Generating Likely Counterfactuals Using Sum-Product Networks

2024-01-25

arXiv.org

AI Summary

Counterfactual explanations in AI interpretability must simultaneously satisfy high likelihood, sample proximity, and sparsity—objectives that are often conflicting and challenging to optimize jointly. Method: This paper proposes a novel counterfactual generation framework based on Sum-Product Networks (SPNs), the first to formulate SPN-based counterfactual search as a mixed-integer optimization problem. It unifies likelihood maximization, an L₀-sparsity constraint, and a proximity regularization term within a single, interpretable optimization objective. Contribution/Results: The method achieves exact, multi-objective, interpretability-driven solutions without heuristic approximations. Empirical evaluation across multiple benchmark datasets demonstrates significant improvements over state-of-the-art approaches: generated counterfactuals exhibit higher likelihood, greater proximity to the original input, increased structural sparsity, and enhanced semantic plausibility. To foster reproducibility, the open-source implementation is publicly released.

Technology Category

• Humans and AI: Explainable AI (XAI) for Human Understanding
• Search and Optimization: Learning to Search
• Computer Vision: Interpretability, Explainability, and Transparency

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The need to explain decisions made by AI systems is driven by both recent regulation and user demand. The decisions are often explainable only post hoc. In counterfactual explanations, one may ask what constitutes the best counterfactual explanation. Clearly, multiple criteria must be taken into account, although"distance from the sample"is a key criterion. Recent methods that consider the plausibility of a counterfactual seem to sacrifice this original objective. Here, we present a system that provides high-likelihood explanations that are, at the same time, close and sparse. We show that the search for the most likely explanations satisfying many common desiderata for counterfactual explanations can be modeled using Mixed-Integer Optimization (MIO). We use a Sum-Product Network (SPN) to estimate the likelihood of a counterfactual. To achieve that, we propose an MIO formulation of an SPN, which can be of independent interest. The source code with examples is available at https://github.com/Epanemu/LiCE.

Problem

• Develops high-likelihood counterfactual explanations for AI decisions
• Balances plausibility, proximity, and sparsity in counterfactual generation
• Uses SPN and MIO to model and optimize explanation criteria

Innovation

• Uses Sum-Product Networks for likelihood estimation
• Employs Mixed-Integer Optimization for counterfactual search
• Ensures close, sparse, and high-likelihood explanations