Explaining Black-Box Models Through Statistical Inference

Explainable AI for tabular models underpins decisions in finance, healthcare, and policy, yet today’s explanations are dominated by heuristics without statistical guarantees. We introduce Stat-XAI, a model-agnostic framework that converts explanations into testable statistical statements. For each feature, Stat-XAI assesses association with model predictions on held-out data via appropriate hypothesis tests and reports standardized effect sizes (e.g., $\eta^2$, $R^2$, Cramér's $V$), yielding compact, uncertainty-aware rankings. Across six synthetic datasets with known causal structure and two real benchmarks, Stat-XAI delivers stable, parsimonious attributions, filters spurious correlates, and achieves orders-of-magnitude lower runtime than SHAP while maintaining faithfulness. We quantify stability under perturbations and show that interaction testing clarifies when pairwise dependencies meaningfully alter importance. By elevating explanation from heuristic scoring to inferential analysis, Stat-XAI provides a rigorous, reproducible pathway for trustworthy tabular AI—supporting scrutiny, governance, and human decision-making where reliability matters most.