Field Theories for Learning Probability Distributions

Details Field Theories for Learning Probability Distributions Field Theories for Learning Probability Distributions

1996-07-25

arxiv.org/abs/cond-mat/9607180v1

Phys.Rev.Lett. 77 (1996) 4693-4697

Physics

Condensed Matter

12 pages, REVTEX

Scientific paper

10.1103/PhysRevLett.77.4693

Imagine being shown $N$ samples of random variables drawn independently from the same distribution. What can you say about the distribution? In general, of course, the answer is nothing, unless we have some prior notions about what to expect. From a Bayesian point of view we need an {\it a priori} distribution on the space of possible probability distributions, which defines a scalar field theory. In one dimension, free field theory with a constraint provides a tractable formulation of the problem, and we also discus generalizations to higher dimensions.

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