Probabilistic Explanations for Linear Models

Explanations need mathematical guarantees: The paper addresses a gap in AI explainability by focusing on "sufficient reasons"—explanations backed by formal mathematical proof rather than heuristic approximations. This matters for responsible AI because stakeholders (regulators, affected individuals, auditors) need to know why a model made a decision with confidence, not just get a plausible-sounding story.

Perfect explanations are computationally impractical: The research shows that finding minimal sufficient reasons—subsets of features that completely justify a decision—is theoretically "hard" even for simple models like decision trees. This finding is important because it reveals a fundamental trade-off: truly rigorous explanations may be computationally expensive or impossible to compute at scale.

Practical compromises are necessary: The authors propose a relaxed version called "(δ, ε)-sufficient reasons" that allows for small probabilities of error rather than demanding absolute certainty. For linear models specifically, this relaxation makes explanations computationally feasible. This suggests that responsible AI systems may need to accept "good enough" explanations rather than perfect ones, with clear disclosure of their confidence levels.

Linear models offer a starting point: The paper demonstrates that efficient, mathematically-guaranteed explanations are achievable for linear models. This is relevant for practitioners because it suggests that simpler, more interpretable models may be preferable to complex "black boxes" when explainability and accountability are priorities.