A Generalization of Amari's Bayesian Duality

Mohammad Emtiyaz Khan; Thomas Möllenhoff

cs.AISep 8, 2026

A Generalization of Amari's Bayesian Duality

Authors: Mohammad Emtiyaz Khan, Thomas Möllenhoff

Organizations: RIKEN Center for Advanced Intelligence Project, 1-4-1 Nihonbashi, Chuo-ku, Tokyo, 103-0027, Tokyo, Japan. · Department of Computer Science, Technische Universität Darmstadt, Hochschulstraße 10, Darmstadt, 64289, Hessen, Germany. · The Hessian Center for Artificial Intelligence, Landwehrstraße 50a, Darmstadt, 64293, Hessen, Germany.

Abstract

Amari's contributions to information geometry and machine learning are well known. Here, we revisit Amari's work on Bayesian duality which has not received as much attention. We connect Amari's Bayesian duality to a convex duality of Bayes' rule. Using this connection, we present a generalization of Amari's Bayesian duality and discuss its relevance for modern artificial intelligence.

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Jul 31, 2026 · cs.AIJ/K move · Enter open · S save

A Generalized-Bayes Perspective on Counterfactual Explanations: Posterior-Based Decision-Making and Evaluation

Keita Kinjo

Faculty of Business, Kyoritsu Women’s University

Counterfactual explanations (CEs) enhance the interpretability of machine learning models by identifying the smallest change to an input required to obtain a desired output. Although CEs are conventionally formulated as a distance-minimization problem, the theoretical basis of this formulation has received limited attention. We show that a distance-minimization-based CE is mathematically equivalent to the maximum a posteriori (MAP) estimate of a Gibbs posterior within the generalized Bayes framework, specifically when a distance-based prior is used. We call this formulation the Distance-Prior Generalized Bayes CE (DP-GBCE). Building on this posterior perspective, we introduce two decision rules beyond MAP within a unified framework: a Bayes decision that minimizes expected decision loss and CVaR-CE, a risk-averse decision rule. We also propose an extension that uses Bayesian model weights to mix the posterior distributions of multiple models, thereby accounting for model multiplicity, where several models have comparable predictive performance. Finally, we define metrics for evaluating both individual CEs and the posterior distribution as a whole, and use experiments on simulated data and Google Trends data to quantify the trade-offs among the decision rules.

Counterfactual Explanation Bayesian Counterfactual Reasoning Decisions

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Abstract

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