Handle numerical issues in SNMoE

- SNMoE: Handle numerical issues when calculating the two conditional expectations 'E1ik' and 'E2ik' in StatSNMoE class;
- CITATION: Update citations;
- logsumexp.R: Correct a typo;
- IRLS.cpp: Correct a typo.

NAMESPACE

@@ -20,6 +20,8 @@ exportClasses(StatNMoE)
 exportClasses(StatSNMoE)
 exportClasses(StatStMoE)
 exportClasses(StatTMoE)
+import(MASS)
 import(methods)
+import(pracma)
 importFrom(Rcpp,sourceCpp)
 useDynLib(meteorits, .registration = TRUE)

R/ParamSNMoE.R

@@ -25,7 +25,7 @@
 #'   \eqn{(1, K)}).
 #' @field lambda The skewness parameters for each experts (matrix of size
 #'   \eqn{(1, K)}).
-#' @field delta delta is equal \eqn{\delta =
+#' @field delta delta is equal to \eqn{\delta =
 #'   \frac{\lambda}{\sqrt{1+\lambda^2}}}{\delta = \lambda /
 #'   (1+\lambda^2)^(1/2)}.
 #' @field df The degree of freedom of the SNMoE model representing the
@@ -123,6 +123,7 @@ ParamSNMoE <- setRefClass(
       Z <- matrix(0, nrow = n, ncol = K)
       Z[klas %*% ones(1, K) == ones(n, 1) %*% seq(K)] <- 1
       tau <- Z
+
       res <- IRLS(phiAlpha$XBeta, tau, ones(nrow(tau), 1), alpha)
       alpha <<- res$W
 
@@ -147,6 +148,7 @@ ParamSNMoE <- setRefClass(
       \\code{statSNMoE} of class \\link{StatSNMoE} (which contains the E-step)."
 
       res_irls <- IRLS(phiAlpha$XBeta, statSNMoE$tik, ones(nrow(statSNMoE$tik), 1), alpha, verbose_IRLS)
+
       statSNMoE$piik <- res_irls$piik
       reg_irls <- res_irls$reg_irls
 
@@ -156,6 +158,7 @@ ParamSNMoE <- setRefClass(
 
         # Update the regression coefficients
         tauik_Xbeta <- (statSNMoE$tik[, k] %*% ones(1, p + 1)) * phiBeta$XBeta
+
         beta[, k] <<- solve((t(tauik_Xbeta) %*% phiBeta$XBeta)) %*% (t(tauik_Xbeta) %*% (Y - delta[k] * statSNMoE$E1ik[, k]))
 
         # Update the variances sigma2k

R/ParamStMoE.R

@@ -25,7 +25,7 @@
 #'   \eqn{(1, K)}).
 #' @field lambda The skewness parameters for each experts (matrix of size
 #'   \eqn{(1, K)}).
-#' @field delta delta is equal \eqn{\delta =
+#' @field delta delta is equal to \eqn{\delta =
 #'   \frac{\lambda}{\sqrt{1+\lambda^2}}}{\delta = \lambda /
 #'   (1+\lambda^2)^(1/2)}.
 #' @field nu The degree of freedom for the Student distribution for each

R/StatSNMoE.R

@@ -166,9 +166,13 @@ StatSNMoE <- setRefClass(
 
         # E1ik = E[Ui|yi,xi,zik=1]
         E1ik[, k] <<- mu_uk + sigma_uk * dnorm(paramSNMoE$lambda[k] * dik, 0, 1) / pnorm(paramSNMoE$lambda[k] * dik, 0, 1)
+        E1ik[is.nan(E1ik[, k]), k] <<- mu_uk[is.nan(E1ik[, k])] - sigma_uk * paramSNMoE$lambda[k] * dik[is.nan(E1ik[, k])]
+        E1ik[is.infinite(E1ik[, k]), k] <<- mu_uk[is.infinite(E1ik[, k])] - sigma_uk * paramSNMoE$lambda[k] * dik[is.infinite(E1ik[, k])]
 
