An Entropic Risk Measure for Robust Counterfactual Explanations
Primary Area: visualization or interpretation of learned representations
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Keywords: Counterfactual Explanations, Explainable AI, Robustness, Risk Measures, Multi-Objective Optimization, Pareto Front, Mini-Max Optimization
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TL;DR: We propose a novel entropic risk measure to quantify the robustness of counterfactuals to model changes, showcasing its desirable properties and its ability to unify existing methods.
Abstract: Counterfactual explanations often become invalid if the underlying model changes because they are usually quite close to the decision boundary. Thus, the robustness of counterfactual explanations to potential model changes is an important desideratum. In this work, we propose entropic risk as a novel measure of robustness for counterfactual explanations. Entropic risk is a convex risk measure and satisfies several desirable properties. Furthermore, we show several ways of incorporating our proposed risk measure in the generation of robust counterfactuals. The main significance of our measure is that it establishes a connection between existing approaches for worst-case robust (min-max optimization) and robustness-constrained counterfactuals. A limiting case of our entropic-risk-based approach yields a worst-case min-max optimization scenario. On the other hand, we also provide a constrained optimization algorithm with probabilistic guarantees that can find counterfactuals, balancing our measure of robustness and the cost of the counterfactual. We study the trade-off between the cost of the counterfactuals and their validity under model changes for varying degrees of risk aversion, as determined by our risk parameter knob. We examine the performance of our algorithm on several datasets. Our proposed risk measure is rooted in large deviation theory and has close connections with mathematical finance and risk-sensitive control.
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Submission Number: 4382
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