7,369 research outputs found
Mean Field Theory for Sigmoid Belief Networks
We develop a mean field theory for sigmoid belief networks based on ideas
from statistical mechanics. Our mean field theory provides a tractable
approximation to the true probability distribution in these networks; it also
yields a lower bound on the likelihood of evidence. We demonstrate the utility
of this framework on a benchmark problem in statistical pattern
recognition---the classification of handwritten digits.Comment: See http://www.jair.org/ for any accompanying file
Mean Field Methods for a Special Class of Belief Networks
The chief aim of this paper is to propose mean-field approximations for a
broad class of Belief networks, of which sigmoid and noisy-or networks can be
seen as special cases. The approximations are based on a powerful mean-field
theory suggested by Plefka. We show that Saul, Jaakkola and Jordan' s approach
is the first order approximation in Plefka's approach, via a variational
derivation. The application of Plefka's theory to belief networks is not
computationally tractable. To tackle this problem we propose new approximations
based on Taylor series. Small scale experiments show that the proposed schemes
are attractive
Deep Exponential Families
We describe \textit{deep exponential families} (DEFs), a class of latent
variable models that are inspired by the hidden structures used in deep neural
networks. DEFs capture a hierarchy of dependencies between latent variables,
and are easily generalized to many settings through exponential families. We
perform inference using recent "black box" variational inference techniques. We
then evaluate various DEFs on text and combine multiple DEFs into a model for
pairwise recommendation data. In an extensive study, we show that going beyond
one layer improves predictions for DEFs. We demonstrate that DEFs find
interesting exploratory structure in large data sets, and give better
predictive performance than state-of-the-art models
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