         # E2ik = E[Ui^2|y,zik=1]
         E2ik[, k] <<- mu_uk ^ 2 + sigma_uk ^ 2 + sigma_uk * mu_uk * dnorm(paramSNMoE$lambda[k] * dik, 0, 1) / pnorm(paramSNMoE$lambda[k] * dik, 0, 1)
+        E2ik[is.nan(E2ik[, k]), k] <<- mu_uk[is.nan(E2ik[, k])] ^ 2 + sigma_uk ^ 2 - sigma_uk * mu_uk[is.nan(E2ik[, k])] * paramSNMoE$lambda[k] * dik[is.nan(E2ik[, k])]
+        E2ik[is.infinite(E2ik[, k]), k] <<- mu_uk[is.infinite(E2ik[, k])] ^ 2 + sigma_uk ^ 2 - sigma_uk * mu_uk[is.infinite(E2ik[, k])] * paramSNMoE$lambda[k] * dik[is.infinite(E2ik[, k])]
 
         # weighted skew normal linear expert likelihood
         piik_fik[, k] <- piik[, k] * (2 / sigmak) * dnorm(dik, 0, 1) * pnorm(paramSNMoE$lambda[k] * dik)
@@ -179,7 +183,9 @@ StatSNMoE <- setRefClass(
       log_sum_piik_fik <<- matrix(log(rowSums(piik_fik)))
 
       # E[Zik|y,x] and E[U^2|y,zik=1]
-      tik <<- piik_fik / (rowSums(piik_fik) %*% ones(1, paramSNMoE$K))
+      # tik <<- piik_fik / (rowSums(piik_fik) %*% ones(1, paramSNMoE$K))
+      log_Tauik <- log_piik_fik - logsumexp(log_piik_fik, 1) %*% ones(1, paramSNMoE$K)
+      tik <<- exp(log_Tauik)
     }
   )
 )

R/logsumexp.R

@@ -7,7 +7,7 @@ logsumexp <- function(A, margin) {
     A <- xstar + log(apply(exp(M), 1, sum))
   } else{
     xstar <- apply(A, 2, max)
-    M <- M -  matrix(1, nrow = row(M), ncol = 1) %*% xstar
+    M <- M -  matrix(1, nrow = nrow(M), ncol = 1) %*% xstar
     A <- xstar + log(apply(exp(M), 2, sum))
   }
   return(A)

R/meteorits-package.R

@@ -10,17 +10,17 @@
 #' `meteorits` contains the following Mixture-of-Experts models:
 #'
 #' \itemize{
-#'   \item NMoE provides a flexible framework for heterogenous data with
-#'   Normal expert regressors network;
-#'   \item SNMoE provides a flexible modeling framework for heterogenous
-#'   data with possibly skewed distributions to generalize the standard Normal
-#'   mixture of expert model;
-#'   \item TMoE provides a flexible and robust modeling framework for
-#'   heterogenous data with possibly heavy-tailed distributions and corrupted by
-#'   atypical observations;
-#'   \item StMoE provides a flexible and robust modeling framework for
-#'   heterogenous data with possibly skewed, heavy-tailed distributions and
-#'   corrupted by atypical observations.
+#'   \item NMoE (Normal Mixtures-of-Experts) provides a flexible framework for
+#'   heterogenous data with Normal expert regressors network;
+#'   \item SNMoE (Skew-Normal Mixtures-of-Experts) provides a flexible
+#'   modeling framework for heterogenous data with possibly skewed
+#'   distributions to generalize the standard Normal mixture of expert model;
+#'   \item tMoE (t Mixtures-of-Experts) provides a flexible and robust
+#'   modeling framework for heterogenous data with possibly heavy-tailed
+#'   distributions and corrupted by atypical observations;
+#'   \item StMoE (Skew t Mixtures-of-Experts) provides a flexible and robust
+#'   modeling framework for heterogenous data with possibly skewed,
+#'   heavy-tailed distributions and corrupted by atypical observations.
 #' }
 #'
 #' For the advantages/differences of each of them, the user is referred to our
@@ -46,6 +46,8 @@
 #' Chamroukhi, F., A. Same, G. Govaert, and P. Aknin. 2009. \emph{Time Series Modeling by a Regression Approach Based on a Latent Process.} Neural Networks 22 (5-6): 593--602. \url{https://chamroukhi.com/papers/Chamroukhi_Neural_Networks_2009.pdf}.
 #'
 #' @import methods
+#' @import pracma
+#' @import MASS
 ## usethis namespace: start
 #' @useDynLib meteorits, .registration = TRUE
 ## usethis namespace: end

inst/CITATION

@@ -1,4 +1,7 @@
-citHeader("To cite meteorits in publications use:")
+citHeader("To cite the package meteorits in a publication please use the
+following reference. To cite the corresponding paper for a specific package
+from meteorits (e.g NMoE, SNMoE, tMoE, StMoE, etc), please choose the
+reference(s) from the list provided below.")
 
