# On Contrastive Divergence Learning

@inproceedings{CarreiraPerpin2005OnCD, title={On Contrastive Divergence Learning}, author={Miguel {\'A}. Carreira-Perpi{\~n}{\'a}n and Geoffrey E. Hinton}, booktitle={International Conference on Artificial Intelligence and Statistics}, year={2005} }

Maximum-likelihood (ML) learning of Markov random fields is challenging because it requires estimates of averages that have an exponential number of terms. Markov chain Monte Carlo methods typically take a long time to converge on unbiased estimates, but Hinton (2002) showed that if the Markov chain is only run for a few steps, the learning can still work well and it approximately minimizes a different function called “contrastive divergence” (CD). CD learning has been successfully applied to…

## 748 Citations

### Empirical Analysis of the Divergence of Gibbs Sampling Based Learning Algorithms for Restricted Boltzmann Machines

- Computer ScienceICANN
- 2010

The results indicate that the log-likelihood seems to diverge especially if the target distribution is difficult to learn for the RBM, and weight- Decay with a carefully chosen weight-decay-parameter can prevent divergence.

### Dynamical analysis of contrastive divergence learning: Restricted Boltzmann machines with Gaussian visible units

- Computer ScienceNeural Networks
- 2016

### Neighborhood-Based Stopping Criterion for Contrastive Divergence

- Computer ScienceIEEE Trans. Neural Networks Learn. Syst.
- 2018

This manuscript presents a simple and cheap alternative to the reconstruction error, based on the inclusion of information contained in neighboring states to the training set, as a stopping criterion for CD learning.

### A Neighbourhood-Based Stopping Criterion for Contrastive Divergence Learning

- Computer ScienceArXiv
- 2015

This manuscript investigates simple alternatives to the reconstruction error, based on the inclusion of information contained in neighboring states to the training set, as a stopping criterion for CD learning.

### A Cyclic Contrastive Divergence Learning Algorithm for High-Order RBMs

- Computer Science2014 13th International Conference on Machine Learning and Applications
- 2014

Experimental results show that CCD is more applicable and consistently outperforms the standard CD in both convergent speed and performance, and both algorithms CCD and standard CD are theoretically analyzed, from which the superiority of CCD learning is revealed.

### On the Convergence Properties of Contrastive Divergence

- Computer ScienceAISTATS
- 2010

This paper analyzes the CD1 update rule for Restricted Boltzmann Machines with binary variables, and shows that the regularized CD update has a fixed point for a large class of regularization functions using Brower’s fixed point theorem.

### Convergence of contrastive divergence algorithm in exponential family

- Mathematics, Computer ScienceThe Annals of Statistics
- 2018

This paper studies the asymptotic properties of the CD algorithm in canonical exponential families, which are special cases of the energy-based model and proves the existence of some bounded $m$ such that any limit point of the time average of any given parameter is a consistent estimate for the true parameter.

### Learning with Blocks: Composite Likelihood and Contrastive Divergence

- Computer ScienceAISTATS
- 2010

This paper shows that composite likelihoods can be stochastically optimized by performing a variant of contrastive divergence with random-scan blocked Gibbs sampling, and demonstrates that using higher-order blocks improves both the accuracy of parameter estimates and the rate of convergence.

### Contrastive Divergence Learning with Chained Belief Propagation

- Computer SciencePGM
- 2020

This work proposes contrastive divergence learning with chained belief propagation (BPChain-CD), which learns better models compared with BP-CD and CD on a range of maximum-likelihood learning experiments.

### Justifying and Generalizing Contrastive Divergence

- Computer ScienceNeural Computation
- 2009

An expansion of the log likelihood in undirected graphical models such as the restricted Boltzmann machine (RBM), where each term in the expansion is associated with a sample in a Gibbs chain alternating between two random variables, shows that its residual term converges to zero, justifying the use of a truncation of only a short Gibbs chain.

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