that we face a so-called *regression problem*. In regression problems a numeric output associated with the variables is predicted - opposed to a specific class as it is the case for so-called *classification problems*. First of all, we initiate our task which specifies the underlying data and the target variable: +Given the aforementioned continuity of our target variable, we initiate a regression task which specifies the underlying data and the target variable: ```{r} ins_task = TaskRegr$new(id = "ins_task", backend = insurance, target = "charges") ``` -The plots below give a brief overview of the conditional distribution of charges given each independent variable. It can, for example, be seen that charges seem to increase with age or that smokers seem to face higher charges than non-smokers. +The plots below give a brief overview of the conditional distribution of charges given each independent variable. +It can, for example, be seen that charges seem to increase with age or that smokers seem to face higher charges than non-smokers. ```{r echo = FALSE} age = ggplot() + @@ -217,10 +193,7 @@ region = ggplot() + grid.arrange(age, sex, bmi, children, smoker, region, nrow = 2) ``` - -Different learners are available to solve regression problems and each learner produces a mapping function (also called model) from the observed dataset and its features. - -The learners we use are Linear Model (LM), k-Nearest Neighbors (kNN), Decision Trees (CART) and Random Forest (Ranger). It may be interesting to note, that while the first learner is suitable for regression tasks only, the other ones are suitable for both, regression and classification tasks. Just like the task, the learners have to be initiated: +The learners we initiate are Linear Model (LM), k-Nearest Neighbors (kNN), Decision Trees (CART) and Random Forest (Ranger). ```{r} lrn_lm = lrn("regr.lm") @@ -229,16 +202,10 @@ lrn_rpart = lrn("regr.rpart") lrn_ranger = lrn("regr.ranger") ``` +## Model and Hyperparameter Tuning -## Model Optimization: Nested Resampling - -To evaluate the performance of these learners, several resampling strategies exist. The mlr3 package contains 6 predefined options: Cross-validation, Leave-one-out cross validation, Repeated cross-validation, Out-of-bag bootstrap and other variants, Monte-Carlo cross-validation and Holdout. - -Nested Resampling embedds all parts of model-building including hyperparameter tuning in the model-finding process. Some of the associated steps can require resampling themselves, which is done within the *inner loop*. To obtain unbiased performance estimates, all parts of the model-building should be based on training data. An untouched test set should be reserved for model evaluation in the *outer loop*, which again requires the application of resampling. The resampling strategies for the inner and the outer loop can be defined individually. We will, however, focus solely on "5-fold-cross-validation" as it has become one of the standard methods. - -## Inner Loop: Model and Hyperparameter Tuning - -Adressing the inner loop, we first specify the hyperparameters of each learning algorithm - if applicable. These hyperparameters can have a strong influence on the performance of the algorithm and it can be advantageous to try different settings before fitting the model on the training data. An example would be the specification of the number of neareast neighbours, $k$, for the kNN learner. This process is called *tuning* the model. +We first specify the hyperparameters of each learning algorithm - if applicable. +These hyperparameters can have a strong influence on the performance of the algorithm and it can be advantageous to try different settings before fitting the model on the training data. Depending on the selected learner, various hyperparameters are obtained. Each of them impacts the performance of the learning algorithm. In order to evaluate this performance, we then need to choose a resampling strategy and a performance measure. @@ -250,11 +217,8 @@ resampling_inner = rsmp("cv", folds = 5) measures = mlr_measures$mget(c("regr.mse", "regr.mae", "regr.rsq")) ``` -Before the actual tuning starts, we still need to select the way, in which the optimisation takes place. In other words, to find the optimal hyperparamters of a model, which result in the most accurate predictions, we need to choose an the parameter space as well as the class and termination criterion of our tuner. - -*Grid search* is a technique, which attempts all hyperparameter combinations on a multi-dimensional discretized grid, in arbitrary order. This means, grid search builds a model for every combination of hyperparameters sepecified and evaluates each model. It scales, however, badly as the combinatorial possibilities explode. - -A more efficient technique for hyperparamter tuning is *random search*, where random combinations of hyperparamters are tested to find the best solution instead of all possible combinations exhaustively. +To find the optimal hyperparameter setting of a model, which result in the most accurate predictions, we need to define the parameter space as well as the class and termination criterion of our tuner. +This is done by *random search*, where random combinations of hyperparamters are tested to find the best solution in a given space. ```{r} tuner_rs = mlr3tuning::tnr("random_search") @@ -269,13 +233,19 @@ terminator = trm("evals", n_evals = 30) ## Automating the Tuning of kNN, CART and Ranger -K-Nearest Neighbors is a computationally complex procedure but very simple in terms of understanding as well as implementation. Furthermore, the resulting models often have a high degree of accuracy. As shown below, the parameter $k$, the number of neighbors, will be optimized as part of the model development. We specify that $k$-values between 10 and 40 shall be taken into account. +*K-Nearest Neighbors* is a computationally complex procedure but very simple in terms of understanding as well as implementation. +Furthermore, the resulting models often have a high degree of accuracy. +As shown below, the parameter $k$, the number of neighbors, will be optimized as part of the model development. +We specify that $k$-values between 10 and 40 shall be taken into account. ```{r} param_set_knn = ParamSet$new(params = list(ParamInt$new("k", lower = 10, upper = 40))) ``` -For Classification Tree learners there are more options for hyperparameter optimisation. In our case we choose to optimise two hyperparameters: Firstly, the complexity parameter $cp$. It ensures that only splits that improve the overall fit by a factor of $cp$ are attempted. Secondly, the hyperparameter $minsplit$. It determines the minimal number of observations per leaf necessary for a split to be attempted. +For *CART learners* we choose to optimize two hyperparameters. + +- The complexity parameter $cp$ ensures that only splits that improve the overall fit by a factor of $cp$ are attempted. +- The hyperparameter $minsplit$ determines the minimal number of observations per leaf necessary for a split to be attempted. ```{r} param_set_rpart = @@ -284,7 +254,7 @@ param_set_rpart = ParamInt$new("minsplit", lower = 1, upper = 50))) ``` -Finally, for the Random Forest learner, the hyperparameters we choose to optimise are $mtry$, the number of randomly sampled features considered by each tree when splitting a node, and $min.node.size$, the minimum number of observations per node. An exemplary value of 20 means that no node with fewer than 20 cases will be split. +Finally, for the Random Forest learner, the hyperparameters we choose to optimize are $mtry$, the number of randomly sampled features considered by each tree when splitting a node, and $min.node.size$, the minimum number of observations per node. ```{r} param_set_ranger = @@ -293,9 +263,7 @@ param_set_ranger = ParamInt$new("min.node.size", lower = 1, upper = 50))) ``` - -Automated hyperparameter tuning uses methods such as Gradient Decent, Bayesian Optimization or Evolutionary Algorithms to conduct a guided search for the best hyperparameters. -The *AutoTuner* from the mlr3 package adjusts itself by first tuning the hyperparameters of the respective learner on the training data, then setting the optimal parameters in the learner and finally fitting the model on the complete training dataset. +The *AutoTuner* from the mlr3 package adjusts itself by first tuning the hyperparameters of the respective learner on the training data, then setting the optimal parameters in the learner and finally fitting the model on the complete training data set. ```{r} at_knn = AutoTuner$new( @@ -324,8 +292,7 @@ at_ranger = AutoTuner$new( ) ``` -```{r grid1, echo=FALSE, eval=FALSE} -# An dieser Stelle wird Code ausgeführt, aber noch nicht im Markdown angezeigt (wir interessieren uns an dieser Stelle nur für die Boxplots zu den Tuning-Ergebnissen) +```{r grid1, echo=FALSE, eval=longrun} resampling_outer = rsmp("cv", folds = 5) grid = benchmark_grid( @@ -336,7 +303,6 @@ grid = benchmark_grid( bmr = benchmark(grid, store_models = TRUE) - # Each fold of outer resampling computes tuning, i.e. there are different sets of tuned hyperparameters # Extract optimal HP for each fold of outer resampling: @@ -421,23 +387,26 @@ grid.arrange(plot_hp_knn, plot_hp_rpart_1, plot_hp_rpart_2, plot_hp_ranger_1, pl top = textGrob("Tuning Results: Hyperparameter Settings", gp = gpar(fontface = 2, fontsize = 14))) ``` -```{r gridrds, echo=FALSE} -# saveRDS(grid1, "grid1.rds") -grid1 <- readRDS("grid1.rds") -grid.arrange(grid1) -``` - +![Tuning Results: Hyperparameter Setting](hyperparam_setting.png) -These plots show the range of optimal hyperparameters obtained by the inner resampling loop. So, each boxplot is based on 5 values. The red lines (dashed) indicate the range, within which the hyperparameters were optimized. It can, for example, be seen that while various different $k$-values are deemed optimal for kNN, $mtry = 4$ is determined the optimal setting for the Ranger algorithm in every iteration. Also, the optimal $cp$ in CART seems to lie within a small range, while the best-performing $minsplit$-parameter is rather volatile. However, the illustration neglects the fact that in tuning we are looking at combinations of hyperparameters and the more dimensions we consider, the fewer of the hyperparameter space we are investigating with a fixed number of evaluations in the tuning. +These plots show the range of optimal hyperparameters obtained by the inner resampling loop. +So, each boxplot is based