Post-Hoc Uncertainty-Aware Explanations for Deployed Power Quality Disturbance Classifiers via Laplace Approximation

Post-hoc explainable AI (XAI) methods typically produce deterministic attribution maps, whereas Bayesian neural networks (BNNs) induce a distribution over explanations. Capturing the variability of this distribution is important for uncertainty-aware decision-making. This paper formalises the explanation distribution as the push-forward measure of the BNN posterior through any Lipschitz-continuous attribution operator. It further proposes the uncertainty-aware relevance attribution operator (UA-RAO), a general family of operators that summarises the explanation distribution using the mean, variance, coefficient of variation, quantiles, and set-theoretic aggregation measures. Theoretical support is provided through Monte Carlo accessibility and Wasserstein approximation bounds. The framework is evaluated on a 15-class power quality disturbance (PQD) classification benchmark, comparing three BNN approximations paired with three attribution operators using relevance mass accuracy and intersection-over-union as localisation metrics. Results show that deep ensembles with the mean UA-RAO improve localisation over the deterministic baseline, while other UA-RAO summaries reveal uncertainty patterns absent from point-estimate attributions. Qualitative results on measured signals further suggest that these patterns generalise beyond the synthetic training distribution. The framework is domain-agnostic and can be applied to any BNN paired with a Lipschitz-continuous attribution operator.

Existing post-hoc explainers for machine learning classifiers primarily focus on feature attribution, assigning importance scores to individual features. While valuable, this approach struggles to articulate the complex, combinatorial patterns that often drive a model's decision-making process. To overcome this limitation, we introduce ProToMEx, a new paradigm for explainability that leverages Probabilistic Topic Models (PTMs). Our model-agnostic framework learns latent ''topics'' that represent distinct, high-level reasons for a classification, moving beyond simple feature importance to reveal underlying semantic structures. ProToMEx naturally provides both global explanations of a model's overall behaviour and local explanations that can disentangle multiple co-existing reasons for a specific prediction. We demonstrate empirically that ProToMEx not only produces explanations of comparable fidelity to popular methods like SHAP and LIME but also drastically reduces the amortised computational cost of generating local explanations, making it highly suitable for real-time applications. Specifically, we show that ProToMEx is ~30-40x faster than SHAP and LIME over standardised tabular datasets and synthetic datasets.

Trust and ethical concerns due to the widespread deployment of opaque machine learning (ML) models motivating the need for reliable model explanations. Post-hoc model-agnostic explanation methods addresses this challenge by learning a surrogate model that approximates the behavior of the deployed black-box ML model in the locality of a sample of interest. In post-hoc scenarios, neither the underlying model parameters nor the training are available, and hence, this local neighborhood must be constructed by generating perturbed inputs in the neighborhood of the sample of interest, and its corresponding model predictions. We propose Expected Active Gain for Local Explanations (EAGLE), a post-hoc model-agnostic explanation framework that formulates perturbation selection as an information-theoretic active learning problem. By adaptively sampling perturbations that maximize the expected information gain, EAGLE efficiently learns a linear surrogate explainable model while producing feature importance scores along with the uncertainty/confidence estimates. Theoretically, we establish that cumulative information gain scales as $\mathcal{O}(d \log t)$, where $d$ is the feature dimension and $t$ represents the number of samples, and that the sample complexity grows linearly with $d$ and logarithmically with the confidence parameter $1/δ$. Empirical results on tabular and image datasets corroborate our theoretical findings and demonstrate that EAGLE improves explanation reproducibility across runs, achieves higher neighborhood stability, and improves perturbation sample quality as compared to state-of-the-art baselines such as Tilia, US-LIME, GLIME and BayesLIME.