 note <- sprintf("R package version %s", meta$Version)
 
@@ -7,69 +10,76 @@ citEntry(
   title = "meteorits: Mixtures-of-Experts Modeling for Complex and Non-Normal Distributions
   ('MEteorits')",
   author = personList(person(given="F.", family="Chamroukhi"),
-                      person(given="M.", family="Bartcus"),
-                      person(given="F.", family="Lecocq")),
+                      person(given="F.", family="Lecocq"),
+                      person(given="M.", family="Bartcus")),
   year = "2019",
   note = note,
   url = "https://github.com/fchamroukhi/MEteorits",
-  textVersion = paste0("Faicel Chamroukhi, Marius Bartcus and Florian Lecocq (2019).
+  textVersion = paste0("Faicel Chamroukhi, Florian Lecocq and Marius Bartcus (2019).
   meteorits: Mixtures-of-Experts Modeling for Complex and Non-Normal Distributions
   ('MEteorits'). ", note, ". https://github.com/fchamroukhi/MEteorits")
 )
 
 citEntry(
-  entry    = "Article",
+  entry = "Article",
   author = personList(person(given="B-T.", family="Huynh"),
                       person(given="F.", family="Chamroukhi")),
-  journal = "Journal de la Societe Francaise de Statistique",
-  title = "Estimation and Feature Selection in Mixtures of Generalized Linear Experts Models.",
+  journal = "Journal de la Soci\\'{e}t\\'{e} Fran\\c{c}aise de Statistique",
+  title = "Estimation and Feature Selection in Mixtures of Generalized Linear Experts Models",
 	year = "2019",
-	url =  "https://chamroukhi.com/papers/Chamroukhi_Huynh_jsfds-published.pdf",
-	textVersion = "B-T. Huynh and F. Chamroukhi (2019). \u201cEstimation and Feature Selection in Mixtures of Generalized Linear Experts Models.\u201d Journal de la Societe Francaise de Statistique. <URL: https://chamroukhi.com/papers/Chamroukhi_Huynh_jsfds-published.pdf."
+	url = "https://chamroukhi.com/papers/Chamroukhi_Huynh_jsfds-published.pdf",
+	textVersion = "Huynh B, Chamroukhi F (2019). \u201cEstimation and Feature Selection
+	in Mixtures of Generalized Linear Experts Models.\u201d Journal de la
+	Soci\u00e9t\u00e9 Fran\u00e7aise de Statistique.
+	<URL: https://chamroukhi.com/papers/Chamroukhi_Huynh_jsfds-published.pdf>."
 )
 
 citEntry(
-  entry    = "Article",
-  title    = "Regularized Maximum Likelihood Estimation and Feature Selection in Mixtures-of-Experts Models.",
+  entry = "Article",
+  title = "Regularized Maximum Likelihood Estimation and Feature Selection in Mixtures-of-Experts Models",
   author = personList(person(given="F.", family="Chamroukhi"),
                       person(given="Bao T.", family="Huynh")),
-  journal  = "Journal de la Soci\u00e9t\u00e9 Fran\u00e7aise de Statistique",
-  volume   = "160(1)",
+  journal = "Journal de la Soci\\'{e}t\\'{e} Fran\\c{c}aise de Statistique",
+  volume  = "160",
+  number = "1",
   pages = "57--85",
   year = "2019",
-  textVersion = "F. Chamroukhi and Bao T. Huynh (2019). \u201cRegularized Maximum Likelihood Estimation and Feature Selection in Mixtures-of-Experts Models.\u201d Journal de la Soci\u00e9t\u00e9 Fran\u00e7aise de Statistique, vol. 160(1), pp. 57--85"
+  textVersion = "Chamroukhi F, Huynh B (2019). \u201cRegularized Maximum
+  Likelihood Estimation and Feature Selection in Mixtures-of-Experts
+  Models.\u201d Journal de la Soci\u00e9t\u00e9 Fran\u00e7aise de Statistique,
+  *160(1)*, 57-85."
 )
 