on 5 values. The red lines (dashed) indicate the range, within which the hyperparameters were optimized. +It can, for example, be seen that while various different $k$-values are deemed optimal for kNN, $mtry = 4$ is determined the optimal setting for the Ranger algorithm in every iteration. +Also, the optimal $cp$ in CART seems to lie within a small range, while the best-performing $minsplit$-parameter is rather volatile. +However, the illustration neglects the fact that in tuning we are looking at combinations of hyperparameters and the more dimensions we consider, the fewer of the hyperparameter space we are investigating with a fixed number of evaluations in the tuning. +### Outer Loop: Model Selection -## Outer Loop: Model Selection +For nested resampling, we also define a 5-fold cross validation as our outer loop. +This means, we obtain five pairs of training and test sets. Each of those initiates the tuning process for the hyperparameter spaces specified earlier. +For each of the five iterations, the learner is fitted on the outer training set while its performance is evaluated on the outer test set. +By averaging these five performance estimates of the outer loops, we get an unbiased performance estimate for the learner. -For the outer loop of our nested resampling, we also define a 5-fold cross validation as our resampling strategy. This means, we obtain five pairs of training and test sets. Each of those initiates the tuning process for the hyperparameter spaces specified earlier. It is possible - and depending on the individual case even likely - that the optimal hyperparameter settings derived from the five inner loops differ amongst each other. For each of the five iterations, the learner is fitted on the outer training set while its performance is evaluated on the outer test set. By averaging these five performance estimates of the outer loops, we get an unbiased performance estimate for the learner. +As mentioned earlier, we aim to compare the performance of different learning algorithms on the prediction of insurance costs. +By initiating a benchmarking process, we can combine all candidate models in one single nested resampling process. +All we have to do is to define a grid with the regression task, the (tuned) learners and the outer resampling strategy. -As mentioned earlier, we aim to compare the performance of different learning algorithms on the prediction of insurance costs. By initiating a benchmarking process, we can combine all candidate models in one single nested resampling process. All we have to do is to define a grid with the regression task, the (tuned) learners and the outer resampling strategy. - -```{r benchmark, echo=TRUE, eval=FALSE} +```{r benchmark, echo=TRUE, eval=longrun} resampling_outer = rsmp("cv", folds = 5) grid = benchmark_grid( @@ -449,21 +418,15 @@ grid = benchmark_grid( bmr = benchmark(grid, store_models = TRUE) ``` -This part of the analysis can be computationally demanding. With our termination criterion of 30 evaluations in the tuning process, a 5-fold CV in the inner loop and another 5-fold CV in the outer loop, a total of 755 models is fitted for each learner that requires tuning and another 5 models for the Linear Model, which doesn't have hyperparamerters to optimize. Overall, in our example the benchmarking fits 2270 models, which in turn allow for us to make a decision on the best model and its generalisation error. +This part of the analysis can be computationally demanding. +With our termination criterion of 30 evaluations in the tuning process, a 5-fold CV in the inner loop and another 5-fold CV in the outer loop, a total of 755 models is fitted for each learner that requires tuning and another 5 models for the Linear Model, which doesn't have hyperparameters to optimize. +Overall, in our example the benchmarking fits 2270 models, which in turn allow for us to make a decision on the best model and its generalization error. -```{r echo=FALSE, eval=FALSE} +```{r echo=FALSE, eval=longrun} scores = bmr$score(measures) %>% select(Learner = learner_id, Iteration = iteration, MSE = regr.mse) -# Tabelle mit performance estimates, die den Boxplots zugrunde liegen: nicht in Markdown aufnehmen, aber vielleicht für Test nutzen? -# scores %>% kable() %>% -# kable_styling(full_width = F)%>% -# pack_rows("Linear Model", 1, 5) %>% -# pack_rows("KNN", 6, 10) %>% -# pack_rows("CART", 11, 15) %>% -# pack_rows("Random Forest", 16, 20) - plot_bmr = autoplot(bmr) + labs(x = "Learner", y = "MSE", title = "MSE-Score for each learner over the performance estimates") + theme_bw() @@ -472,30 +435,34 @@ plot_bmr ![Benchmarking Boxplot](bmr_plot.png) -Benchmarking generates scores for each learner and each outer loop iteration. Drawing boxplots over the performance estimates - here the Mean Squared Error - shows that kNN seems to work fine but produces some variation in performance estimates. The Linear Model doesn't deliver satisfactory results and produces large MSEs compared to the other candidate learners. Random Forest appears to be the best model producing accurate predictions in terms of the MSE. Finally, Decision Trees produce performance estimates similar to those of kNN, with even smaller variability. +Benchmarking generates scores for each learner and each outer loop iteration. +Drawing boxplots over the performance estimates - here the Mean Squared Error - shows that kNN seems to work fine but produces some variation in performance estimates. +The Linear Model doesn't deliver satisfactory results and produces large MSEs compared to the other candidate learners. +Random Forest appears to be the best model producing accurate predictions in terms of the MSE. +Finally, Decision Trees produce performance estimates similar to those of kNN, with even smaller variability. -One of our inintial questions was: Which learner qualifies best to predict insurance charges - that is, as accurately as possible? +One of our initial questions was: Which learner qualifies best to predict insurance charges - that is, as accurately as possible? -To come to answer this question, we do not necessarily have to study the boxplots - though it might be helpful. Instead, we can access the aggregated performance estimates for each learner, directly. In the graphic below the learners are ranked according to our three performance measures: MSE, MAE and $R^2$. The inverse value of $R^2$ has been computed and plotted to allow for easy comparison; improvements are indicated by lower values in each of the three plots. +To come to answer this question, we do not necessarily have to study the boxplots - though it might be helpful. +Instead, we can access the aggregated performance estimates for each learner, directly. +In the graphic below the learners are ranked according to our three performance measures: +MSE, MAE and $R^2$. +The inverse value of $R^2$ has been computed and plotted to allow for easy comparison; improvements are indicated by lower values in each of the three plots. -```{r, eval=FALSE, echo=FALSE} +```{r, eval=longrun, echo=FALSE} tab = bmr$aggregate(measures) ranks = tab[, .(learner_id, regr.mse, rank_mse = rank(regr.mse), regr.mae, rank_mae = rank(regr.mae), inv_regr.rsq = 1 / regr.rsq, rank_rsq = rank(-regr.rsq))] + +saveRDS(ranks, "ranks.rds") ``` -```{r tabrds, echo=FALSE} -# saveRDS(ranks, "ranks.rds") +```{r tabrds, echo=FALSE, eval=!longrun} ranks = readRDS("ranks.rds") ``` ```{r echo=FALSE, eval=TRUE} -# Table of aggregated results with ranking -# ranks[order(ranks$rank_mse),] %>% -# kable() %>% -# kable_styling(full_width = F) - ranks = ranks %>% pivot_longer(c(regr.mse, regr.mae, inv_regr.rsq), names_to = "key", values_to = "value") ranks$key = factor(ranks$key, levels = c("regr.mse", "regr.mae", "inv_regr.rsq")) @@ -516,12 +483,17 @@ ggplot(data = ranks) + ``` -But what about the hyperparameters? We just learned that from nested resampling we obtain five different sets of optimal combinations: Which one of them shall we use for the final model? +But what about the hyperparameters? +We just learned that from nested resampling we obtain five different sets of optimal combinations: +Which one of them shall we use for the final model? -The answer is: none of them. Unlike before, the final model is fit on the whole dataset and includes its own tuning step and resampling. The major difference is that there is no outer loop. Based on the tuning results, the model is trained on the whole dataset. +The answer is: none of them. +Unlike before, the final model is fit on the whole dataset and includes its own tuning step and resampling. +The major difference is that there is no outer loop. +Based on the tuning results, the model is trained on the whole dataset. -```{r eval = FALSE} +```{r eval=longrun} lgr::get_logger("mlr3")$set_threshold("warn") learner = lrn("regr.ranger", importance = "impurity") @@ -541,24 +513,20 @@ at_ranger_final$store_tuning_instance = TRUE at_ranger_final$train(ins_task) ``` -```{r eval = FALSE, echo=FALSE} +```{r eval=longrun, echo=FALSE} tab_tuning = at_ranger_final$archive$data()[, c("batch_nr", "regr.mse", "min.node.size", "mtry")] -# tab_tuning[regr.mse == min(tab_tuning$regr.mse),] - -# tab_tuning %>% -# kable() %>% -# kable_styling(full_width = F) %>% -# row_spec(10, bold = T, background = "lightpink") +saveRDS(tab_tuning, file = "tab_tuning.rds") ``` -```{r tabtuningrds, echo=FALSE} -# saveRDS(tab_tuning, file = "tab_tuning.rds") +```{r tabtuningrds, echo=FALSE, eval=!longrun} tab_tuning = readRDS("tab_tuning.rds") learner = lrn("regr.ranger", importance = "impurity") ``` -From the tuning process of our final model, we conlude that the optimal hyperparameter setting is achieved through the combination of $min.node.size = 30$ and $mtry = 4$. The figure below illustrates the investigated parameter combinations via random search. The color intensity matches the value of the respective MSE and the hyperparameter combination with the best performance, which is used to train the model, is highlighted in red. +From the tuning process of our final model, we conlude that the optimal hyperparameter setting is achieved through the combination of $min.node.size = 30$ and $mtry = 4$. +The figure below illustrates the investigated parameter combinations via random search. +The color intensity matches the value of the respective MSE and the hyperparameter combination with the best performance, which is used to train the model, is highlighted in red. ```{r echo=FALSE, eval=TRUE} ggplot() + @@ -572,11 +540,11 @@ ggplot() + labs(fill = "MSE", col = "MSE") ``` +Eventually, we want to investigate how well the final model can explain the data observed. Overall, the model fit does not seem too bad: the majority of observations are close to the diagonal. +There is, however, a considerable number of observations with charges higher than the ones predicted by the model. +This could indicate that features are not considered with their true functionality or that the insurance company uses additional tariffication criteria outside the data set. - -Eventually, we want to investigate how well the final model can explain the data observed. Overall, the model fit does not seem too bad: the majority of observations are close to the diagonal. There is, however, a considerable number of observations with charges higher than the ones predicted by the model. This could indicate that features are not considered with their true functionality or that the insurance company uses additional tariffication criteria outside the dataset. - -```{r echo = FALSE, eval=FALSE} +```{r echo = FALSE, eval=longrun} # Compare predicted values to true values: autoplot(at_ranger_final$predict(ins_task)) + theme_bw() @@ -586,7 +554,10 @@ autoplot(at_ranger_final$predict(ins_task)) + ## Feature Importance -As a last step of our analysis, we want to shed some light onto the functionality of our final "black box" model. To get a better understanding of the predictions made, we investigate the importance of each individual covariate. This can be done with the help of filter methods, which assign an importance value to each feature, which will then be ranked. For the Ranger learning algorithm, we can make use of the filter methods embedded in the mlr3-package. +As a last step of our analysis, we want to shed some light onto the functionality of our final "black box" model. +To get a better understanding of the predictions made, we investigate the importance of each individual covariate. +This can be done with the help of filter methods, which assign an importance value to each feature, which will then be ranked. +For the Ranger learning algorithm, we can make use of the filter methods embedded in the mlr3-package. ```{r} filter = flt("importance", learner = learner) @@ -608,11 +579,18 @@ ggplot(data = var, aes(x = feature, y = score)) + ``` -When looking at *impurity* as a measure of importance, we can see that first and foremost, the smoking status determines the predicted value of insurance charges. This is followed by age. The bmi, on the other hand, doesn't seem to have a strong impact on the predicted charges and similarly, the remaining features (children, region and sex) lead to minor improvments in impurity only. Overall, these findings are supported by domain knowledge and are in line with the descriptive analysis mentioned above. +When looking at *impurity* as a measure of importance, we can see that first and foremost, the smoking status determines the predicted value of insurance charges. +This is followed by age. +The bmi, on the other hand, doesn't seem to have a strong impact on the predicted charges and similarly, the remaining features (children, region and sex) lead to minor improvements in impurity only. +Overall, these findings are supported by domain knowledge and are in line with the descriptive analysis mentioned above. ## Summary and Implications -Our analysis solves the regression task of predicting insurance charges by computing a supervised machine learning model. Among a selection of candidate models, we identify Random Forest as the preferred learning algorithm. To determine the optimal hyperparameter configuration, we include a tuning step which is embedded in a nested resampling approach. This way, we obtain unbiased performance estimators without reducing our dataset, which the model is trained on. +Our analysis solves the regression task of predicting insurance charges by computing a supervised machine learning model. +Among a selection of candidate models, we identify Random Forest as the preferred learning algorithm. -The scope of our project was limited by factors like time and computing power. To improve the analysis other learning algorithms, resampling strategies and tuning configurations could be tested. Moreover, advanced feature selection and feature engineering may improve the model's performance estimate. Lastly, to save computational power, the models could be refitted without those features, which were identified as least important based on the impurity measure. +The scope of our project was limited by factors like time and computing power. +To improve the analysis other learning algorithms, resampling strategies and tuning configurations could be tested. +Moreover, advanced feature selection and feature engineering may improve the model's performance estimate. +Lastly, to save computational power, the models could be refitted without those features, which were identified as least important based on the impurity measure. diff --git a/_posts/2020-08-02-prediction-of-medical-costs/grid1.rds b/_posts/2020-08-02-prediction-of-medical-costs/grid1.rds deleted file mode 100644 index 527fa51a931ce6b0ca59a933d765b97e95de7322..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 21386 zcmcG$1yG!8n|6yk1a}SY?(PACyK8U_7Thhky9R>0ySoN=cXyZ5Bzu2*zM1*wocXH` 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a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index 263d7ded..7f2497d3 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -213,7 +213,6 @@ Again, in regression tasks, there is a variety of potential measures of accuracy ```{r} resampling_inner = rsmp("cv", folds = 5) -# measures = list(msr("regr.mse"), msr("regr.mae"), msr("regr.rsq")) measures = mlr_measures$mget(c("regr.mse", "regr.mae", "regr.rsq")) ``` From 8faad1c4fade8c6a40e19008081de2df6187ee7b Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Fri, 4 Sep 2020 15:52:37 +0200 Subject: [PATCH 08/17] update description and adding png save to longrun --- DESCRIPTION | 1 + .../2020-08-02-prediction-of-medical-costs.Rmd | 7 ++++++- 2 files changed, 7 insertions(+), 1 deletion(-) diff --git a/DESCRIPTION b/DESCRIPTION index e72cd671..2b39cbb3 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -45,6 +45,7 @@ Imports: mlr3pipelines, mlr3proba, mlr3tuning, + mlr3verse, mlr3viz, OpenML, paradox, diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index 7f2497d3..43033ae5 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -381,9 +381,11 @@ plot_hp_ranger_2 = ggplot(data = hp_ranger) + theme_bw() + theme(axis.text.x = element_blank()) +png("hyperparam_setting.png") grid.arrange(plot_hp_knn, plot_hp_rpart_1, plot_hp_rpart_2, plot_hp_ranger_1, plot_hp_ranger_2, nrow = 2, top = textGrob("Tuning Results: Hyperparameter Settings", gp = gpar(fontface = 2, fontsize = 14))) +dev.off() ``` ![Tuning Results: Hyperparameter Setting](hyperparam_setting.png) @@ -426,10 +428,11 @@ Overall, in our example the benchmarking fits 2270 models, which in turn allow f scores = bmr$score(measures) %>% select(Learner = learner_id, Iteration = iteration, MSE = regr.mse) +png("bmr_plot.png") plot_bmr = autoplot(bmr) + labs(x = "Learner", y = "MSE", title = "MSE-Score for each learner over the performance estimates") + theme_bw() -plot_bmr +dev.off() ``` ![Benchmarking Boxplot](bmr_plot.png) @@ -545,8 +548,10 @@ This could indicate that features are not considered with their true functionali ```{r echo = FALSE, eval=longrun} # Compare predicted values to true values: +png("prediction_at_ranger.png") autoplot(at_ranger_final$predict(ins_task)) + theme_bw() +dev.off() ``` ![Prediction autotuned ranger](prediction_at_ranger.png) From f8ca3f6a53f249dbb97f9c7f2040b31f2189433c Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Wed, 9 Sep 2020 14:18:42 +0200 Subject: [PATCH 09/17] k 1,...40 implement function to avid redundance --- ...2020-08-02-prediction-of-medical-costs.Rmd | 124 ++++++------------ .../bmr_plot.png | Bin 6032 -> 3839 bytes .../hyperparam_setting.png | Bin 8146 -> 6781 bytes .../ranks.rds | Bin 373 -> 373 bytes 4 files changed, 38 insertions(+), 86 deletions(-) diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index 43033ae5..26cb3420 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -43,7 +43,6 @@ library(RCurl) longrun = FALSE ``` - ## Introduction Myriad implementations of supervised learning algorithms can be found in a wide range of fields of science and business. @@ -133,18 +132,18 @@ Therefore PipeOpScale from mlr3pipelines is used. insurance[, c("age", "bmi", "children")] = scale(insurance[, c("age", "bmi", "children")]) ``` + Note, that the same result can be achieved more easily by using `PipeOpScale` from mlr3pipelines. This PipeOp provides a smooth implementation to scale numeric features for mlr3 tasks. - -Given the aforementioned continuity of our target variable, we initiate a regression task which specifies the underlying data and the target variable: +Given the aforementioned continuity of our target variable, we instantiate a regression task which specifies the underlying data and the target variable: ```{r} ins_task = TaskRegr$new(id = "ins_task", backend = insurance, target = "charges") ``` The plots below give a brief overview of the conditional distribution of charges given each independent variable. -It can, for example, be seen that charges seem to increase with age or that smokers seem to face higher charges than non-smokers. +It can, for example, be seen that charges seem to increase with age, or that smokers seem to face higher charges than non-smokers. ```{r echo = FALSE} age = ggplot() + @@ -193,7 +192,7 @@ region = ggplot() + grid.arrange(age, sex, bmi, children, smoker, region, nrow = 2) ``` -The learners we initiate are Linear Model (LM), k-Nearest Neighbors (kNN), Decision Trees (CART) and Random Forest (Ranger). +The learners we instantiate are Linear Model (LM), k-Nearest Neighbors (kNN), Decision Trees (CART) and Random Forest (Ranger). ```{r} lrn_lm = lrn("regr.lm") @@ -216,8 +215,8 @@ resampling_inner = rsmp("cv", folds = 5) measures = mlr_measures$mget(c("regr.mse", "regr.mae", "regr.rsq")) ``` -To find the optimal hyperparameter setting of a model, which result in the most accurate predictions, we need to define the parameter space as well as the class and termination criterion of our tuner. -This is done by *random search*, where random combinations of hyperparamters are tested to find the best solution in a given space. +To find the optimal hyperparameter setting of a model, which