dorsal/arxiv
View SchemaRelative Entropy and Inductive Inference
| Authors | Ariel Caticha |
|---|---|
| Categories | |
| ArXiv ID | physics/0311093 |
| URL | https://arxiv.org/abs/physics/0311093 |
| DOI | 10.1063/1.1751358 |
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.
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"abstract": "We discuss how the method of maximum entropy, MaxEnt, can be extended beyond\nits original scope, as a rule to assign a probability distribution, to a\nfull-fledged method for inductive inference. The main concept is the (relative)\nentropy S[p|q] which is designed as a tool to update from a prior probability\ndistribution q to a posterior probability distribution p when new information\nin the form of a constraint becomes available. The extended method goes beyond\nthe mere selection of a single posterior p, but also addresses the question of\nhow much less probable other distributions might be. Our approach clarifies how\nthe entropy S[p|q] is used while avoiding the question of its meaning.\nUltimately, entropy is a tool for induction which needs no interpretation.\nFinally, being a tool for generalization from special examples, we ask whether\nthe functional form of the entropy depends on the choice of the examples and we\nfind that it does. The conclusion is that there is no single general theory of\ninductive inference and that alternative expressions for the entropy are\npossible.",
"arxiv_id": "physics/0311093",
"authors": [
"Ariel Caticha"
],
"categories": [
"physics.data-an",
"physics.gen-ph"
],
"doi": "10.1063/1.1751358",
"title": "Relative Entropy and Inductive Inference",
"url": "https://arxiv.org/abs/physics/0311093"
},
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