2010
AISTATS
AISTATS 2010
On the Convergence Properties of Contrastive Divergence
Abstract
Contrastive Divergence (CD) is a popular method for estimating the parameters of Markov Random Fields (MRFs) by rapidly approximating an intractable term in the gradient of the log probability. Despite CD’s empirical success, little is known about its theoretical convergence properties. In this paper, we analyze the CD$_1$ update rule for Restricted Boltzmann Machines (RBMs) with binary variables. We show that this update is not the gradient of any function, and construct a counterintuitive “regularization function” that causes CD learning to cycle indefinitely. Nonetheless, we show that the regularized CD update has a fixed point for a large class of regularization functions using Brower’s fixed point theorem.
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Conference Pioneer
— AISTATS 2010
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Interdisciplinary Bridge
— Deep Learning and Machine Learning
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Trend Setter
— Theory
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Keyword Pioneer
— gradient approximation
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Hot Topic Early Bird
— convergence analysis
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