Bayesian duality expanded with new insight from convex geometry
A Generalization of Amari's Bayesian Duality
Artificial IntelligenceMachine Learning
Summary
Bayesian duality is a concept from information geometry that helps understand how probabilities are updated with new information. The authors explore a different angle by linking this idea to convex duality, which is about pairing mathematical problems in a specific way. By connecting these two ideas, they offer a broader form of Bayesian duality. This could be useful for improving how artificial intelligence systems learn and reason with uncertain information.
Bayesian dualityinformation geometryBayes' ruleconvex dualityprobabilitymachine learningartificial intelligenceconvex analysisstatistical inferenceduality theory
Authors
Mohammad Emtiyaz Khan, Thomas Möllenhoff
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.