Probabilistic Shapley Value Modeling and Inference

We propose probabilistic Shapley inference (PSI), a novel probabilistic framework to model and infer sufficient statistics of feature attributions in flexible predictive models, via latent random variables whose mean recovers Shapley values. PSI enables efficient, scalable inference over input-to-output attributions, and their uncertainty, via a variational objective that jointly trains a predictive (regression or classification) model and its attribution distributions. To address the challenge of marginalizing over variable-length input feature subsets in Shapley value calculation, we introduce a masking-based neural network architecture, with a modular training and inference procedure. We evaluate PSI on synthetic and real-world datasets, showing that it achieves competitive predictive performance compared to strong baselines, while learning feature attribution distributions -- centered at Shapley values -- that reveal meaningful attribution uncertainty across data modalities.