Variable Importance Identification Through Lazy Training for Binary Classification

Deep neural networks often exploit spurious associations, a failure known as shortcut learning. Before deployment, models should be audited for reliance on a set of concepts, such as acquisition artifacts or demographics. Current methods, such as linear probes and concept activation vectors, measure reliance by asking whether each concept, in isolation, is decodable from a layer. Their scores therefore reflect not only reliance but also correlations in the audit dataset. We introduce Independent Canonical cONcept (ICON) decomposition, which quantifies the share of a layer's variance each concept explains, conditional on all other concepts and the outcome. ICON scores are variance shares, comparable across layers and between continuous and categorical concepts. ICON also reports the share the set leaves unexplained. On simulated data, ICON recovers the true importance more accurately than seven baselines. On skin-cancer and neuroimaging models, ICON distinguishes learned shortcuts from correlated concepts, confirmed by retraining and out-of-distribution tests.

Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions. However, ANNs often suffer from over-parameterization, complicating interpretation and raising uncertainty issues. Bayesian neural networks (BNNs) address the latter by representing weights as probability distributions, allowing for predictive uncertainty evaluation. Latent binary Bayesian neural networks (LBBNNs) further handle structural uncertainty and sparsify models by removing redundant weights. This article advances LBBNNs by enabling covariates to skip to any succeeding layer or be excluded, simplifying networks and clarifying input impacts on predictions. This further allows us to learn simpler structures (e.g., linear or even constant intercept only models) when appropriate. Furthermore, the input-skip LBBNN (ISLaB) approach reduces network density significantly compared to standard LBBNNs, achieving over 99% reduction for small networks and over 99.9% for larger ones, while still maintaining high predictive accuracy and uncertainty quantification. For example, on MNIST, we reached 97% accuracy and great calibration with just 935 weights, reaching state-of-the-art for compression of neural networks. Furthermore, the proposed method accurately identifies the true covariates and adjusts for system non-linearity. The main contribution is the introduction of active paths, enhancing directly designed global and local explanations within the LBBNN framework. The latter are exact with theoretical guarantees and do not require post hoc external tools.

Prototype-based explanations offer an intuitive, example-based approach to support the interpretability of machine learning black box classifiers but often lack feature-level granularity. We introduce a framework that integrates feature importance at two levels to address this gap. First, for local explanations, we propose \textit{alike parts}: a method that uses feature importance scores to highlight the most relevant, shared feature subsets between a classified instance and its nearest prototype, guiding user attention. Second, we augment the global prototype selection objective function with a feature importance term to actively promote diversity in the feature attributions of the selected prototypes. Experiments on six benchmark datasets show that this augmented selection process maintains or, in some cases, increases the prediction fidelity of the surrogate model, suggesting that feature diversity does not compromise model fidelity.