Occam factors and model-independent Bayesian learning of continuous distributions

Details Occam factors and model-independent Bayesian learning of continuous distributions Occam factors and model-independent Bayesian learning of continuous distributions

2000-09-11

arxiv.org/abs/cond-mat/0009165v2

Phys. Rev. E, 65 (2), 2002

Physics

Condensed Matter

publication revisions: extended introduction, new references, other minor corrections; 6 pages, 6 figures, revtex

Scientific paper

10.1103/PhysRevE.65.026137

Learning of a smooth but nonparametric probability density can be regularized using methods of Quantum Field Theory. We implement a field theoretic prior numerically, test its efficacy, and show that the data and the phase space factors arising from the integration over the model space determine the free parameter of the theory ("smoothness scale") self-consistently. This persists even for distributions that are atypical in the prior and is a step towards a model-independent theory for learning continuous distributions. Finally, we point out that a wrong parameterization of a model family may sometimes be advantageous for small data sets.

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