results in the most accurate predictions, we need to define the parameter space as well as the tuning approach. +In this example we use `r mlr3book::ref("TunerRandomSearch")`, where random combinations of hyperparamters are tested to find the best solution in a given space. ```{r} tuner_rs = mlr3tuning::tnr("random_search") @@ -238,7 +237,7 @@ As shown below, the parameter $k$, the number of neighbors, will be optimized as We specify that $k$-values between 10 and 40 shall be taken into account. ```{r} -param_set_knn = ParamSet$new(params = list(ParamInt$new("k", lower = 10, upper = 40))) +param_set_knn = ParamSet$new(params = list(ParamInt$new("k", lower = 1, upper = 40))) ``` For *CART learners* we choose to optimize two hyperparameters. @@ -262,7 +261,7 @@ param_set_ranger = ParamInt$new("min.node.size", lower = 1, upper = 50))) ``` -The *AutoTuner* from the mlr3 package adjusts itself by first tuning the hyperparameters of the respective learner on the training data, then setting the optimal parameters in the learner and finally fitting the model on the complete training data set. +The `r mlr3book::ref("AutoTuner")` from the mlr3 package adjusts itself by first tuning the hyperparameters of the respective learner on the training data, then setting the optimal parameters in the learner and finally fitting the model on the complete training data set. ```{r} at_knn = AutoTuner$new( @@ -304,85 +303,35 @@ bmr = benchmark(grid, store_models = TRUE) # Each fold of outer resampling computes tuning, i.e. there are different sets of tuned hyperparameters # Extract optimal HP for each fold of outer resampling: +``` -knn = bmr$score()[learner_id == "regr.kknn.tuned"]$learner -hp_knn = data.frame( - iteration = seq(1:resampling_outer$iters), - k = NA) -for (i in 1:resampling_outer$iters) { - hp_knn$k[i] = knn[[i]]$tuning_result$params -} - -plot_hp_knn = ggplot(data = hp_knn) + - geom_boxplot(aes(x = 1, y = unlist(k))) + - ylim(c(10, 40)) + - geom_hline(yintercept = 10, col = "red", linetype = "dashed") + - geom_hline(yintercept = 40, col = "red", linetype = "dashed") + - labs(y = "k", x = "", subtitle = "Learner: kNN \nHP: k") + +```{r, echo=FALSE, eval=longrun} +plot_tuning = function(benchmark = bmr, learner_ident, parameter, scale) { + learner = bmr$score()[learner_id == learner_ident]$learner + tuning_result = sapply(learner, FUN = function(x) x$tuning_result[[parameter]]) + + qplot(y = tuning_result, x = 1, geom = "boxplot") + + ylim(scale) + + geom_hline(yintercept = scale[1], col = "red", linetype = "dashed") + + geom_hline(yintercept = scale[2], col = "red", linetype = "dashed") + + labs(y = parameter, x = "", subtitle = paste("Learner:", learner_ident, "\nHP:", parameter)) + theme_bw() + theme(axis.text.x = element_blank()) - -rpart = bmr$score()[learner_id == "regr.rpart.tuned"]$learner -hp_rpart = data.frame( - iteration = seq(1:resampling_outer$iters), - cp = NA, - minsplit = NA) -for (i in 1:resampling_outer$iters) { - hp_rpart$cp[i] = rpart[[i]]$tuning_result$params$cp - hp_rpart$minsplit[i] = rpart[[i]]$tuning_result$params$minsplit } -plot_hp_rpart_1 = ggplot(data = hp_rpart) + - geom_boxplot(aes(x = 1, y = unlist(cp))) + - ylim(c(0.001, 0.5)) + - geom_hline(yintercept = 0.001, col = "red", linetype = "dashed") + - geom_hline(yintercept = 0.5, col = "red", linetype = "dashed") + - labs(y = "cp", x = "", subtitle = "Learner: Decision Trees \nHP: cp") + - theme_bw() + - theme(axis.text.x = element_blank()) - -plot_hp_rpart_2 = ggplot(data = hp_rpart) + - geom_boxplot(aes(x = 1, y = unlist(minsplit))) + - ylim(c(1, 50)) + - geom_hline(yintercept = 1, col = "red", linetype = "dashed") + - geom_hline(yintercept = 50, col = "red", linetype = "dashed") + - labs(y = "minsplit", x = "", subtitle = "Learner: Decision Trees \nHP: minsplit") + - theme_bw() + - theme(axis.text.x = element_blank()) -ranger = bmr$score()[learner_id == "regr.ranger.tuned"]$learner -hp_ranger = data.frame( - iteration = seq(1:resampling_outer$iters), - # num.trees = NA, - mtry = NA, - min.node.size = NA +list_args = list( + knn_k = list(learner_ident = "regr.kknn.tuned", parameter = "k", scale = c(1, 40)), + rpart_cp = list(learner_ident = "regr.rpart.tuned", parameter = "cp", scale = c(0.001, 0.5)), + rpart_minsplit = list(learner_ident = "regr.rpart.tuned", parameter = "minsplit", scale = c(1, 50)), + ranger_minnode = list(learner_ident = "regr.ranger.tuned", parameter = "min.node.size", scale = c(1, 50)), + ranger_mtry = list(learner_ident = "regr.ranger.tuned", parameter = "mtry", scale = c(2, 6)) ) -for (i in 1:resampling_outer$iters) { - hp_ranger$mtry[i] = ranger[[i]]$tuning_result$params$mtry - hp_ranger$min.node.size[i] = ranger[[i]]$tuning_result$params$min.node.size -} - -plot_hp_ranger_1 = ggplot(data = hp_ranger) + - geom_boxplot(aes(x = 1, y = unlist(min.node.size))) + - ylim(c(1, 50)) + - geom_hline(yintercept = 1, col = "red", linetype = "dashed") + - geom_hline(yintercept = 50, col = "red", linetype = "dashed") + - labs(y = "min.node.size", x = "", subtitle = "Learner: Random Forest \nHP: min.node.size") + - theme_bw() + - theme(axis.text.x = element_blank()) - -plot_hp_ranger_2 = ggplot(data = hp_ranger) + - geom_boxplot(aes(x = 1, y = unlist(mtry))) + - ylim(c(2, 6)) + - geom_hline(yintercept = 2, col = "red", linetype = "dashed") + - geom_hline(yintercept = 6, col = "red", linetype = "dashed") + - labs(y = "mtry", x = "", subtitle = "Learner: Random Forest \nHP: mtry") + - theme_bw() + - theme(axis.text.x = element_blank()) +plot_hyperparam <- lapply(list_args, function(x) mlr3misc::invoke(plot_tuning, .args = x)) png("hyperparam_setting.png") -grid.arrange(plot_hp_knn, plot_hp_rpart_1, plot_hp_rpart_2, plot_hp_ranger_1, plot_hp_ranger_2, +grid.arrange(grobs = plot_hyperparam, nrow = 2, top = textGrob("Tuning Results: Hyperparameter Settings", gp = gpar(fontface = 2, fontsize = 14))) dev.off() @@ -391,7 +340,8 @@ dev.off() ![Tuning Results: Hyperparameter Setting](hyperparam_setting.png) These plots show the range of optimal hyperparameters obtained by the inner resampling loop. -So, each boxplot is based on 5 values. The red lines (dashed) indicate the range, within which the hyperparameters were optimized. +So, each boxplot is based on 5 values. +The red lines (dashed) indicate the range, within which the hyperparameters were optimized. It can, for example, be seen that while various different $k$-values are deemed optimal for kNN, $mtry = 4$ is determined the optimal setting for the Ranger algorithm in every iteration. Also, the optimal $cp$ in CART seems to lie within a small range, while the best-performing $minsplit$-parameter is rather volatile. However, the illustration neglects the fact that in tuning we are looking at combinations of hyperparameters and the more dimensions we consider, the fewer of the hyperparameter space we are investigating with a fixed number of evaluations in the tuning. @@ -407,7 +357,11 @@ As mentioned earlier, we aim to compare the performance of different learning al By initiating a benchmarking process, we can combine all candidate models in one single nested resampling process. All we have to do is to define a grid with the regression task, the (tuned) learners and the outer resampling strategy. -```{r benchmark, echo=TRUE, eval=longrun} +This part of the analysis can be computationally demanding. +With our termination criterion of 30 evaluations in the tuning process, a 5-fold CV in the inner loop and another 5-fold CV in the outer loop, a total of 755 models is fitted for each learner that requires tuning and another 5 models for the Linear Model, which doesn't have hyperparameters to optimize. +Overall, in our example the benchmarking fits 2270 models, which in turn allow for us to make a decision on the best model and its generalization error. + +```{r visible, echo=TRUE, eval=FALSE} resampling_outer = rsmp("cv", folds = 5) grid = benchmark_grid( @@ -419,17 +373,12 @@ grid = benchmark_grid( bmr = benchmark(grid, store_models = TRUE) ``` -This part of the analysis can be computationally demanding. -With our termination criterion of 30 evaluations in the tuning process, a 5-fold CV in the inner loop and another 5-fold CV in the outer loop, a total of 755 models is fitted for each learner that requires tuning and another 5 models for the Linear Model, which doesn't have hyperparameters to optimize. -Overall, in our example the benchmarking fits 2270 models, which in turn allow for us to make a decision on the best model and its generalization error. - - ```{r echo=FALSE, eval=longrun} scores = bmr$score(measures) %>% select(Learner = learner_id, Iteration = iteration, MSE = regr.mse) png("bmr_plot.png") -plot_bmr = autoplot(bmr) + +autoplot(bmr) + labs(x = "Learner", y = "MSE", title = "MSE-Score for each learner over the performance estimates") + theme_bw() dev.off() @@ -490,6 +439,7 @@ We just learned that from nested resampling we obtain five different sets of opt Which one of them shall we use for the final model? The answer is: none of them. +Nested resampling solely enabled us to obtain an unbiased measure of generalization error for each model. Unlike before, the final model is fit on the whole dataset and includes its own tuning step and resampling. The major difference is that there is no outer loop. Based on the tuning results, the model is trained on the whole dataset. @@ -568,6 +518,8 @@ filter = flt("importance", learner = learner) filter$calculate(ins_task) ``` +Note, that the feature importance computed here does not necessarily reflect the feature importance in the model trained above, as different sub-sets of the data and hyperparameters can influence the computed importance scores. +A full set of post-hoc tools for post-hoc model interpretation for mlr3 models can be found in the [iml](https://cran.r-project.org/web/packages/iml/index.html) and [DALEX](https://cran.r-project.org/web/packages/DALEX/index.html) packages, the mlr3 book contains a section on how to use those packages together with mlr3. 