Exact Shapley Value for Local and Global Explanation of Additive Gaussian Processes
Keywords: gaussian processes, shapley value, interpretable, functional decomposition
TL;DR: We compute exact Shapley value for a class of Gaussian processes
Abstract: Additive Gaussian Processes (AGPs) have emerged as an extension of Gaussian Processes (GPs), offering a more interpretable and flexible approach by decomposing the target function into sums of multiple GPs, each influenced by different subsets of features. Despite their enhanced, expressive structure, AGPs struggle to provide local explanations and offer only global feature importance with notable shortcomings. To bridge this gap, this paper introduces an interpretative framework for AGPs that utilizes Shapley values to provide both local and global explanations of feature importance. For local explanation, we use the relationship between the AGP and the Shapley value and guarantee the additivity of the explanation. We then develop a dynamic programming algorithm for efficient computation of \textit{exact} Shapley values, whose complexity scales polynomially rather than exponentially with the number of features. In addition, we use a variance-based sensitivity approach for the global explanation and develop an efficient dynamic programming-based algorithm to compute the \textit{exact} Shapley value as the global feature importance. We present the effectiveness of the proposed methods on several real experiments and discuss their potential in interpretable machine learning, feature selection, and global sensitivity analysis.
Primary Area: interpretability and explainable AI
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Submission Number: 4404
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