Relative Entropy and Inductive Inference

Details Relative Entropy and Inductive Inference Relative Entropy and Inductive Inference

2003-11-19

arxiv.org/abs/physics/0311093v1

Physics

Data Analysis, Statistics and Probability

Presented at MaxEnt23, the 23rd International Workshop on Bayesian Inference and Maximum Entropy Methods (August 3-8, 2003, Ja

Scientific paper

10.1063/1.1751358

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.

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