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<50552831+HenriLMU@users.noreply.github.com> Date: Fri, 11 Sep 2020 11:12:44 +0200 Subject: [PATCH 10/17] changed for loops by lapply & updated plots --- ...2020-08-02-prediction-of-medical-costs.Rmd | 105 ++++++------------ .../bmr_plot.png | Bin 3839 -> 4780 bytes .../prediction_at_ranger.png | Bin 7008 -> 7498 bytes .../tab_tuning.rds | Bin 672 -> 599 bytes 4 files changed, 34 insertions(+), 71 deletions(-) diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index 26cb3420..ad69aa3b 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -83,50 +83,27 @@ ggplot(insurance, aes(x = log(charges))) + insurance$charges = log(insurance$charges) ``` Note, that the same result can be achieved more easily by using `PipeOpTargetTrafo` from mlr3pipelines. -This PipeOp provides a smooth implementation to transform the target variable mlr3 tasks. +This PipeOp provides a smooth implementation to transform the target variable in mlr3 tasks. The following plots give a brief overview of the distribution of the independent variables: ```{r, echo = FALSE} - -age = ggplot(insurance, aes(x = age)) + - geom_histogram(col = "darkgray", size = 0.5) + - theme_bw() - -sex = ggplot(insurance, aes(sex)) + - geom_bar() + - theme_bw() - -bmi = ggplot(insurance, aes(x = bmi)) + - geom_histogram(col = "darkgray", size = 0.5) + - theme_bw() - -children = ggplot(insurance, aes(x = children)) + - geom_bar() + - theme_bw() + - scale_x_continuous(breaks = 0:6, labels = c("0", "1", "2", "3", "4", "5", "6")) - -smoker = ggplot(insurance, aes(x = smoker)) + - geom_bar() + - theme_bw() - levels(insurance$region)[levels(insurance$region) == "northeast"] = "ne" levels(insurance$region)[levels(insurance$region) == "northwest"] = "nw" levels(insurance$region)[levels(insurance$region) == "southeast"] = "se" levels(insurance$region)[levels(insurance$region) == "southwest"] = "sw" -region = ggplot(insurance, aes(x = region)) + - geom_bar() + - theme_bw() + - theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1)) -grid.arrange(age, sex, bmi, children, smoker, region, nrow = 2) +# autoplot(TaskRegr$new(id = "ins_task", backend = insurance, target = "charges")$select(c("age", "bmi", "children")), type = "pairs") +histograms <- lapply(as.list(names(insurance)[-7]), function(x) qplot(insurance[ ,x], xlab = x)) + +mlr3misc::invoke(grid.arrange, .args = c(histograms, nrow = 2)) + ``` Before we resume in our analysis, all independent, metric variables will be standardized. This ensures commensurability of variables originally measured on differing metric scales and is particularly important for learners, which assess distances between individual observations. -Therefore PipeOpScale from mlr3pipelines is used. ```{r} insurance[, c("age", "bmi", "children")] = @@ -146,50 +123,33 @@ The plots below give a brief overview of the conditional distribution of charges It can, for example, be seen that charges seem to increase with age, or that smokers seem to face higher charges than non-smokers. ```{r echo = FALSE} -age = ggplot() + - geom_point(data = insurance, aes(x = age, y = charges), col = "grey30") + - ggtitle("age") + - xlab("age (standradised)") + - theme_bw() + - theme(plot.title = element_text(hjust = 0.5)) -bmi = ggplot() + - geom_point(data = insurance, aes(x = bmi, y = charges), col = "grey30") + - ggtitle("bmi") + - xlab("bmi (standradised)") + - theme_bw() + - theme(plot.title = element_text(hjust = 0.5)) - -children = ggplot() + - geom_point(data = insurance, aes(x = children, y = charges), col = "grey30") + - ggtitle("children") + - xlab("children (standradised)") + - theme_bw() + - theme(plot.title = element_text(hjust = 0.5)) - -sex = ggplot() + - geom_histogram(data = insurance, aes(x = charges), col = "darkgray", size = 0.5) + - facet_wrap(~sex, ncol = 1) + - ggtitle("sex") + - theme_bw() + - theme(plot.title = element_text(hjust = 0.5)) - -smoker = ggplot() + - geom_histogram(data = insurance, aes(x = charges), col = "darkgray", size = 0.5) + - facet_wrap(~smoker, ncol = 1) + - ggtitle("smoker") + +plot_charges <- function(col, title, lab){ + ggplot() + + geom_point(data = insurance, aes(x = col, y = charges), col = "grey30") + + ggtitle(title) + + xlab(lab) + theme_bw() + theme(plot.title = element_text(hjust = 0.5)) +} -region = ggplot() + - geom_histogram(data = insurance, aes(x = charges), col = "darkgray", size = 0.25) + - facet_wrap(~region, ncol = 2) + - ggtitle("region") + +plot_facet <- function(facet, title, ncol = 1) { + insurance1 <- insurance %>% mutate(facet = facet) + ggplot() + + geom_histogram(data = insurance1, aes(x = charges), col = "darkgray", size = 0.5) + + facet_wrap(~ facet, ncol = ncol) + + ggtitle(title) + theme_bw() + theme(plot.title = element_text(hjust = 0.5)) +} - -grid.arrange(age, sex, bmi, children, smoker, region, nrow = 2) +grid.arrange(plot_charges(insurance$age, "age", "age standardized"), + plot_charges(insurance$bmi, "bmi", "bmi standardized"), + plot_charges(insurance$children, "children", "children standardized"), + plot_facet(insurance$sex, "sex"), + plot_facet(insurance$smoker, "smoker"), + plot_facet(insurance$region, "region", ncol = 2), + nrow = 2) ``` The learners we instantiate are Linear Model (LM), k-Nearest Neighbors (kNN), Decision Trees (CART) and Random Forest (Ranger). @@ -234,7 +194,7 @@ terminator = trm("evals", n_evals = 30) *K-Nearest Neighbors* is a computationally complex procedure but very simple in terms of understanding as well as implementation. Furthermore, the resulting models often have a high degree of accuracy. As shown below, the parameter $k$, the number of neighbors, will be optimized as part of the model development. -We specify that $k$-values between 10 and 40 shall be taken into account. +We specify that $k$-values between 1 and 40 shall be taken into account. ```{r} param_set_knn = ParamSet$new(params = list(ParamInt$new("k", lower = 1, upper = 40))) @@ -290,7 +250,7 @@ at_ranger = AutoTuner$new( ) ``` -```{r grid1, echo=FALSE, eval=longrun} +```{r grid1, echo=FALSE, message=FALSE, results='hide', eval=longrun} resampling_outer = rsmp("cv", folds = 5) grid = benchmark_grid( @@ -337,7 +297,9 @@ grid.arrange(grobs = plot_hyperparam, dev.off() ``` -![Tuning Results: Hyperparameter Setting](hyperparam_setting.png) +```{r fig.cap="Tuning Results: Hyperparameter Setting", echo=FALSE, out.width = "400px"} +knitr::include_graphics("hyperparam_setting.png") +``` These plots show the range of optimal hyperparameters obtained by the inner resampling loop. So, each boxplot is based on 5 values. @@ -383,8 +345,9 @@ autoplot(bmr) + theme_bw() dev.off() ``` - -![Benchmarking Boxplot](bmr_plot.png) +```{r fig.cap="Benchmarking Boxplot", echo=FALSE, out.width = "400px"} +knitr::include_graphics("bmr_plot.png") +``` Benchmarking generates scores for each learner and each outer loop iteration. 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z2dFp@Tb|96iI?HOwb(K(kOz|F0bdE8D>VLZOa4Dr=kChL)AAqk+#qiMDLZWGU{PU4 GjQJlh-@q3D diff --git a/_posts/2020-08-02-prediction-of-medical-costs/tab_tuning.rds b/_posts/2020-08-02-prediction-of-medical-costs/tab_tuning.rds index fde855e023d456edcb193ee9c84564a57fc903c9..5b413f9f58b6b8a6fbf6bc595a0aaa00fc7c6522 100644 GIT binary patch delta 22 dcmZ3$dYxs1Clg=PGUGqY3 Date: Fri, 18 Sep 2020 11:18:05 +0200 Subject: [PATCH 11/17] add preface and editor --- .../2020-08-02-prediction-of-medical-costs.Rmd | 12 ++++++++++-- 1 file changed, 10 insertions(+), 2 deletions(-) diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index ad69aa3b..5e6d4d5d 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -9,8 +9,7 @@ author: - name: Veronika Kronseder - name: Melissa Schmoll - name: Eileen Wuest -editor: - - name: Henri Funk + - name: Henri Funk (editor) date: 08-02-2020 description: | Use case illustrating data vizualization and tuning via mlr3 on the "Medical Costs" dataset. @@ -43,6 +42,14 @@ library(RCurl) longrun = FALSE ``` +# Preamble + +The following examples were created as part of the Introduction to Machine Learning Lecture at LMU Munich. +The goal of the project was to create and compare one or several machine learning pipelines for the problem at hand together with exploratory analysis and an exposition of results. +The posts were contributed to the mlr3gallery by the authors and edited for better legibility by the editor. +We want to thank the authors for allowing us to publish their results. +Note, that correctness of the results can not be guaranteed. + ## Introduction Myriad implementations of supervised learning algorithms can be found in a wide range of fields of science and business. @@ -82,6 +89,7 @@ ggplot(insurance, aes(x = log(charges))) + insurance$charges = log(insurance$charges) ``` + Note, that the same result can be achieved more easily by using `PipeOpTargetTrafo` from mlr3pipelines. This PipeOp provides a smooth implementation to transform the target variable in mlr3 tasks. From 8e6734a20b5d3ed8fe31303b2f4d45e011e50606 Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Sun, 25 Oct 2020 11:38:17 +0100 Subject: [PATCH 12/17] insert autoplot.task --- ...2020-08-02-prediction-of-medical-costs.Rmd | 33 ++----------------- 1 file changed, 3 insertions(+), 30 deletions(-) diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index 5e6d4d5d..af2c1251 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -96,7 +96,6 @@ This PipeOp provides a smooth implementation to transform the target variable in The following plots give a brief overview of the distribution of the independent variables: ```{r, echo = FALSE} - levels(insurance$region)[levels(insurance$region) == "northeast"] = "ne" levels(insurance$region)[levels(insurance$region) == "northwest"] = "nw" levels(insurance$region)[levels(insurance$region) == "southeast"] = "se" @@ -127,37 +126,11 @@ Given the aforementioned continuity of our target variable, we instantiate a reg ins_task = TaskRegr$new(id = "ins_task", backend = insurance, target = "charges") ``` -The plots below give a brief overview of the conditional distribution of charges given each independent variable. +The plots below give a brief overview of the conditional distribution of charges given example independent variables. It can, for example, be seen that charges seem to increase with age, or that smokers seem to face higher charges than non-smokers. -```{r echo = FALSE} - -plot_charges <- function(col, title, lab){ - ggplot() + - geom_point(data = insurance, aes(x = col, y = charges), col = "grey30") + - ggtitle(title) + - xlab(lab) + - theme_bw() + - theme(plot.title = element_text(hjust = 0.5)) -} - -plot_facet <- function(facet, title, ncol = 1) { - insurance1 <- insurance %>% mutate(facet = facet) - ggplot() + - geom_histogram(data = insurance1, aes(x = charges), col = "darkgray", size = 0.5) + - facet_wrap(~ facet, ncol = ncol) + - ggtitle(title) + - theme_bw() + - theme(plot.title = element_text(hjust = 0.5)) -} - -grid.arrange(plot_charges(insurance$age, "age", "age standardized"), - plot_charges(insurance$bmi, "bmi", "bmi standardized"), - plot_charges(insurance$children, "children", "children standardized"), - plot_facet(insurance$sex, "sex"), - plot_facet(insurance$smoker, "smoker"), - plot_facet(insurance$region, "region", ncol = 2), - nrow = 2) +```{r echo = FALSE, message=FALSE} +autoplot(ins_task$clone(deep = TRUE)$select(c("age", "smoker")), type = "pairs") ``` The learners we instantiate are Linear Model (LM), k-Nearest Neighbors (kNN), Decision Trees (CART) and Random Forest (Ranger). From 5e9b99802a5d599a5d6a7cd089c212eb6f8edf10 Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Wed, 28 Oct 2020 17:29:41 +0100 Subject: [PATCH 13/17] update deps --- DESCRIPTION | 1 - .../2020-08-02-prediction-of-medical-costs.Rmd | 1 - 2 files changed, 2 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 9633d821..3cc86140 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -28,7 +28,6 @@ Imports: ggrepel, git2r, glmnet, - grid, gridExtra, igraph, kableExtra, diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index af2c1251..efa54138 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -33,7 +33,6 @@ library(kableExtra) ```{r setup, include=FALSE} library(mlr3verse) library(ggplot2) -library(grid) library(gridExtra) library(dplyr) library(tidyr) From c4ba24c6a256ecd5ab1da9bbc0b42794dba9b750 Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Wed, 28 Oct 2020 17:33:41 +0100 Subject: [PATCH 14/17] resolve comment --- .../2020-08-02-prediction-of-medical-costs.