Relative Entropy and Inductive Inference

Abstract

We discuss how the method of maximum entropy, MaxEnt, can be extended beyond its original scope, as a rule to assign a probability distribution, to a full-fledged method for inductive inference. The main concept is the (relative) entropy S[p|q] which is designed as a tool to update from a prior probability distribution q to a posterior probability distribution p when new information in the form of a constraint becomes available. The extended method goes beyond the mere selection of a single posterior p, but also addresses the question of how much less probable other distributions might be. Our approach clarifies how the entropy S[p|q] is used while avoiding the question of its meaning. Ultimately, entropy is a tool for induction which needs no interpretation. Finally, being a tool for generalization from special examples, we ask whether the functional form of the entropy depends on the choice of the examples and we find that it does. The conclusion is that there is no single general theory of inductive inference and that alternative expressions for the entropy are possible.

Presented at MaxEnt23, the 23rd International Workshop on Bayesian Inference and Maximum Entropy Methods (August 3-8, 2003, Jackson Hole, WY, USA)

Cited by in corpus (17)

• Using the Maximum Entropy Principle to Combine Simulations and Solution Experiments
• Deep Active Inference
• Entropy, Information, and the Updating of Probabilities
• Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?
• Optimal Belief Approximation
• Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature
• Entropic criterion for model selection
• Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach
• Entropic dynamics on Gibbs statistical manifolds
• Active Inference and Epistemic Value in Graphical Models
• On The Complexity Of Statistical Models Admitting Correlations
• A Bayesian Account of Quantum Histories
• Measurement of statistical evidence on an absolute scale following thermodynamic principles
• Entropic Density Functional Theory
• Bayesian Probabilities and the Histories Algebra
• Approximating the entire spectrum of nonequilibrium steady state distributions using relative entropy: An application to thermal conduction
• Legendre transformation and information geometry for the maximum entropy theory of ecology