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Locally-Minimal Probabilistic Explanations

Yacine Izza, Kuldeep S. Meel, Joao Marques-Silva

TL;DR

This work tackles the challenge of producing rigorous yet compact explanations for complex ML models by focusing on locally-minimal probabilistic abductive explanations (LmPAXp). It formalizes probabilistic AXps (PAXp) and their locally-minimal variant, discusses their non-monotonic nature, and introduces efficient approximate computation methods using either PAC-based approximate model counting or Monte-Carlo sampling. The authors develop logic-based encodings for BNNs and RFs to support these explanations and propose a deletion-based algorithm to extract small LmPAXps with practical guarantees. Empirical results on RFs and BNNs show substantial reductions in explanation size with high precision, demonstrating the practicality of the approach for scalable XAI in real-world classifiers. The work highlights a trade-off between explanation compactness and probabilistic precision, and points to future integration with SMT to broaden applicability beyondBoolean domains.

Abstract

Explainable Artificial Intelligence (XAI) is widely regarding as a cornerstone of trustworthy AI. Unfortunately, most work on XAI offers no guarantees of rigor. In high-stakes domains, e.g. uses of AI that impact humans, the lack of rigor of explanations can have disastrous consequences. Formal abductive explanations offer crucial guarantees of rigor and so are of interest in high-stakes uses of machine learning (ML). One drawback of abductive explanations is explanation size, justified by the cognitive limits of human decision-makers. Probabilistic abductive explanations (PAXps) address this limitation, but their theoretical and practical complexity makes their exact computation most often unrealistic. This paper proposes novel efficient algorithms for the computation of locally-minimal PXAps, which offer high-quality approximations of PXAps in practice. The experimental results demonstrate the practical efficiency of the proposed algorithms.

Locally-Minimal Probabilistic Explanations

TL;DR

This work tackles the challenge of producing rigorous yet compact explanations for complex ML models by focusing on locally-minimal probabilistic abductive explanations (LmPAXp). It formalizes probabilistic AXps (PAXp) and their locally-minimal variant, discusses their non-monotonic nature, and introduces efficient approximate computation methods using either PAC-based approximate model counting or Monte-Carlo sampling. The authors develop logic-based encodings for BNNs and RFs to support these explanations and propose a deletion-based algorithm to extract small LmPAXps with practical guarantees. Empirical results on RFs and BNNs show substantial reductions in explanation size with high precision, demonstrating the practicality of the approach for scalable XAI in real-world classifiers. The work highlights a trade-off between explanation compactness and probabilistic precision, and points to future integration with SMT to broaden applicability beyondBoolean domains.

Abstract

Explainable Artificial Intelligence (XAI) is widely regarding as a cornerstone of trustworthy AI. Unfortunately, most work on XAI offers no guarantees of rigor. In high-stakes domains, e.g. uses of AI that impact humans, the lack of rigor of explanations can have disastrous consequences. Formal abductive explanations offer crucial guarantees of rigor and so are of interest in high-stakes uses of machine learning (ML). One drawback of abductive explanations is explanation size, justified by the cognitive limits of human decision-makers. Probabilistic abductive explanations (PAXps) address this limitation, but their theoretical and practical complexity makes their exact computation most often unrealistic. This paper proposes novel efficient algorithms for the computation of locally-minimal PXAps, which offer high-quality approximations of PXAps in practice. The experimental results demonstrate the practical efficiency of the proposed algorithms.
Paper Structure (26 sections, 1 theorem, 15 equations, 1 figure, 4 tables, 1 algorithm)

This paper contains 26 sections, 1 theorem, 15 equations, 1 figure, 4 tables, 1 algorithm.

Table of Contents

  1. Background
  2. Classification problems
  3. Binarized Neural Network (BNNs)
  4. Random Forests (RFs)
  5. Logic-based Explainability
  6. Abductive explanations.
  7. Running Example.
  8. Formal Feature Attribution AXp's.
  9. Formal Probabilistic Explanations
  10. Probabilistic AXp.
  11. Locally-minimal Probabilistic AXp.
  12. Logic Encodings
  13. BNN Encoding
  14. RF Encoding
  15. Approximate Locally Minimal Probabilistic Explanations
  16. ...and 11 more sections

Key Result

Proposition 1

Given independent 0--1 random variables $X_i$, $X = \frac{1}{N}\sum\nolimits_{i=1}^{N} X_i$, the expected value $\mu = \mathbb{E}(X)$ and $\epsilon > 0$, $\textnormal{Pr}(\mid X - \mu \mid \ge \epsilon ) \le 2 e^{-2\epsilon^2 N}$.

Figures (1)

  • Figure 1: Example decision tree. Nodes of the tree are enumerate from 1 to 9; a tree path is represented by a sequence of nodes (e.g. $\langle1,2,4\rangle$, $\langle1,3,6\rangle$, etc).

Theorems & Definitions (3)

  • Example 1
  • Example 2
  • Proposition 1: Hoeffding game-theory-book