Explainability of Complex AI Models with Correlation Impact Ratio

TL;DR

ExCIR introduces a bounded, monotone correlation–ratio attribution framework that unifies scalar, block, and multi‑output explanations within a canonical correlation and information‑theoretic context. It delivers lightweight, single‑pass explanations that remain stable under sampling, noise, and data shifts, and extends to class‑conditioned and multi‑output settings via BlockCIR/CC‑CIR and CCA directions. Empirical results across EEG, synthetic vehicular, Digits, and Cats–Dogs demonstrate strong explainability fidelity, predictive sufficiency at tight budgets, and substantial efficiency gains over SHAP/LIME, with robust uncertainty quantification. The approach offers practical, domain‑general interpretability for complex AI systems, enabling scalable, reliable explanations suitable for edge deployment and cross‑dataset comparisons.

Abstract

Complex AI systems make better predictions but often lack transparency, limiting trustworthiness, interpretability, and safe deployment. Common post hoc AI explainers, such as LIME, SHAP, HSIC, and SAGE, are model agnostic but are too restricted in one significant regard: they tend to misrank correlated features and require costly perturbations, which do not scale to high dimensional data. We introduce ExCIR (Explainability through Correlation Impact Ratio), a theoretically grounded, simple, and reliable metric for explaining the contribution of input features to model outputs, which remains stable and consistent under noise and sampling variations. We demonstrate that ExCIR captures dependencies arising from correlated features through a lightweight single pass formulation. Experimental evaluations on diverse datasets, including EEG, synthetic vehicular data, Digits, and Cats-Dogs, validate the effectiveness and stability of ExCIR across domains, achieving more interpretable feature explanations than existing methods while remaining computationally efficient. To this end, we further extend ExCIR with an information theoretic foundation that unifies the correlation ratio with Canonical Correlation Analysis under mutual information bounds, enabling multi output and class conditioned explainability at scale.

Figures (8)

• Figure 1: CIR geometry. We center $f_i$ and $y$ at the mid-mean $m_i=\tfrac{1}{2}(\hat{f}_i+\hat{y})$. The alignment (numerator) uses symmetric offsets $|\hat{f}_i-m_i|$ and $|\hat{y}-m_i|$; the scatter (denominator) aggregates sample deviations around the same pivot $m_i$.
• Figure 2: Linear vs. nonlinear dependence scores.
• Figure 3: Inception module used in CAU-EEG backbone.
• Figure 4: ExCIR Key Findings-Performance summary.
• Figure 5: ExCIR uncertainty and agreement under bootstrapping (vehicular). (Left) 95% CI of ExCIR scores (top features; $B{=}100$) (Right) Top-set overlap across bootstraps (vertical guide at $k{=}8$).

Theorems & Definitions (36)

• Definition 1
• Theorem 1: Observation-only factorization
• proof
• Definition 2: Lightweight Environment
• Definition 3: Similar environment
• Definition 4: BlockCIR
• Theorem 2: Boundedness of CIR
• proof
• Theorem 3: Monotonicity of CIR
• proof