This is a tutorial and survey paper on Boltzmann Machine (BM), Restricted Boltzmann Machine (RBM), and Deep Belief Network (DBN). We start with the required background on probabilistic graphical models, Markov random field, Gibbs sampling, statistical physics, Ising model, and the Hopfield network. Then, we introduce the structures of BM and RBM. The conditional distributions of visible and hidden variables, Gibbs sampling in RBM for generating variables, training BM and RBM by maximum likelihood estimation, and contrastive divergence are explained. Then, we discuss different possible discrete and continuous distributions for the variables. We introduce conditional RBM and how it is trained. Finally, we explain deep belief network as a stack of RBM models. This paper on Boltzmann machines can be useful in various fields including data science, statistics, neural computation, and statistical physics.

中文翻译：

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受限玻尔兹曼机和深度信念网络：教程和调查

这是一篇关于玻尔兹曼机 (BM)、受限玻尔兹曼机 (RBM) 和深度信念网络 (DBN) 的教程和调查论文。我们从概率图形模型、马尔可夫随机场、吉布斯采样、统计物理学、伊辛模型和霍普菲尔德网络所需的背景开始。然后，我们介绍BM和RBM的结构。解释了可见变量和隐藏变量的条件分布、RBM 中用于生成变量的 Gibbs 采样、通过最大似然估计训练 BM 和 RBM 以及对比散度。然后，我们讨论变量的不同可能的离散和连续分布。我们介绍了条件 RBM 及其训练方式。最后，我们将深度信念网络解释为一堆 RBM 模型。这篇关于玻尔兹曼机的论文可用于各个领域，包括数据科学、