# Deep Boltzmann Machines

@inproceedings{Salakhutdinov2009DeepBM, title={Deep Boltzmann Machines}, author={Ruslan Salakhutdinov and Geoffrey E. Hinton}, booktitle={International Conference on Artificial Intelligence and Statistics}, year={2009} }

We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent expectations are estimated using a variational approximation that tends to focus on a single mode, and dataindependent expectations are approximated using persistent Markov chains. The use of two quite different techniques for estimating the two types of expectation that enter into the gradient of the log-likelihood makes it practical to learn Boltzmann machines with multiple…

## 2,159 Citations

### An Efficient Learning Procedure for Deep Boltzmann Machines

- Computer ScienceNeural Computation
- 2012

A new learning algorithm for Boltzmann machines that contain many layers of hidden variables is presented and results on the MNIST and NORB data sets are presented showing that deep BoltZmann machines learn very good generative models of handwritten digits and 3D objects.

### Efficient Learning of Deep Boltzmann Machines

- Computer ScienceAISTATS
- 2010

We present a new approximate inference algorithm for Deep Boltzmann Machines (DBM’s), a generative model with many layers of hidden variables. The algorithm learns a separate “recognition” model that…

### A Two-Stage Pretraining Algorithm for Deep Boltzmann Machines

- Computer ScienceICANN
- 2013

This paper shows empirically that the proposed method overcomes the difficulty in training DBMs from randomly initialized parameters and results in a better, or comparable, generative model when compared to the conventional pretraining algorithm.

### Joint Training Deep Boltzmann Machines for Classification

- Computer ScienceICLR
- 2013

This work introduces a new method for training deep Boltzmann machines jointly, and shows that this approach performs competitively for classification and outperforms previous methods in terms of accuracy of approximate inference and classification with missing inputs.

### How to Pretrain Deep Boltzmann Machines in Two Stages

- Computer Science
- 2015

This paper shows empirically that the proposed method overcomes the difficulty in training DBMs from randomly initialized parameters and results in a better, or comparable, generative model when compared to the conventional pretraining algorithm.

### Variational EM Learning of DSBNs with Conditional Deep Boltzmann Machines

- Computer ScienceICANN
- 2014

This paper describes a variational EM learning method of DSBNs with a new inference model known as the conditional deep Boltzmann machine (cDBM), which is an undirected graphical model capable of representing complex dependencies among latent variables.

### Gaussian-Bernoulli deep Boltzmann machine

- Computer ScienceThe 2013 International Joint Conference on Neural Networks (IJCNN)
- 2013

Improvements of the learning algorithm for GDBM help avoid some of the common difficulties found in training deep Boltzmann machines such as divergence of learning, the difficulty in choosing right learning rate scheduling, and the existence of meaningless higher layers.

### An Infinite Deep Boltzmann Machine

- Computer ScienceICCDA 2018
- 2018

Experimental results indicate that iDBM can learn a generative and discriminative model as good as the original DBM, and has successfully eliminated the requirement of model selection for hidden layer sizes of DBMs.

### An Introduction to Restricted Boltzmann Machines

- Computer ScienceCIARP
- 2012

This tutorial introduces RBMs as undirected graphical models as building blocks of multi-layer learning systems called deep belief networks based on Markov chain Monte Carlo methods.

### Enhanced Gradient and Adaptive Learning Rate for Training Restricted Boltzmann Machines

- Computer ScienceICML
- 2011

This work presents an enhanced gradient which is derived such that it is invariant to bit-flipping transformations and proposes a way to automatically adjust the learning rate by maximizing a local likelihood estimate.

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