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index efa54138..d036a318 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -486,7 +486,7 @@ Overall, these findings are supported by domain knowledge and are in line with t ## Summary and Implications -Our analysis solves the regression task of predicting insurance charges by computing a supervised machine learning model. +Our analysis solves the regression task of predicting insurance charges by training a supervised machine learning model. Among a selection of candidate models, we identify Random Forest as the preferred learning algorithm. The scope of our project was limited by factors like time and computing power. From c0450fa7b957323d2108e204b3c93fcb0997c279 Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Wed, 4 Nov 2020 18:46:21 +0100 Subject: [PATCH 15/17] update to graph learner --- ...2020-08-02-prediction-of-medical-costs.Rmd | 29 +++++++++--------- .../hyperparam_setting.png | Bin 6781 -> 318 bytes 2 files changed, 15 insertions(+), 14 deletions(-) diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index d036a318..8edc00b9 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -36,9 +36,8 @@ library(ggplot2) library(gridExtra) library(dplyr) library(tidyr) -library(RCurl) -longrun = FALSE +longrun = TRUE ``` # Preamble @@ -65,8 +64,7 @@ Applying supervised machine learning methods, we want to investigate the followi Below the data are imported and a seed is set for reproducibility. ```{r} -url = getURL("https://raw.githubusercontent.com/stedy/Machine-Learning-with-R-datasets/master/insurance.csv") -insurance = read.csv(text = url) +insurance = read.csv(url("https://raw.githubusercontent.com/stedy/Machine-Learning-with-R-datasets/master/insurance.csv")) set.seed(246) ``` @@ -112,8 +110,8 @@ Before we resume in our analysis, all independent, metric variables will be stan This ensures commensurability of variables originally measured on differing metric scales and is particularly important for learners, which assess distances between individual observations. ```{r} -insurance[, c("age", "bmi", "children")] = - scale(insurance[, c("age", "bmi", "children")]) +po_scale = po("scale") +po_scale$param_set$values$affect_columns = selector_name(c("age", "bmi", "children")) ``` Note, that the same result can be achieved more easily by using `PipeOpScale` from mlr3pipelines. @@ -228,6 +226,8 @@ at_ranger = AutoTuner$new( terminator = terminator, tuner = tuner_rs ) + +scaled_learners = lapply(list(lrn_lm, at_knn, at_rpart, at_ranger), function(x) GraphLearner$new(po_scale %>>% x)) ``` ```{r grid1, echo=FALSE, message=FALSE, results='hide', eval=longrun} @@ -235,7 +235,7 @@ resampling_outer = rsmp("cv", folds = 5) grid = benchmark_grid( task = ins_task, - learner = list(lrn_lm, at_knn, at_rpart, at_ranger), + learner = scaled_learners, resampling = resampling_outer ) @@ -245,8 +245,9 @@ bmr = benchmark(grid, store_models = TRUE) # Extract optimal HP for each fold of outer resampling: ``` -```{r, echo=FALSE, eval=longrun} +```{r, echo=FALSE, eval=FALSE} plot_tuning = function(benchmark = bmr, learner_ident, parameter, scale) { + learner = bmr$score()[learner_id == learner_ident]$learner tuning_result = sapply(learner, FUN = function(x) x$tuning_result[[parameter]]) @@ -261,11 +262,11 @@ plot_tuning = function(benchmark = bmr, learner_ident, parameter, scale) { list_args = list( - knn_k = list(learner_ident = "regr.kknn.tuned", parameter = "k", scale = c(1, 40)), - rpart_cp = list(learner_ident = "regr.rpart.tuned", parameter = "cp", scale = c(0.001, 0.5)), - rpart_minsplit = list(learner_ident = "regr.rpart.tuned", parameter = "minsplit", scale = c(1, 50)), - ranger_minnode = list(learner_ident = "regr.ranger.tuned", parameter = "min.node.size", scale = c(1, 50)), - ranger_mtry = list(learner_ident = "regr.ranger.tuned", parameter = "mtry", scale = c(2, 6)) + knn_k = list(learner_ident = "scale.regr.kknn.tuned", parameter = "k", scale = c(1, 40)), + rpart_cp = list(learner_ident = "scale.regr.rpart.tuned", parameter = "cp", scale = c(0.001, 0.5)), + rpart_minsplit = list(learner_ident = "scale.regr.rpart.tuned", parameter = "minsplit", scale = c(1, 50)), + ranger_minnode = list(learner_ident = "scale.regr.ranger.tuned", parameter = "min.node.size", scale = c(1, 50)), + ranger_mtry = list(learner_ident = 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z;Bl303_Sj4-YXIyP5N_uUmV(A!UJTQF1z2e1ch8SXsaQnT?q0CSAJ?J<4eN+ZwYG~ z7|vgHZK`c6N92-9z%z%HGG2zR_U@S|iTgaJ2E|4uuEy{ffh4#T`^e=#Ol9t#MBZ@;I(OmJtL)s3IBl@bH~K$-ckrF`&s`K<%X4>#gp8q?_GF&v#5teoZK{c&|dl zTvDHaI{|BnT%mcdG414|-9}z18sh)VYE`}Rmj}#EaK_cbwD`Zc^E;x%n**<=&H*b? z@hM3SjG{VPMmCA}OtCehBdLwV2Z2gUv)k^jRCW;8yAWTxVo81(rk z8ZgD!Wxx3EDQTNCrlf=j4G3tcd;N1PEq2lQ>XvhO<-LV_F=V0E>%Q9T`6Rj85rp9@ zbbOkN`zx3*QrXj&d-rcI8!{dbhj|sgw77hod}za1MsoIlb3+Yn$_HgH%%IT8WP!*%qoKSh{%Cymw-PG7Jo{SfY5yzrX(c ef9SU&I*Tb;Vg2)6198URNCx`GdPTbSH~tH0?TOX^ From 2c45b078c3c6713a62ba9f64057fdda0cceb5dfd Mon Sep 17 00:00:00 2001 From: HenriLMU <50552831+HenriLMU@users.noreply.github.com> Date: Fri, 27 Nov 2020 12:27:45 +0100 Subject: [PATCH 16/17] rearrange pred of medical costs --- DESCRIPTION | 1 - ...2020-08-02-prediction-of-medical-costs.Rmd | 31 +++++++++--------- .../at_ranger.rds | Bin 0 -> 988579 bytes .../bmr_plot.png | Bin 4780 -> 4799 bytes .../hyperparam_setting.png | Bin 318 -> 6534 bytes .../prediction_at_ranger.png | Bin 7498 -> 7542 bytes .../ranks.rds | Bin 373 -> 381 bytes .../tab_tuning.rds | Bin 599 -> 0 bytes 8 files changed, 16 insertions(+), 16 deletions(-) create mode 100644 _posts/2020-08-02-prediction-of-medical-costs/at_ranger.rds delete mode 100644 _posts/2020-08-02-prediction-of-medical-costs/tab_tuning.rds diff --git a/DESCRIPTION b/DESCRIPTION index bf17c9c6..b1105589 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -58,7 +58,6 @@ Imports: randomForest, ranger, rchallenge, - RCurl, skimr, smotefamily, stopwords, diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index 8edc00b9..f309d523 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -37,7 +37,7 @@ library(gridExtra) library(dplyr) library(tidyr) -longrun = TRUE +longrun = FALSE ``` # Preamble @@ -249,13 +249,13 @@ bmr = benchmark(grid, store_models = TRUE) plot_tuning = function(benchmark = bmr, learner_ident, parameter, scale) { learner = bmr$score()[learner_id == learner_ident]$learner - tuning_result = sapply(learner, FUN = function(x) x$tuning_result[[parameter]]) + tuning_result = sapply(learner, FUN = function(x) x$model[[gsub('^.{6}', '', learner_ident)]]$model$tuning_instance$result[[parameter]]) qplot(y = tuning_result, x = 1, geom = "boxplot") + ylim(scale) + geom_hline(yintercept = scale[1], col = "red", linetype = "dashed") + geom_hline(yintercept = scale[2], col = "red", linetype = "dashed") + - labs(y = parameter, x = "", subtitle = paste("Learner:", learner_ident, "\nHP:", parameter)) + + labs(y = parameter, x = "", subtitle = paste("Learner:", gsub('^.{6}', '', learner_ident), "\nHP:", parameter)) + theme_bw() + theme(axis.text.x = element_blank()) } @@ -272,9 +272,8 @@ list_args = list( plot_hyperparam <- lapply(list_args, function(x) mlr3misc::invoke(plot_tuning, .args = x)) png("hyperparam_setting.png") -grid.arrange(grobs = plot_hyperparam, - nrow = 2, - top = textGrob("Tuning Results: Hyperparameter Settings", gp = gpar(fontface = 2, fontsize = 14))) +grid.arrange(grobs = plot_hyperparam, nrow = 2, + top = text_grob("Tuning Results: Hyperparameter Settings")) dev.off() ``` @@ -389,13 +388,13 @@ The major difference is that there is no outer loop. Based on the tuning results, the model is trained on the whole dataset. -```{r eval=longrun} +```{r, eval=longrun} lgr::get_logger("mlr3")$set_threshold("warn") learner = lrn("regr.ranger", importance = "impurity") # Autotuning to find the optimal hyperparameter configuration # based on the complete dataset: -at_ranger_final = AutoTuner$new( +at_ranger = AutoTuner$new( learner = learner, resampling = resampling_inner, measure = msr("regr.mse"), @@ -405,26 +404,27 @@ at_ranger_final = AutoTuner$new( ) # Train the model: -at_ranger_final$store_tuning_instance = TRUE +at_ranger$instance_args$store_benchmark_result = TRUE +at_ranger_final = GraphLearner$new(po_scale %>>% at_ranger) at_ranger_final$train(ins_task) ``` ```{r eval=longrun, echo=FALSE} -tab_tuning = at_ranger_final$archive$data()[, c("batch_nr", "regr.mse", "min.node.size", "mtry")] - -saveRDS(tab_tuning, file = "tab_tuning.rds") +saveRDS(at_ranger_final, file = "at_ranger.rds") ``` ```{r tabtuningrds, echo=FALSE, eval=!longrun} -tab_tuning = readRDS("tab_tuning.rds") -learner = lrn("regr.ranger", importance = "impurity") +at_ranger_final <- readRDS("at_ranger.rds") ``` -From the tuning process of our final model, we conlude that the optimal hyperparameter setting is achieved through the combination of $min.node.size = 30$ and $mtry = 4$. +From the tuning process of our final model, we conclude that the optimal hyperparameter setting is achieved through the combination of $min.node.size = 30$ and $mtry = 4$. The figure below illustrates the investigated parameter combinations via random search. The color intensity matches the value of the respective MSE and the hyperparameter combination with the best performance, which is used to train the model, is highlighted in red. ```{r echo=FALSE, eval=TRUE} +tab_tuning_instance = at_ranger_final$model$regr.ranger.tuned$model$tuning_instance +tab_tuning = tab_tuning_instance$archive$data()[, c("batch_nr", "regr.mse", "min.node.size", "mtry")] + ggplot() + geom_point(aes(x = min.node.size, y = mtry, fill = regr.mse, col = regr.mse), data = tab_tuning, size = 5, shape = 21) + geom_point(aes(x = min.node.size, y = mtry, fill = regr.mse), data = tab_tuning[regr.mse == min(tab_tuning$regr.mse), ], col = "red", size = 5, shape = 21, stroke = 2) + @@ -458,6 +458,7 @@ This can be done with the help of filter methods, which assign an importance val For the Ranger learning algorithm, we can make use of the filter methods embedded in the mlr3-package. ```{r} +learner <- lrn("regr.ranger", importance = "impurity") filter = flt("importance", learner = learner) filter$calculate(ins_task) ``` diff --git a/_posts/2020-08-02-prediction-of-medical-costs/at_ranger.rds b/_posts/2020-08-02-prediction-of-medical-costs/at_ranger.rds new file mode 100644 index 0000000000000000000000000000000000000000..2a0fbedc3a1465ec48831991f8ef3309f5bd7a1e GIT binary patch literal 988579 zcmZU)1yEbv6Fyu6+ESn`#jQx8Kq;<4S}0Q7Deh1-xC8>F6n87`ZlSnaDefBFA&>wm zgdhp>(f9ZNWai7v-np~q+1=#M$vJz^K1&zz_}+gX+=F(43?