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Simple Steps to Success: A Method for Step-Based Counterfactual Explanations

Jenny Hamer, Nicholas Perello, Jake Valladares, Vignesh Viswanathan, Yair Zick

TL;DR

StEP is introduced, a computationally efficient method that offers incremental steps along the data manifold that directs users towards their desired outcome and it is shown that StEP uniquely satisfies a desirable set of axioms.

Abstract

Algorithmic recourse is a process that leverages counterfactual explanations, going beyond understanding why a system produced a given classification, to providing a user with actions they can take to change their predicted outcome. Existing approaches to compute such interventions -- known as recourse -- identify a set of points that satisfy some desiderata -- e.g. an intervention in the underlying causal graph, minimizing a cost function, etc. Satisfying these criteria, however, requires extensive knowledge of the underlying model structure, an often unrealistic amount of information in several domains. We propose a data-driven and model-agnostic framework to compute counterfactual explanations. We introduce StEP, a computationally efficient method that offers incremental steps along the data manifold that directs users towards their desired outcome. We show that StEP uniquely satisfies a desirable set of axioms. Furthermore, via a thorough empirical and theoretical investigation, we show that StEP offers provable robustness and privacy guarantees while outperforming popular methods along important metrics.

Simple Steps to Success: A Method for Step-Based Counterfactual Explanations

TL;DR

StEP is introduced, a computationally efficient method that offers incremental steps along the data manifold that directs users towards their desired outcome and it is shown that StEP uniquely satisfies a desirable set of axioms.

Abstract

Algorithmic recourse is a process that leverages counterfactual explanations, going beyond understanding why a system produced a given classification, to providing a user with actions they can take to change their predicted outcome. Existing approaches to compute such interventions -- known as recourse -- identify a set of points that satisfy some desiderata -- e.g. an intervention in the underlying causal graph, minimizing a cost function, etc. Satisfying these criteria, however, requires extensive knowledge of the underlying model structure, an often unrealistic amount of information in several domains. We propose a data-driven and model-agnostic framework to compute counterfactual explanations. We introduce StEP, a computationally efficient method that offers incremental steps along the data manifold that directs users towards their desired outcome. We show that StEP uniquely satisfies a desirable set of axioms. Furthermore, via a thorough empirical and theoretical investigation, we show that StEP offers provable robustness and privacy guarantees while outperforming popular methods along important metrics.
Paper Structure (34 sections, 4 theorems, 19 equations, 4 figures, 7 tables, 1 algorithm)

This paper contains 34 sections, 4 theorems, 19 equations, 4 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Related Work
  4. Preliminaries
  5. Data-driven Recourse
  6. Stepwise Explainable Paths (StEP)
  7. An Axiomatically Justified Direction
  8. Diverse and On-Manifold Recourse via Clustering
  9. Privacy-Preserving Direction Selection
  10. Empirical Evaluation & Analysis
  11. Categorical Variables and Actionability
  12. Comparative Analysis of StEP, DiCE, FACE, and C-CHVAE
  13. Practical Robustness Considerations for StEP
  14. Clustering.
  15. User interference.
  16. ...and 19 more sections

Key Result

Theorem 3.1

A recourse direction for a point of interest $\vec{x}$ given a dataset $\mathcal{X}_c$, a model of interest $f$ and a rotation invariant distance metric $\|.\|$ satisfies SI, RRF, C, DMS, NCI and PCM if and only if it is given by equation eq:step-direction.

Figures (4)

  • Figure 1: (Left) The training dataset that the loan approval algorithm uses, (Middle) Plotting possible recourse directions for Example \ref{['ex:loan-recourse']} and (Right) plotting a stakeholder path toward loan acceptance.
  • Figure 2: (Left) The training dataset that the loan approval algorithm uses, and (Right) Off manifold $(\vec{d}_1)$ and On manifold $(\vec{d}_2)$ directions.
  • Figure 3: Directly applying the direction formula equation \ref{['eq:step-direction']} without clustering to find recourse directions may result in undesirable behavior, e.g. excluding a variety of options and picking an off-manifold direction (Left). Clustering resolves this issue (Right).
  • Figure 4: An example where the MIM direction points away from all the positively classified points.

Theorems & Definitions (8)

  • Example 2.1
  • Theorem 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.2
  • proof
  • Theorem 3.3