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I Nemenman and W Bialek. Occam factors and model-independent Bayesian learning of continuous distributions. Phys. Rev. E, 65(2):026137, 2002. PDF, arXiv.
- Preliminary version: I Nemenman and W Bialek, "Learning Continuous Distributions: Simulations With Field Theoretic Priors," in T. Leen, T. Dietterich, and V. Tresp, eds. Adv. Neural Inf. Proc. Syst. 13, pp. 287-293, MIT Press, 2001. PDF.
- 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.