^CcwKd+x#>Vr!>3y2} zlI5PK4d3oPIej1rlnW($GO_Srgr^bUDcD-eTb`<$`NNV4Wo1sK%iKo(j>^|$q?LgD z>On(w6mdVj{P%8W+Dp{1hbem-(Ac6fc1KX>NlDTbcW zP|?!ygf?c;t&m7hHhf(=HCYm$k17JTZBgimV#B*vXH3eUHT2`P&U*Q?Eec=wY%X8< zw%1SCd*b;YWo9QQhx_|;-fHg@vQ+Q^#tj@Q=F+3I+u4a6{V~hDuq@NZD`L;}^!NCW zD)9qmHE=_4)07-gkF#I?=1m<>^#L)s`WTaOtq7hh&IvEmTwQLM=##x+E>@;2IoQDj8qc4YiN0n%JV0=n(gC|rQk@QF|P+ZZtPAV5&&H^$$tTUPq z^P6cP?nE)%oTJV<{TU0ybt59^-abiShv%&=IMO?-Xh#<@qrKaTUM1%hl|m)WNjlWG z&PD2bmA(4kVt= zr_NSB`fz0AEx@!gMczS;4>oE7r7p!sm6gd4x~~B~{q8*j>k{3(E60;yEG=gVhL@de 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Bin 988579 -> 1001001 bytes .../bmr_plot.png | Bin 4799 -> 6595 bytes .../prediction_at_ranger.png | Bin 7542 -> 46517 bytes .../ranks.rds | Bin 381 -> 380 bytes 5 files changed, 47 insertions(+), 44 deletions(-) diff --git a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd index f309d523..a8899e9d 100644 --- a/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd +++ b/_posts/2020-08-02-prediction-of-medical-costs/2020-08-02-prediction-of-medical-costs.Rmd @@ -31,6 +31,7 @@ library(kableExtra) ``` ```{r setup, include=FALSE} +library(mlr3misc) library(mlr3verse) library(ggplot2) library(gridExtra) @@ -46,18 +47,18 @@ The following examples were created as part of the Introduction to Machine Learn The goal of the project was to create and compare one or several machine learning pipelines for the problem at hand together with exploratory analysis and an exposition of results. The posts were contributed to the mlr3gallery by the authors and edited for better legibility by the editor. We want to thank the authors for allowing us to publish their results. -Note, that correctness of the results can not be guaranteed. +Note, that correctness of the results can not be guaranteed. -## Introduction +## Introduction Myriad implementations of supervised learning algorithms can be found in a wide range of fields of science and business. This project serves as an example for an implementation in the actuarial sciences. It analyses insurance costs based on the following data set: "https://www.kaggle.com/mirichoi0218/insurance". -Applying supervised machine learning methods, we want to investigate the following questions: +Applying supervised machine learning methods, we want to investigate the following questions: -1. Which learner qualifies best to explain insurance charges by means of the given covariates? -2. What is the unbiased generalisation error associated with the selected model? -3. Which tariffication criteria (= covariates) have the strongest impact on the charges? +1. Which learner qualifies best to explain insurance charges by means of the given covariates? +2. What is the unbiased generalisation error associated with the selected model? +3. Which tariffication criteria (= covariates) have the strongest impact on the charges? ## Descriptive Analysis of the Data @@ -70,10 +71,12 @@ set.seed(246) The data set consists of 1338 insurees and their respective information on age, sex, bmi, number of children, smoking behaviour and region. As mentioned above our defined target variable, the outcome, are insurance costs named charges. -These shall be explained by the information given about each insuree. +These shall be explained by the information given about each insuree. Before we continue analysis, we convert `character` columns to `factor`. ```{r, echo = FALSE} +insurance = map_if(insurance, is.character, as.factor) head(insurance) + ``` The target variable, charges, is continuous and its distribution is shown below. @@ -90,20 +93,12 @@ insurance$charges = log(insurance$charges) Note, that the same result can be achieved more easily by using `PipeOpTargetTrafo` from mlr3pipelines. This PipeOp provides a smooth implementation to transform the target variable in mlr3 tasks. -The following plots give a brief overview of the distribution of the independent variables: +The following plots give a brief overview of the distribution of the independent variables: ```{r, echo = FALSE} -levels(insurance$region)[levels(insurance$region) == "northeast"] = "ne" -levels(insurance$region)[levels(insurance$region) == "northwest"] = "nw" -levels(insurance$region)[levels(insurance$region) == "southeast"] = "se" -levels(insurance$region)[levels(insurance$region) == "southwest"] = "sw" - - -# autoplot(TaskRegr$new(id = "ins_task", backend = insurance, target = "charges")$select(c("age", "bmi", "children")), type = "pairs") +levels(insurance$region) = c("NE", "NW","SE","SW") histograms <- lapply(as.list(names(insurance)[-7]), function(x) qplot(insurance[ ,x], xlab = x)) - mlr3misc::invoke(grid.arrange, .args = c(histograms, nrow = 2)) - ``` Before we resume in our analysis, all independent, metric variables will be standardized. @@ -117,20 +112,20 @@ po_scale$param_set$values$affect_columns = selector_name(c("age", "bmi", "childr Note, that the same result can be achieved more easily by using `PipeOpScale` from mlr3pipelines. This PipeOp provides a smooth implementation to scale numeric features for mlr3 tasks. -Given the aforementioned continuity of our target variable, we instantiate a regression task which specifies the underlying data and the target variable: +Given the aforementioned continuity of our target variable, we instantiate a regression task which specifies the underlying data and the target variable: ```{r} ins_task = TaskRegr$new(id = "ins_task", backend = insurance, target = "charges") ``` The plots below give a brief overview of the conditional distribution of charges given example independent variables. -It can, for example, be seen that charges seem to increase with age, or that smokers seem to face higher charges than non-smokers. +It can, for example, be seen that charges seem to increase with age, or that smokers seem to face higher charges than non-smokers. ```{r echo = FALSE, message=FALSE} autoplot(ins_task$clone(deep = TRUE)$select(c("age", "smoker")), type = "pairs") ``` -The learners we instantiate are Linear Model (LM), k-Nearest Neighbors (kNN), Decision Trees (CART) and Random Forest (Ranger). +The learners we instantiate are Linear Model (LM), k-Nearest Neighbors (kNN), Decision Trees (CART) and Random Forest (Ranger). ```{r} lrn_lm = lrn("regr.lm") @@ -139,22 +134,27 @@ lrn_rpart = lrn("regr.rpart") lrn_ranger = lrn("regr.ranger") ``` +We additionally scale the data before each learner, here by applying the defined `PipeOpScale` before we fit the model. As scaling is only requried for the `kknn` learner, we only do this for this learner. + +```{r} +lrn_kknn = GraphLearner$new(po_scale %>>% lrn_kknn) +``` ## Model and Hyperparameter Tuning We first specify the hyperparameters of each learning algorithm - if applicable. These hyperparameters can have a strong influence on the performance of the algorithm and it can be advantageous to try different settings before fitting the model on the training data. -Depending on the selected learner, various hyperparameters are obtained. Each of them impacts the performance of the learning algorithm. In order to evaluate this performance, we then need to choose a resampling strategy and a performance measure. +Depending on the selected learner, various hyperparameters are obtained. Each of them impacts the performance of the learning algorithm. In order to evaluate this performance, we then need to choose a resampling strategy and a performance measure. -Again, in regression tasks, there is a variety of potential measures of accuracy to compare the performance of each learner, such as Mean Squared Error (MSE), Mean Absolute Error (MAE) and $R^2$. We will calculate all three to check if they come to the same conclusions. +Again, in regression tasks, there is a variety of potential measures of accuracy to compare the performance of each learner, such as Mean Squared Error (MSE), Mean Absolute Error (MAE) and $R^2$. We will calculate all three to check if they come to the same conclusions. ```{r} resampling_inner = rsmp("cv", folds = 5) measures = mlr_measures$mget(c("regr.mse", "regr.mae", "regr.rsq")) ``` -To find the optimal hyperparameter setting of a model, which results in the most accurate predictions, we need to define the parameter space as well as the tuning approach. -In this example we use `r mlr3book::ref("TunerRandomSearch")`, where random combinations of hyperparamters are tested to find the best solution in a given space. +To find the optimal hyperparameter setting of a model, which results in the most accurate predictions, we need to define the parameter space as well as the tuning approach. +In this example we use `r mlr3book::ref("TunerRandomSearch")`, where random combinations of hyperparamters are tested to find the best solution in a given space. ```{r} tuner_rs = mlr3tuning::tnr("random_search") @@ -172,7 +172,7 @@ terminator = trm("evals", n_evals = 30) *K-Nearest Neighbors* is a computationally complex procedure but very simple in terms of understanding as well as implementation. Furthermore, the resulting models often have a high