Probabilistic linear models improve clear sparse explanations for ai predictions
Probabilistic Linear Explanations
Machine LearningArtificial Intelligence
Summary
It can be hard for people to understand why artificial intelligence (AI) makes certain predictions, especially when explanations involve too many details. The authors created a flexible way to explain AI decisions using simple linear models that focus on just a few important features. Their method works for both yes/no decisions and continuous predictions, and it guarantees explanations that are both sparse and anchored, meaning they highlight the key reasons without overwhelming detail. They show their approach is better than popular existing tools, providing clearer and more accurate explanations.
What this means in practice
- •For machine learning engineers: Produce simpler and more reliable explanations of AI model predictions for end-user trust and model debugging in classification and regression tasks.
- •For data science teams: Improve interpretability of complex models by generating user-friendly, sparse explanations that meet prescribed feature budget constraints.
Authors
Frederic Koriche, Jean-Marie Lagniez, Chi Tran
Abstract
Formal 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. We present a unified framework for probabilistic explainability based on sparse, anchored linear models, applicable to both binary classification and continuous regression. By mapping instances to the Boolean hypercube, our linear explanations strictly generalize subset-based approaches: they capture both the magnitude and direction of feature contributions while enforcing a prescribed sparsity budget $k$. We show that minimizing the relevance error for such explanations is \ClassNPPP-hard when the underlying model is a neural network, and we relate this intractable objective to a tractable surrogate---the fidelity error. For a parameterized family of local distributions, the relevance error of any $k$-sparse explanation is bounded by its fidelity error up to a multiplicative factor that remains small locally. We address the resulting empirical problem using two complementary approaches: a Mixed Integer Programming (MIP) formulation that yields provably optimal empirical solutions while maintaining polynomial sample complexity, and a polynomial-time Iterative Hard Thresholding (IHT) algorithm with provable approximation guarantees. Empirical evaluations show that, unlike state-of-the-art baselines such as LIME and MAPLE, our explanations satisfy both the anchoring and sparsity constraints by construction, while consistently achieving lower relevance error.