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<p>With an increasing demand for understanding AI models, explainable artificial intelligence (XAI) methods based on the Shapley value have attracted much attention. The application of the Shapley value to feature-importance analysis faces two major challenges: the impact of the choice of performance metric for a specific model, and the high computational cost. To address the high computational complexity of the Shapley value, we introduce a computationally efficient XAI method based on the center of imputation set (CIS) for evaluating feature importance. We focus on comparing Exact Shapley, SHAP (SHapley Additive exPlanations), including Sampling SHAP and Kernel SHAP, ShapG (Explanations based on the Shapley value for Graphs), Improved ShapG, and CIS methods, applied to a linear regression model under different performance metrics (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(R^2_{adj}\)</EquationSource> </InlineEquation>, <i>F</i>-statistic, and Akaike information criterion). We evaluate these methods on four benchmark datasets with different numbers of features (from 7 to 15) and report results over multiple random seeds for statistical rigor. We also compare the feature rankings produced by XAI methods with those obtained by classical statistical methods used in linear regression. The experimental results show that the Exact CIS method yields consistent feature rankings across different performance metrics and offers a significant computational-efficiency advantage over the Exact Shapley method. Finally, we systematically study the effect of multicollinearity on XAI methods using controlled synthetic experiments in two complementary regimes, with the weighted decreasing slope as the evaluation metric.</p>

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Feature importance methods for linear regression model

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Jing Liu,
  • Chi Zhao,
  • Elena Parilina

摘要

With an increasing demand for understanding AI models, explainable artificial intelligence (XAI) methods based on the Shapley value have attracted much attention. The application of the Shapley value to feature-importance analysis faces two major challenges: the impact of the choice of performance metric for a specific model, and the high computational cost. To address the high computational complexity of the Shapley value, we introduce a computationally efficient XAI method based on the center of imputation set (CIS) for evaluating feature importance. We focus on comparing Exact Shapley, SHAP (SHapley Additive exPlanations), including Sampling SHAP and Kernel SHAP, ShapG (Explanations based on the Shapley value for Graphs), Improved ShapG, and CIS methods, applied to a linear regression model under different performance metrics ( \(R^2\) , \(R^2_{adj}\) , F-statistic, and Akaike information criterion). We evaluate these methods on four benchmark datasets with different numbers of features (from 7 to 15) and report results over multiple random seeds for statistical rigor. We also compare the feature rankings produced by XAI methods with those obtained by classical statistical methods used in linear regression. The experimental results show that the Exact CIS method yields consistent feature rankings across different performance metrics and offers a significant computational-efficiency advantage over the Exact Shapley method. Finally, we systematically study the effect of multicollinearity on XAI methods using controlled synthetic experiments in two complementary regimes, with the weighted decreasing slope as the evaluation metric.