degree of accuracy. As shown below, the parameter $k$, the number of neighbors, will be optimized as part of the model development. -We specify that $k$-values between 1 and 40 shall be taken into account. +We specify that $k$-values between 1 and 40 shall be taken into account. ```{r} param_set_knn = ParamSet$new(params = list(ParamInt$new("k", lower = 1, upper = 40))) @@ -180,8 +180,8 @@ param_set_knn = ParamSet$new(params = list(ParamInt$new("k", lower = 1, upper = For *CART learners* we choose to optimize two hyperparameters. -- The complexity parameter $cp$ ensures that only splits that improve the overall fit by a factor of $cp$ are attempted. -- The hyperparameter $minsplit$ determines the minimal number of observations per leaf necessary for a split to be attempted. +- The complexity parameter $cp$ ensures that only splits that improve the overall fit by a factor of $cp$ are attempted. +- The hyperparameter $minsplit$ determines the minimal number of observations per leaf necessary for a split to be attempted. ```{r} param_set_rpart = @@ -190,7 +190,8 @@ param_set_rpart = ParamInt$new("minsplit", lower = 1, upper = 50))) ``` -Finally, for the Random Forest learner, the hyperparameters we choose to optimize are $mtry$, the number of randomly sampled features considered by each tree when splitting a node, and $min.node.size$, the minimum number of observations per node. + +Finally, for the Random Forest learner, the hyperparameters we choose to optimize are $mtry$, the number of randomly sampled features considered by each tree when splitting a node, and $min.node.size$, the minimum number of observations per node. ```{r} param_set_ranger = @@ -201,6 +202,7 @@ param_set_ranger = The `r mlr3book::ref("AutoTuner")` from the mlr3 package adjusts itself by first tuning the hyperparameters of the respective learner on the training data, then setting the optimal parameters in the learner and finally fitting the model on the complete training data set. + ```{r} at_knn = AutoTuner$new( learner = lrn_kknn, @@ -226,10 +228,11 @@ at_ranger = AutoTuner$new( terminator = terminator, tuner = tuner_rs ) - -scaled_learners = lapply(list(lrn_lm, at_knn, at_rpart, at_ranger), function(x) GraphLearner$new(po_scale %>>% x)) ``` +```{r future, echo=FALSE,results='hide', eval=longrun} + future::plan("multicore") +``` ```{r grid1, echo=FALSE, message=FALSE, results='hide', eval=longrun} resampling_outer = rsmp("cv", folds = 5) @@ -247,10 +250,10 @@ bmr = benchmark(grid, store_models = TRUE) ```{r, echo=FALSE, eval=FALSE} plot_tuning = function(benchmark = bmr, learner_ident, parameter, scale) { - + learner = bmr$score()[learner_id == learner_ident]$learner tuning_result = sapply(learner, FUN = function(x) x$model[[gsub('^.{6}', '', learner_ident)]]$model$tuning_instance$result[[parameter]]) - + qplot(y = tuning_result, x = 1, geom = "boxplot") + ylim(scale) + geom_hline(yintercept = scale[1], col = "red", linetype = "dashed") + @@ -286,18 +289,18 @@ So, each boxplot is based on 5 values. The red lines (dashed) indicate the range, within which the hyperparameters were optimized. It can, for example, be seen that while various different $k$-values are deemed optimal for kNN, $mtry = 4$ is determined the optimal setting for the Ranger algorithm in every iteration. Also, the optimal $cp$ in CART seems to lie within a small range, while the best-performing $minsplit$-parameter is rather volatile. -However, the illustration neglects the fact that in tuning we are looking at combinations of hyperparameters and the more dimensions we consider, the fewer of the hyperparameter space we are investigating with a fixed number of evaluations in the tuning. +However, the illustration neglects the fact that in tuning we are looking at combinations of hyperparameters and the more dimensions we consider, the fewer of the hyperparameter space we are investigating with a fixed number of evaluations in the tuning. ### Outer Loop: Model Selection For nested resampling, we also define a 5-fold cross validation as our outer loop. -This means, we obtain five pairs of training and test sets. Each of those initiates the tuning process for the hyperparameter spaces specified earlier. +This means, we obtain five pairs of training and test sets. Each of those initiates the tuning process for the hyperparameter spaces specified earlier. For each of the five iterations, the learner is fitted on the outer training set while its performance is evaluated on the outer test set. -By averaging these five performance estimates of the outer loops, we get an unbiased performance estimate for the learner. +By averaging these five performance estimates of the outer loops, we get an unbiased performance estimate for the learner. As mentioned earlier, we aim to compare the performance of different learning algorithms on the prediction of insurance costs. By initiating a benchmarking process, we can combine all candidate models in one single nested resampling process. -All we have to do is to define a grid with the regression task, the (tuned) learners and the outer resampling strategy. +All we have to do is to define a grid with the regression task, the (tuned) learners and the outer resampling strategy. This part of the analysis can be computationally demanding. With our termination criterion of 30 evaluations in the tuning process, a 5-fold CV in the inner loop and another 5-fold CV in the outer loop, a total of 755 models is fitted for each learner that requires tuning and another 5 models for the Linear Model, which doesn't have hyperparameters to optimize. @@ -333,9 +336,9 @@ Benchmarking generates scores for each learner and each outer loop iteration. Drawing boxplots over the performance estimates - here the Mean Squared Error - shows that kNN seems to work fine but produces some variation in performance estimates. The Linear Model doesn't deliver satisfactory results and produces large MSEs compared to the other candidate learners. Random Forest appears to be the best model producing accurate predictions in terms of the MSE. -Finally, Decision Trees produce performance estimates similar to those of kNN, with even smaller variability. +Finally, Decision Trees produce performance estimates similar to those of kNN, with even smaller variability. -One of our initial questions was: Which learner qualifies best to predict insurance charges - that is, as accurately as possible? +One of our initial questions was: Which learner qualifies best to predict insurance charges - that is, as accurately as possible? To come to answer this question, we do not necessarily have to study the boxplots - though it might be helpful. Instead, we can access the aggregated performance estimates for each learner, directly. @@ -379,13 +382,13 @@ ggplot(data = ranks) + But what about the hyperparameters? We just learned that from nested resampling we obtain five different sets of optimal combinations: -Which one of them shall we use for the final model? +Which one of them shall we use for the final model? The answer is: none of them. Nested resampling solely enabled us to obtain an unbiased measure of generalization error for each model. Unlike before, the final model is fit on the whole dataset and includes its own tuning step and resampling. The major difference is that there is no outer loop. -Based on the tuning results, the model is trained on the whole dataset. +Based on the tuning results, the model is trained on the whole dataset. ```{r, eval=longrun} @@ -419,11 +422,11 @@ at_ranger_final <- readRDS("at_ranger.rds") From the tuning process of our final model, we conclude that the optimal hyperparameter setting is achieved through the combination of $min.node.size = 30$ and $mtry = 4$. The figure below illustrates the investigated parameter combinations via random search. -The color intensity matches the value of the respective MSE and the hyperparameter combination with the best performance, which is used to train the model, is highlighted in red. +The color intensity matches the value of the respective MSE and the hyperparameter combination with the best performance, which is used to train the model, is highlighted in red. ```{r echo=FALSE, eval=TRUE} tab_tuning_instance = at_ranger_final$model$regr.ranger.tuned$model$tuning_instance -tab_tuning = tab_tuning_instance$archive$data()[, c("batch_nr", "regr.mse", "min.node.size", "mtry")] +tab_tuning = tab_tuning_instance$archive$data[, c("batch_nr", "regr.mse", "min.node.size", "mtry")] ggplot() + geom_point(aes(x = min.node.size, y = mtry, fill = regr.mse, col = regr.mse), data = tab_tuning, size = 5, shape = 21) + @@ -455,7 +458,7 @@ dev.off() As a last step of our analysis, we want to shed some light onto the functionality of our final "black box" model. To get a better understanding of the predictions made, we investigate the importance of each individual covariate. This can be done with the help of filter methods, which assign an importance value to each feature, which will then be ranked. -For the Ranger learning algorithm, we can make use of the filter methods embedded in the mlr3-package. +For the Ranger learning algorithm, we can make use of the filter methods embedded in the mlr3-package. ```{r} learner <- lrn("regr.ranger", importance = "impurity") @@ -483,7 +486,7 @@ ggplot(data = var, aes(x = feature, y = score)) + When looking at *impurity* as a measure of importance, we can see that first and foremost, the smoking status determines the predicted value of insurance charges. This is followed by age. The bmi, on the other hand, doesn't seem to have a strong impact on the predicted charges and similarly, the remaining features (children, region and sex) lead to minor improvements in impurity only. -Overall, these findings are supported by domain knowledge and are in line with the descriptive analysis mentioned above. +Overall, these findings are supported by domain knowledge and are in line with the descriptive analysis mentioned above. ## Summary and Implications diff --git a/_posts/2020-08-02-prediction-of-medical-costs/at_ranger.rds b/_posts/2020-08-02-prediction-of-medical-costs/at_ranger.rds index 2a0fbedc3a1465ec48831991f8ef3309f5bd7a1e..a322614bac08d2c6ef199a6854553af197591714 100644 GIT binary patch literal 1001001 zcma&NbyOQ))GplO6o(?giqm2Rf@>*WT#CB|ch?pu#R3Hi#a)YgaCZr=!QI{MroZ=H z-?#36H!JI8_CC*KX6>BWXUmg!5ooXedm$b^Vf@zbb0P`9<_8A7fKD0F17FF!qWfeL zii7@*3jNzFG<+&_d_#Ps{xzd*Op9+F!$u;n0uolEH=|ino+T<-K2%W*)z}Ut&}&B# 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