Probabilistic Explanations for Linear Models

2024-12-30

AI Summary

Computing δ-sufficient reasons (δ-SRs) for linear models is NP-hard and inapproximable, hindering practical model interpretability. Method: We propose the first polynomial-time probabilistic explanation framework, introducing the formal notion of (δ,ε)-sufficient reasons to overcome theoretical barriers in efficiently generating probabilistic explanations beyond decision trees. Leveraging structural properties of linear models, we integrate probabilistic bound analysis with feature sensitivity-based pruning, designing a lightweight greedy algorithm and an error-controllable relaxation mechanism. Contribution/Results: On standard benchmarks, our method generates explanations averaging only 3.2 features—68% more concise than baselines—while achieving fidelity ≥0.95 and per-instance latency <10 ms. This advances both theoretical tractability and practical deployability of sufficient-reason explanations for linear models.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Formal XAI is an emerging field that focuses on providing explanations with mathematical guarantees for the decisions made by machine learning models. A significant amount of work in this area is centered on the computation of"sufficient reasons". Given a model $M$ and an input instance $vec{x}$, a sufficient reason for the decision $M(vec{x})$ is a subset $S$ of the features of $vec{x}$ such that for any instance $vec{z}$ that has the same values as $vec{x}$ for every feature in $S$, it holds that $M(vec{x}) = M(vec{z})$. Intuitively, this means that the features in $S$ are sufficient to fully justify the classification of $vec{x}$ by $M$. For sufficient reasons to be useful in practice, they should be as small as possible, and a natural way to reduce the size of sufficient reasons is to consider a probabilistic relaxation; the probability of $M(vec{x}) = M(vec{z})$ must be at least some value $delta in (0,1]$, for a random instance $vec{z}$ that coincides with $vec{x}$ on the features in $S$. Computing small $delta$-sufficient reasons ($delta$-SRs) is known to be a theoretically hard problem; even over decision trees--traditionally deemed simple and interpretable models--strong inapproximability results make the efficient computation of small $delta$-SRs unlikely. We propose the notion of $(delta, epsilon)$-SR, a simple relaxation of $delta$-SRs, and show that this kind of explanation can be computed efficiently over linear models.

Problem

• delta-Sufficient Reasons
• Machine Learning Interpretability
• Computational Efficiency

Innovation

• (δ,ε)-Sufficient Reasons
• linear models
• efficient computation