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Contrastive Divergence (CD) and Persistent Contrastive Divergence (PCD) are popular methods for training the weights of Restricted Boltzmann Machines. However, both methods use an approximate method for sampling from the model distribution.…

Neural and Evolutionary Computing · Computer Science 2014-02-17 Mathias Berglund , Tapani Raiko

Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the…

Machine Learning · Computer Science 2014-04-10 David Buchaca , Enrique Romero , Ferran Mazzanti , Jordi Delgado

Restricted Boltzmann Machines (RBMs) are probabilistic generative models that can be trained by maximum likelihood in principle, but are usually trained by an approximate algorithm called Contrastive Divergence (CD) in practice. In general,…

Machine Learning · Computer Science 2022-11-07 Charles K. Fisher

Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the…

Neural and Evolutionary Computing · Computer Science 2015-07-27 E. Romero , F. Mazzanti , J. Delgado

Estimating the log-likelihood gradient with respect to the parameters of a Restricted Boltzmann Machine (RBM) typically requires sampling using Markov Chain Monte Carlo (MCMC) techniques. To save computation time, the Markov chains are only…

Machine Learning · Computer Science 2017-06-29 Oswin Krause , Asja Fischer , Christian Igel

A restricted Boltzmann machine (RBM) is a two-layer neural network with shared weights and has been extensively studied for dimensionality reduction, data representation and recommendation systems in the literature. The traditional RBM…

Machine Learning · Computer Science 2026-05-27 Jiangsheng You , Chun-Yen Liu

Contrastive divergence is a popular method of training energy-based models, but is known to have difficulties with training stability. We propose an adaptation to improve contrastive divergence training by scrutinizing a gradient term that…

Machine Learning · Computer Science 2021-06-14 Yilun Du , Shuang Li , Joshua Tenenbaum , Igor Mordatch

Contrastive divergence (CD) learning is a classical method for fitting unnormalized statistical models to data samples. Despite its wide-spread use, the convergence properties of this algorithm are still not well understood. The main source…

Machine Learning · Computer Science 2021-03-17 Omer Yair , Tomer Michaeli

The Contrastive Divergence (CD) algorithm has achieved notable success in training energy-based models including Restricted Boltzmann Machines and played a key role in the emergence of deep learning. The idea of this algorithm is to…

Machine Learning · Statistics 2018-03-01 Bai Jiang , Tung-Yu Wu , Yifan Jin , Wing H. Wong

The Gaussian-Bernoulli restricted Boltzmann machine (GB-RBM) is a useful generative model that captures meaningful features from the given $n$-dimensional continuous data. The difficulties associated with learning GB-RBM are reported…

Machine Learning · Computer Science 2021-02-15 Vidyadhar Upadhya , P S Sastry

We present an efficient classical algorithm for training deep Boltzmann machines (DBMs) that uses rejection sampling in concert with variational approximations to estimate the gradients of the training objective function. Our algorithm is…

Machine Learning · Computer Science 2015-07-10 Nathan Wiebe , Ashish Kapoor , Christopher Granade , Krysta M Svore

Restricted Boltzmann machines (RBMs) are a powerful class of generative models, but their training requires computing a gradient that, unlike supervised backpropagation on typical loss functions, is notoriously difficult even to…

Machine Learning · Computer Science 2020-11-03 Haik Manukian , Yan Ru Pei , Sean R. B. Bearden , Massimiliano Di Ventra

Restricted Boltzmann Machine (RBM) is an energy based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD…

Machine Learning · Computer Science 2021-07-02 Vivek Dixit , Raja Selvarajan , Muhammad A. Alam , Travis S. Humble , Sabre Kais

Learning RBMs using standard algorithms such as CD(k) involves gradient descent on the negative log-likelihood. One of the terms in the gradient, which involves expectation w.r.t. the model distribution, is intractable and is obtained…

Machine Learning · Computer Science 2019-10-02 Vidyadhar Upadhya , P. S. Sastry

Restricted Boltzmann Machines (RBMs) and Deep Belief Networks have been demonstrated to perform efficiently in a variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on…

Neural and Evolutionary Computing · Computer Science 2015-11-17 Emre Neftci , Srinjoy Das , Bruno Pedroni , Kenneth Kreutz-Delgado , Gert Cauwenberghs

Energy-based models are popular in machine learning due to the elegance of their formulation and their relationship to statistical physics. Among these, the Restricted Boltzmann Machine (RBM), and its staple training algorithm contrastive…

Machine Learning · Computer Science 2015-04-09 Daniel Jiwoong Im , Ethan Buchman , Graham W. Taylor

Conditional Restricted Boltzmann Machines (CRBMs) are rich probabilistic models that have recently been applied to a wide range of problems, including collaborative filtering, classification, and modeling motion capture data. While much…

Machine Learning · Computer Science 2012-02-20 Volodymyr Mnih , Hugo Larochelle , Geoffrey E. Hinton

Energy-based learning algorithms are alternatives to backpropagation and are well-suited to distributed implementations in analog electronic devices. However, a rigorous theory of convergence is lacking. We make a first step in this…

Optimization and Control · Mathematics 2026-01-28 Anne-Men Huijzer , Thomas Chaffey , Bart Besselink , Henk J. van Waarde

The Energy-Based Model (EBM) framework is a very general approach to generative modeling that tries to learn and exploit probability distributions only defined though unnormalized scores. It has risen in popularity recently thanks to the…

Machine Learning · Computer Science 2022-02-25 Léo Gagnon , Guillaume Lajoie

We propose ratio divergence (RD) learning for discrete energy-based models, a method that utilizes both training data and a tractable target energy function. We apply RD learning to restricted Boltzmann machines (RBMs), which are a minimal…

Machine Learning · Statistics 2025-10-09 Yuichi Ishida , Yuma Ichikawa , Aki Dote , Toshiyuki Miyazawa , Koji Hukushima
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