Restricted Boltzmann machines (RBM) are bilayer neural networks used for the unsupervised learning of model distributions from data. The bipartite architecture of RBM naturally defines an elegant sampling procedure, called alternating Gibbs sampling (AGS), where the configurations of the latent-variable layer are sampled conditional to the data-variable layer and vice versa. We study here the performance of AGS on several analytically tractable models borrowed from statistical mechanics. We show that standard AGS is not more efficient than classical Metropolis-Hastings (MH) sampling of the effective energy landscape defined on the data layer. However, RBM can identify meaningful representations of training data in their latent space. Furthermore, using these representations and combining Gibbs sampling with the MH algorithm in the latent space can enhance the sampling performance of the RBM when the hidden units encode weakly dependent features of the data. We illustrate our findings on three datasets: Bars and Stripes and MNIST, well known in machine learning, and the so-called lattice proteins dataset, introduced in theoretical biology to study the sequence-to-structure mapping in proteins.

中文翻译：

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受限玻尔兹曼机的交替吉布斯采样中的障碍和动态路径

受限玻尔兹曼机 (RBM) 是双层神经网络，用于从数据中无监督地学习模型分布。RBM 的二分架构自然地定义了一个优雅的采样过程，称为交替吉布斯采样 (AGS)，其中潜在变量层的配置以数据变量层为条件进行采样，反之亦然。我们在这里研究了 AGS 在几个从统计力学中借来的易于分析的模型上的性能。我们表明，标准 AGS 并不比数据层上定义的有效能源景观的经典 Metropolis-Hastings (MH) 采样更有效。然而，RBM ​​可以在潜在空间中识别训练数据的有意义的表示。此外，当隐藏单元编码数据的弱相关特征时，使用这些表示并将 Gibbs 采样与潜在空间中的 MH 算法相结合可以提高 RBM 的采样性能。我们在三个数据集上说明了我们的发现：条形图和 MNIST，在机器学习中广为人知，以及所谓的格子蛋白质数据集，在理论生物学中引入以研究蛋白质的序列到结构映射。