 citEntry(
-  entry    = "Article",
-  title    = "Practical and theoretical aspects of mixture-of-experts modeling: An overview",
+  entry = "Article",
+  title = "Practical and theoretical aspects of mixture-of-experts modeling: An overview",
   author = personList(person(given="Hien D.", family="Nguyen"),
                       person(given="F.", family="Chamroukhi")),
-  journal  = "Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery",
+  journal = "Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery",
   publisher = "Wiley Periodicals, Inc",
-  year     = "2018",
+  year = "2018",
   pages = "e1246--n/a",
   doi = "10.1002/widm.1246",
-  url      = "https://chamroukhi.com/papers/Nguyen-Chamroukhi-MoE-DMKD-2018",
-  textVersion = "Nguyen H and Chamroukhi F (2018). \u201cPractical and theoretical aspects
-  of mixture-of-experts modeling: An overview.\u201d Wiley Interdisciplinary Reviews:
-  Data Mining and Knowledge Discovery, pp. e1246-n/a.
-  doi: 10.1002/widm.1246 (URL:https://doi.org/10.1002/widm.1246),
+  url = "https://chamroukhi.com/papers/Nguyen-Chamroukhi-MoE-DMKD-2018",
+  textVersion = "Nguyen H, Chamroukhi F (2018). \u201cPractical and theoretical
+  aspects of mixture-of-experts modeling: An overview.\u201d Wiley
+  Interdisciplinary Reviews: Data Mining and Knowledge Discovery, e1246-n/a.
+  doi: 10.1002/widm.1246 (URL: http://doi.org/10.1002/widm.1246),
   <URL: https://chamroukhi.com/papers/Nguyen-Chamroukhi-MoE-DMKD-2018>."
 )
 
 citEntry(
-  entry    = "Article",
-  title    = "Skew t mixture of experts",
-  author   = personList(person(given="F.", family="Chamroukhi")),
-  journal  = "Neurocomputing - Elsevier",
-  year     = "2017",
-  volume   = "266",
-  pages    = "390--408",
-  url      = "https://chamroukhi.com/papers/STMoE.pdf",
+  entry = "Article",
+  title = "Skew t mixture of experts",
+  author = personList(person(given="F.", family="Chamroukhi")),
+  journal = "Neurocomputing - Elsevier",
+  year = "2017",
+  volume = "266",
+  pages = "390--408",
+  url = "https://chamroukhi.com/papers/STMoE.pdf",
   textVersion = "Chamroukhi F (2017). \u201cSkew t mixture of experts.\u201d
-  Neurocomputing - Elsevier,
-  266, pp. 390-408. <URL:https://chamroukhi.com/papers/STMoE.pdf>."
+  Neurocomputing - Elsevier, *266*, 390-408.
+  <URL: https://chamroukhi.com/papers/STMoE.pdf>."
 )
 
 citEntry(
@@ -81,60 +91,62 @@ citEntry(
   volume = "79",
   pages = "20--36",
   url = "https://chamroukhi.com/papers/TMoE.pdf",
-  textVersion = "Chamroukhi F (2016). \u201cRobust mixture of experts modeling using the
-  t-distribution.\u201d Neural Networks - Elsevier, 79, pp. 20-36.
+  textVersion = "Chamroukhi F (2016). \u201cRobust mixture of experts modeling
+  using the t-distribution.\u201d Neural Networks - Elsevier, *79*, 20-36.
   <URL: https://chamroukhi.com/papers/TMoE.pdf>."
 )
 
 citEntry(
-  entry    = "InProceedings",
-  title    = "Skew-Normal Mixture of Experts",
+  entry = "InProceedings",
+  title = "Skew-Normal Mixture of Experts",
   author = personList(person(given="F.", family="Chamroukhi")),
-  booktitle  = "The International Joint Conference on Neural Networks (IJCNN)",
-  year     = "2016",
-  url      = "https://chamroukhi.com/papers/Chamroukhi-SNMoE-IJCNN2016.pdf",
-  textVersion = "Chamroukhi F (2016). \u201cSkew-Normal Mixture of Experts.\u201d In
-  The International Joint Conference on Neural Networks (IJCNN).
-  <URL:https://chamroukhi.com/papers/Chamroukhi-SNMoE-IJCNN2016.pdf>."
+  booktitle = "The International Joint Conference on Neural Networks (IJCNN)",
+  year = "2016",
+  url = "https://chamroukhi.com/papers/Chamroukhi-SNMoE-IJCNN2016.pdf",
+  textVersion = "Chamroukhi F (2016). \u201cSkew-Normal Mixture of
+  Experts.\u201d In The International Joint Conference on Neural Networks (IJCNN).
+  <URL: https://chamroukhi.com/papers/Chamroukhi-SNMoE-IJCNN2016.pdf>."
 )
 
