TY - JOUR

T1 - Field theories for learning probability distributions

AU - Bialek, William

AU - Callan, Curtis Gove

AU - Strong, Steven P.

PY - 1996

Y1 - 1996

N2 - 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 you have some prior notions about what to expect. From a Bayesian point of view one needs an a priori distribution on the space of possible probability distributions, which defines a scalar field theory. In one dimension, free field theory with a normalization constraint provides a tractable formulation of the problem, and we discuss generalizations to higher dimensions.

AB - 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 you have some prior notions about what to expect. From a Bayesian point of view one needs an a priori distribution on the space of possible probability distributions, which defines a scalar field theory. In one dimension, free field theory with a normalization constraint provides a tractable formulation of the problem, and we discuss generalizations to higher dimensions.

UR - http://www.scopus.com/inward/record.url?scp=0000395622&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000395622&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.77.4693

DO - 10.1103/PhysRevLett.77.4693

M3 - Article

C2 - 10062607

AN - SCOPUS:0000395622

VL - 77

SP - 4693

EP - 4697

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 23

ER -