Multicollinearity Correction and Combined Feature Effect in Shapley Values

TL;DR

This paper introduces a unified framework to accurately compute Shapley values in the presence of correlated features, addressing a key limitation and enabling reliable feature importance analysis in complex models.

Contribution

It proposes a matrix-based adjustment method for Shapley values that accounts for feature correlations, with mathematical proof and extension to feature combinations.

Findings

Adjusted Shapley values are independent of feature correlations.

The method is computationally efficient compared to traditional approaches.

Extension to multiple features improves combined effect analysis.

Abstract

Model interpretability is one of the most intriguing problems in most of the Machine Learning models, particularly for those that are mathematically sophisticated. Computing Shapley Values are arguably the best approach so far to find the importance of each feature in a model, at the row level. In other words, Shapley values represent the importance of a feature for a particular row, especially for Classification or Regression problems. One of the biggest limitations of Shapley vales is that, Shapley value calculations assume all the features are uncorrelated (independent of each other), this assumption is often incorrect. To address this problem, we present a unified framework to calculate Shapley values with correlated features. To be more specific, we do an adjustment (Matrix formulation) of the features while calculating Independent Shapley values for the rows. Moreover, we have given a Mathematical proof against the said adjustments. With these adjustments, Shapley values (Importance) for the features become independent of the correlations existing between them. We have also enhanced this adjustment concept for more than features. As the Shapley values are additive, to calculate combined effect of two features, we just have to add their individual Shapley values. This is again not right if one or more of the features (used in the combination) are correlated with the other features (not in the combination). We have addressed this problem also by extending the correlation adjustment for one feature to multiple features in the said combination for which Shapley values are determined. Our implementation of this method proves that our method is computationally efficient also, compared to original Shapley method.