To combat potential collinearity issues, eliminate variables from the regression one at a time

LICENSE

@@ -186,7 +186,7 @@
       same "printed page" as the copyright notice for easier
       identification within third-party archives.
 
-   Copyright [2024] [Wise PLC]
+   Copyright 2024 Wise PLC
 
    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.

shap_select/select.py

@@ -223,6 +223,46 @@ def shap_features_to_significance(
     return result_df_sorted
 
 
+def iterative_shap_feature_reduction(
+    shap_features: pd.DataFrame | List[pd.DataFrame],
+    target: pd.Series,
+    task: str,
+    alpha: float=1e-6,
+) -> pd.DataFrame:
+    collected_rows = []  # List to store the rows we collect during each iteration
+
+    features_left = True
+    while features_left:
+        # Call the original shap_features_to_significance function
+        significance_df = shap_features_to_significance(shap_features, target, task, alpha)
+
+        # Find the feature with the lowest t-value
+        min_t_value_row = significance_df.loc[significance_df["t-value"].idxmin()]
+
+        # Remember this row (collect it in our list)
+        collected_rows.append(min_t_value_row)
+
+        # Drop the feature corresponding to the lowest t-value from shap_features
+        feature_to_remove = min_t_value_row["feature name"]
+        if isinstance(shap_features, pd.DataFrame):
+            shap_features = shap_features.drop(columns=[feature_to_remove])
+            features_left = len(shap_features.columns)
+        else:
+            shap_features = {
+                k: v.drop(columns=[feature_to_remove]) for k, v in shap_features.items()
+            }
+            features_left = len(list(shap_features.values())[0].columns)
+
+    # Convert collected rows back to a dataframe
+    result_df = (
+        pd.DataFrame(collected_rows)
+        .sort_values(by="t-value", ascending=False)
+        .reset_index()
+    )
+
+    return result_df
+
+
 def shap_select(
     tree_model: Any,
     validation_df: pd.DataFrame,
@@ -274,8 +314,8 @@ def shap_select(
     else:
         shap_features = create_shap_features(tree_model, validation_df[feature_names])
 
-    # Compute statistical significance of each feature
-    significance_df = shap_features_to_significance(shap_features, target, task, alpha)
+    # Compute statistical significance of each feature, recursively ablating
+    significance_df = iterative_shap_feature_reduction(shap_features, target, task, alpha)
 
     # Add 'Selected' column based on the threshold
     significance_df["selected"] = (