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Predictive uncertainties in classification tasks are often a consequence of model inadequacy or insufficient training data. In popular applications, such as image processing, we are often required to scrutinise these uncertainties by meaningfully attributing them to input features. This helps to improve interpretability assessments. However, there exist few effective frameworks for this purpose. Vanilla forms of popular methods for the provision of saliency masks, such as SHAP or integrated gradients, adapt poorly to target measures of uncertainty. Thus, state-of-the-art tools instead proceed by creating counterfactual or adversarial feature vectors, and assign attributions by direct comparison to original images. In this paper, we present a novel framework that combines path integrals, counterfactual explanations and generative models, in order to procure attributions that contain few observable artefacts or noise. We evidence that this outperforms existing alternatives through quantitative evaluations with popular benchmarking methods and data sets of varying complexity.

Bayesian inference for Markov jump processes (MJPs) where available observations relate to either system states or jumps typically relies on data-augmentation Markov Chain Monte Carlo. State-of-the-art developments involve representing MJP paths with auxiliary candidate jump times that are later thinned. However, these algorithms are i) unfeasible in situations involving large or infinite capacity systems and ii) not amenable for all observation types. In this paper we establish and present a general data-augmentation framework for population MJPs based on uniformized representations of the underlying non-stationary jump processes. This leads to multiple novel MCMC samplers which enable exact (in the Monte Carlo sense) inference tasks for model parameters. We show that proposed samplers outperform existing popular approaches, and offer substantial efficiency gains in applications to partially observed stochastic epidemics, immigration processes and predator-prey dynamical systems.