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Verified Training for Counterfactual Explanation Robustness under Data Shift

Anna P. Meyer, Yuhao Zhang, Aws Albarghouthi, Loris D'Antoni

TL;DR

VeriTraCER is introduced, an approach that jointly trains a classifier and an explainer to explicitly consider the robustness of the generated CEs to small model shifts and displays competitive robustness to state-of-the-art approaches in handling empirical model updates including random initialization, leave-one-out, and distribution shifts.

Abstract

Counterfactual explanations (CEs) enhance the interpretability of machine learning models by describing what changes to an input are necessary to change its prediction to a desired class. These explanations are commonly used to guide users' actions, e.g., by describing how a user whose loan application was denied can be approved for a loan in the future. Existing approaches generate CEs by focusing on a single, fixed model, and do not provide any formal guarantees on the CEs' future validity. When models are updated periodically to account for data shift, if the generated CEs are not robust to the shifts, users' actions may no longer have the desired impacts on their predictions. This paper introduces VeriTraCER, an approach that jointly trains a classifier and an explainer to explicitly consider the robustness of the generated CEs to small model shifts. VeriTraCER optimizes over a carefully designed loss function that ensures the verifiable robustness of CEs to local model updates, thus providing deterministic guarantees to CE validity. Our empirical evaluation demonstrates that VeriTraCER generates CEs that (1) are verifiably robust to small model updates and (2) display competitive robustness to state-of-the-art approaches in handling empirical model updates including random initialization, leave-one-out, and distribution shifts.

Verified Training for Counterfactual Explanation Robustness under Data Shift

TL;DR

VeriTraCER is introduced, an approach that jointly trains a classifier and an explainer to explicitly consider the robustness of the generated CEs to small model shifts and displays competitive robustness to state-of-the-art approaches in handling empirical model updates including random initialization, leave-one-out, and distribution shifts.

Abstract

Counterfactual explanations (CEs) enhance the interpretability of machine learning models by describing what changes to an input are necessary to change its prediction to a desired class. These explanations are commonly used to guide users' actions, e.g., by describing how a user whose loan application was denied can be approved for a loan in the future. Existing approaches generate CEs by focusing on a single, fixed model, and do not provide any formal guarantees on the CEs' future validity. When models are updated periodically to account for data shift, if the generated CEs are not robust to the shifts, users' actions may no longer have the desired impacts on their predictions. This paper introduces VeriTraCER, an approach that jointly trains a classifier and an explainer to explicitly consider the robustness of the generated CEs to small model shifts. VeriTraCER optimizes over a carefully designed loss function that ensures the verifiable robustness of CEs to local model updates, thus providing deterministic guarantees to CE validity. Our empirical evaluation demonstrates that VeriTraCER generates CEs that (1) are verifiably robust to small model updates and (2) display competitive robustness to state-of-the-art approaches in handling empirical model updates including random initialization, leave-one-out, and distribution shifts.
Paper Structure (37 sections, 3 theorems, 11 equations, 2 figures, 7 tables, 2 algorithms)

This paper contains 37 sections, 3 theorems, 11 equations, 2 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Explainable AI
  4. Robust explanations
  5. Problem Definition
  6. Counterfactual explanations
  7. Multiplicity set of $f$
  8. CE robustness
  9. Goal
  10. Approach
  11. Training the model $f$ and the CE generator $g$ in tandem
  12. Computing the RobustCE loss
  13. Overapproximating the RobustCE loss using existing techniques
  14. Overapproximation the RobustCE Loss using Simul-CROWN
  15. Experimental Evaluation
  16. ...and 22 more sections

Key Result

Theorem 4.1

For any $\mathbf{x}$, $\mathbf{x}'$, and $f$, the CROWN-IBP-overapproximated loss $\mathcal{L}_\mathrm{R}^{\sharp\mathrm{CIBP}}(\mathbf{x}, \mathbf{x}', \theta_{f})$ is an upper bound of the RobustCE loss $\mathcal{L}_\mathrm{R}(\mathbf{x}, \mathbf{x}', \theta_{f})$ and a lower bound of the IBP-over

Figures (2)

  • Figure 1: Plots of three linear models and their multiplicity sets. The black line shows the original linear model $f_i$. The green and red regions contain all samples that are robust under the multiplicity set $\mathcal{M}_{f_i, \mathbf{x}}$, receiving predictions $+$ and $-$, respectively. The yellow region corresponds to all samples that are not robust under the multiplicity set $\mathcal{M}_{f_i,\mathbf{x}}$.
  • Figure 2: Our approach Simul-CROWN achieves a tighter overapproximation than IBP and CROWN-IBP because the latter techniques include portions of the red region where the CE is not robust.

Theorems & Definitions (11)

  • Definition 3.1: Multiplicity set
  • Definition 3.2: $\mathcal{M}_{f,\mathbf{x}}$-robustness of a CE
  • Example 3.1
  • Theorem 4.1: Soundness and Tightness
  • Example 4.1
  • Example 4.2
  • Theorem 4.2: Overapproximation by Simul-CROWN
  • Theorem 4.3: Soundness and Tightness
  • Example 4.3
  • proof : Proof of \ref{['theorem: cibp']}
  • ...and 1 more