fix for parameter uncertainty in additive generic models

cyclic_boosting/generic_loss.py

@@ -550,7 +550,32 @@ def uncertainty_gamma(y: np.ndarray, weights: np.ndarray) -> float:
 
 
 def uncertainty_gaussian(y: np.ndarray, weights: np.ndarray) -> float:
-    return np.sqrt(np.sum(weights * y) / (np.sum(weights) - 1) / np.sum(weights))
+    weighted_mean_y = np.sum(y * weights) / np.sum(weights)
+    variance_prior = np.sum((y - weighted_mean_y) * (y - weighted_mean_y) * weights) / np.sum(weights)
+    if variance_prior <= 1e-9:
+        variance_prior = 1.0
+
+    sum_y = np.sum(weights * y)
+    sum_weights = np.sum(weights)
+    mean_y = sum_y / sum_weights
+    weighted_squared_residual_sum = np.sum(weights * (y - mean_y) ** 2)
+
+    n_prior = 1
+    a_0 = 0.5 * n_prior
+    b_0 = a_0 * variance_prior
+    a = a_0 + 0.5 * sum_weights
+    b = b_0 + 0.5 * weighted_squared_residual_sum
+    variance_y = b / a
+    w = weights / variance_y
+
+    sum_w = np.sum(w)
+    sum_vw = np.sum(weights * w)
+    w0 = 1e-2
+    sum_w += w0
+    sum_vw += w0
+    variance_weighted_mean = sum_vw / sum_w**2
+
+    return np.sqrt(variance_weighted_mean)
 
 
 def uncertainty_beta(y: np.ndarray, weights: np.ndarray, link_func) -> float:

pyproject.toml

@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "cyclic-boosting"
-version = "1.2.2"
+version = "1.2.3"
 description = "Implementation of Cyclic Boosting machine learning algorithms"
 authors = ["Blue Yonder GmbH"]
 packages = [{include = "cyclic_boosting"}]

tests/test_integration.py

@@ -724,10 +724,10 @@ def test_additive_quantile_regression_median(is_plot, prepare_data, default_feat
     yhat = CB_est.predict(X.copy())
 
     quantile_acc = evaluate_quantile(y, yhat)
-    np.testing.assert_almost_equal(quantile_acc, 0.4973, 3)
+    np.testing.assert_almost_equal(quantile_acc, 0.4950, 3)
 
     mad = np.nanmean(np.abs(y - yhat))
-    np.testing.assert_almost_equal(mad, 1.6991, 3)
+    np.testing.assert_almost_equal(mad, 1.7062, 3)
 
 
 def test_additive_quantile_regression_90(is_plot, prepare_data, default_features, feature_properties):
@@ -743,23 +743,32 @@ def test_additive_quantile_regression_90(is_plot, prepare_data, default_features
     yhat = CB_est.predict(X.copy())
 
     quantile_acc = evaluate_quantile(y, yhat)
-    np.testing.assert_almost_equal(quantile_acc, 0.8969, 3)
+    np.testing.assert_almost_equal(quantile_acc, 0.8934, 3)
 
 
 def test_additive_regression_mad(is_plot, prepare_data, default_features, feature_properties):
     X, y = prepare_data
     X = X[default_features]
 
+    plobs = [
+        observers.PlottingObserver(iteration=1),
+        observers.PlottingObserver(iteration=-1),
+    ]
+
     CB_est = pipeline_CBAdditiveGenericCRegressor(
         feature_properties=feature_properties,
         costs=costs_mad,
+        observers=plobs,
     )
     CB_est.fit(X.copy(), y)
 
+    if is_plot:
+        plot_CB("analysis_CB_iterlast", [CB_est[-1].observers[-1]], CB_est[-2])
+
     yhat = CB_est.predict(X.copy())
 
     mad = np.nanmean(np.abs(y - yhat))
-    np.testing.assert_almost_equal(mad, 1.6991, 3)
+    np.testing.assert_almost_equal(mad, 1.7062, 3)
 
 
 def test_additive_regression_mse(is_plot, prepare_data, default_features, feature_properties):
@@ -775,7 +784,7 @@ def test_additive_regression_mse(is_plot, prepare_data, default_features, featur
     yhat = CB_est.predict(X.copy())
 
     mad = np.nanmean(np.abs(y - yhat))
-    np.testing.assert_almost_equal(mad, 1.748, 3)
+    np.testing.assert_almost_equal(mad, 1.738, 3)
 
 
 def test_multiplicative_regression_mad(is_plot, prepare_data, default_features, feature_properties):