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Trustworthy Actionable Perturbations

Jesse Friedbaum, Sudarshan Adiga, Ravi Tandon

TL;DR

This work tackles the risk that counterfactual explanations do not translate to real-world improvements by introducing Trustworthy Actionable Perturbations (TAP), a two-step framework that (i) optimizes feasible input changes to move the true outcome distribution toward a user-defined target set $T$ using a differentiable distance $d_{\mathcal{Y}}(\mathbf{y},T)$ based on an $f$-divergence, and (ii) verifies the effect with a separate pairwise classifier $V$ to ensure changes influence the true probabilities $\mathbf{y}(\tilde{\mathbf{x}})$ rather than simply fooling the classifier; A formal $(\epsilon,\delta)$-trustworthy perturbation is defined to bound action cost and proximity to $T$. The paper provides a differentiable closed-form for $d_{\mathcal{Y}}$ when using $f$-divergences, proves PAC-style generalization bounds for the verifier, and presents a practical two-step TAP generation algorithm that enforces actionability and coherence with a verification threshold $\gamma$. Empirically, TAP outperforms prior counterfactual methods and remains robust to adversarial perturbations across four real-world datasets, offering cost-effective and trustworthy recourse for high-stakes decisions.

Abstract

Counterfactuals, or modified inputs that lead to a different outcome, are an important tool for understanding the logic used by machine learning classifiers and how to change an undesirable classification. Even if a counterfactual changes a classifier's decision, however, it may not affect the true underlying class probabilities, i.e. the counterfactual may act like an adversarial attack and ``fool'' the classifier. We propose a new framework for creating modified inputs that change the true underlying probabilities in a beneficial way which we call Trustworthy Actionable Perturbations (TAP). This includes a novel verification procedure to ensure that TAP change the true class probabilities instead of acting adversarially. Our framework also includes new cost, reward, and goal definitions that are better suited to effectuating change in the real world. We present PAC-learnability results for our verification procedure and theoretically analyze our new method for measuring reward. We also develop a methodology for creating TAP and compare our results to those achieved by previous counterfactual methods.

Trustworthy Actionable Perturbations

TL;DR

This work tackles the risk that counterfactual explanations do not translate to real-world improvements by introducing Trustworthy Actionable Perturbations (TAP), a two-step framework that (i) optimizes feasible input changes to move the true outcome distribution toward a user-defined target set using a differentiable distance based on an -divergence, and (ii) verifies the effect with a separate pairwise classifier to ensure changes influence the true probabilities rather than simply fooling the classifier; A formal -trustworthy perturbation is defined to bound action cost and proximity to . The paper provides a differentiable closed-form for when using -divergences, proves PAC-style generalization bounds for the verifier, and presents a practical two-step TAP generation algorithm that enforces actionability and coherence with a verification threshold . Empirically, TAP outperforms prior counterfactual methods and remains robust to adversarial perturbations across four real-world datasets, offering cost-effective and trustworthy recourse for high-stakes decisions.

Abstract

Counterfactuals, or modified inputs that lead to a different outcome, are an important tool for understanding the logic used by machine learning classifiers and how to change an undesirable classification. Even if a counterfactual changes a classifier's decision, however, it may not affect the true underlying class probabilities, i.e. the counterfactual may act like an adversarial attack and ``fool'' the classifier. We propose a new framework for creating modified inputs that change the true underlying probabilities in a beneficial way which we call Trustworthy Actionable Perturbations (TAP). This includes a novel verification procedure to ensure that TAP change the true class probabilities instead of acting adversarially. Our framework also includes new cost, reward, and goal definitions that are better suited to effectuating change in the real world. We present PAC-learnability results for our verification procedure and theoretically analyze our new method for measuring reward. We also develop a methodology for creating TAP and compare our results to those achieved by previous counterfactual methods.
Paper Structure (12 sections, 4 theorems, 72 equations, 8 figures, 1 algorithm)

This paper contains 12 sections, 4 theorems, 72 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Trustworthy Actionable Perturbations
  3. Generating TAP
  4. Experimental Results
  5. Appendix
  6. Proof of Theorem \ref{['theorem_closedform']} (Analysis of statistical distance $d_\mathcal{Y}$ to the target set $T$)
  7. Proofs of Theorem \ref{['theorem_PAC']} (PAC generalization bounds for Verifier)
  8. Additional Implementation Details
  9. Data Set and Cost Function Details
  10. Model Details
  11. Objective Function Details
  12. Additional Experimental Results

Key Result

Theorem 2.2

If $D({\mathbf{y}} || \mathbf{z})$ is an $f$-Divergence with twice differentiable $f$ and $T$ is of form (gen_target_fam), then where $\mathcal{S}_\mathcal{W} = \sum _{i \in \mathcal{W}} {y}_i$, $\mathcal{S}_\mathcal{U} = \sum _{i \in \mathcal{U}} {y}_i$ and the sets $A,B,C$ and $D$ are a partition of $\mathcal{Y}$ defined and visualized in Figure img:probability_partitions. Furthermore, $d_{\mat

Figures (8)

  • Figure 1: a) Overview of the framework for creating Trustworthy Actionable Perturbations (TAP). b) Comparison of objectives and features of TAP and Counterfactual Explanations (CE) original_CF, Actionable Counterfactuals/Algorithmic Recourse (AC/AR) linearrecourse_CFalgorithmicrecourse_CFface_CF, Improvement-Focused Causal Recourse (ICR) ICR_CF.
  • Figure 2: Illustration of the partition on $\mathcal{Y}$ used to calculate the distance from the target set $T$ in Theorem \ref{['theorem_closedform']}. Although the cost function takes different functional form(s) in the four regions, it is continuously differentiable in the entire space.
  • Figure 3: Table containing details on data sets used for testing.
  • Figure 4: Cost-Benefit plots of TAP and counterfactuals for an individually from the Law School data set with grades measured in standard deviations from the mean (a) and an individual in the Adult Income data set (b).
  • Figure 5: a) & b) show average success rate for moving individuals within a variety of distances ($\delta$) to the target set. The y-axis shows the percentage of individuals within the goal distance, and the x-axis, represents different costs ($\epsilon$ values). c) Summarizes success values for all data sets. The upper (red) value for each row is the success rate before the verification procedure and the lower (green) value is the success rate after verification with a $10\%$ chance of rejecting valid examples.
  • ...and 3 more figures

Theorems & Definitions (7)

  • Definition 2.1: $(\epsilon,\delta)$-Trustworthy Actionable Perturbation
  • Theorem 2.2
  • Theorem 2.3
  • Remark 2.4
  • Lemma 1.1
  • Corollary 1.2
  • Definition 1.3