 citEntry(
   entry = "PhdThesis",
   title = "Statistical learning of latent data models for complex data analysis",
   author = person(given="F.", family="Chamroukhi"),
-  school = "Universit\u00e9 de Toulon",
+  school = "Universit\\'{e} de Toulon",
   year = "2015",
   type = "Habilitation Thesis (HDR)",
   url = "https://chamroukhi.com/Dossier/FChamroukhi-Habilitation.pdf",
-  textVersion = "Chamroukhi F (2015). Statistical learning of latent data models for
-  complex data analysis. Habilitation Thesis (HDR), Universit\u00e9 de Toulon.
+  textVersion = "Chamroukhi F (2015). Statistical learning of latent data models
+  for complex data analysis. PhD thesis, Universit\u00e9 de Toulon.
   <URL: https://chamroukhi.com/Dossier/FChamroukhi-Habilitation.pdf>."
 )
 
 citEntry(
   entry = "PhdThesis",
   title = "Hidden process regression for curve modeling, classification and tracking",
   author = person(given="F.", family="Chamroukhi"),
-  school = "Universit\'{e} de Technologie de Compi\`{e}gne",
+  school = "Universit\\'{e} de Technologie de Compi\\`{e}gne",
   year = "2010",
   type = "Ph.D. Thesis",
   url = "https://chamroukhi.com/papers/FChamroukhi-Thesis.pdf",
-  textVersion = "Chamroukhi F (2010). \u201cHidden process regression for curve
-  modeling, classification and tracking\u201d. Ph.D. Thesis, Universit\u00e9 de
-  Technologie de Compi\u00e8gne.
-  <URL: https://chamroukhi.com/papers/FChamroukhi-Thesis.pdf>."
+  textVersion = "Chamroukhi F (2010). Hidden process regression for curve
+  modeling, classification and tracking. PhD thesis, Universit\u00e9 de Technologie
+  de Compi\u00e8gne. <URL: https://chamroukhi.com/papers/FChamroukhi-Thesis.pdf>."
 )
 
 citEntry(
   entry = "Article",
-  title = "Time series modeling by a regression approach based on a latent process.",
+  title = "Time series modeling by a regression approach based on a latent process",
   author = personList(person(given="F.", family="Chamroukhi"),
-                      person(given="A.", family="Sam\u00e9"),
+                      person(given="A.", family="Sam\\'{e}"),
                       person(given="G.", family="Govaert"),
                       person(given="P.", family="Aknin")),
   journal = "Neural Networks Elsevier Science Ltd.",
   year = "2009",
-  volume = "22(5-6)",
+  volume = "22",
+  number = "5-6",
   pages = "593--602",
-  textVersion = "F. Chamroukhi and A. Sam\u00e9 and G. Govaert and P. Aknin (2009). \u201cTime series modeling by a regression approach based on a latent process.\u201d Neural Networks Elsevier Science Ltd., vol. 22(5-6), pp. 593--602."
+  textVersion = "Chamroukhi F, Sam\u00e9 A, Govaert G, Aknin P (2009). \u201cTime
+  series modeling by a regression approach based on a latent process.\u201d
+  Neural Networks Elsevier Science Ltd., *22(5-6)*, 593-602."
 )

src/IRLS.cpp

@@ -250,7 +250,7 @@ List IRLS(arma::mat& X, arma::mat& Tau, arma::mat& Gamma, arma::mat& Winit, bool
     }
   } else {
     Rcout << "\n";
-    Rcout << "IRLS : doesn't converged (increase the number of iterations > "  + std::to_string(iter) + ")\n";
+    Rcout << "IRLS : did not converge (increase the number of iterations > "  + std::to_string(max_iter) + ")\n";
   }
 
   double reg_irls = 0;