Probabilistic Linear Explanations
Researchers introduce a unified probabilistic explainability framework using sparse anchored linear models that outperforms LIME and MAPLE on relevance error.
The paper proposes probabilistic explanations based on sparse, anchored linear models applicable to both binary classification and continuous regression. It proves that minimizing relevance error for neural-network models is NP-hard and relates it to a tractable fidelity-error surrogate. Solutions are computed via a mixed integer programming formulation with provably optimal empirical solutions and a polynomial-time iterative hard thresholding algorithm with approximation guarantees. Empirical evaluations show lower relevance error than LIME and MAPLE while satisfying anchoring and sparsity constraints by construction.
- Sparse anchored linear explanations generalize subset-based approaches by capturing feature magnitude and direction
- Relevance-error minimization is NP-hard for neural networks; fidelity error serves as tractable surrogate
- MIP formulation yields provably optimal solutions; IHT algorithm provides approximation guarantees
- Explanations satisfy anchoring and sparsity constraints by construction, beating LIME and MAPLE
From the original article
1 min read at arxiv.orgFormal explainability provides mathematically grounded justifications for individual predictions. However, abductive explanations often exceed human cognitive limits by involving too many features, while probabilistic relaxations have remained largely limited to categorical classification.
By Frederic Koriche · arxiv.org
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