标题： 深度置信网络的核与子模型 显示英文标题

标题： Kernels and Submodels of Deep Belief Networks

摘要： 我们研究了表示为随机分层网络可见边缘分布的概率分布混合。我们采用分布核变换的观点，这为来自深度置信网络（DBN）和其他没有横向连接的网络的分布式表示提供了一个统一的画面。我们描述了当网络参数变化时，由DBN实现的核集及其核积的组合和几何性质。我们描述了可以被DBN学习的显式概率分布类，包括指数族。我们利用这些子模型从上方对DBN的最大和期望的Kullback-Leibler近似误差进行界值分析，这取决于它们所包含的隐藏层数和单元数。 显示英文摘要

摘要： We study the mixtures of factorizing probability distributions represented as visible marginal distributions in stochastic layered networks. We take the perspective of kernel transitions of distributions, which gives a unified picture of distributed representations arising from Deep Belief Networks (DBN) and other networks without lateral connections. We describe combinatorial and geometric properties of the set of kernels and products of kernels realizable by DBNs as the network parameters vary. We describe explicit classes of probability distributions, including exponential families, that can be learned by DBNs. We use these submodels to bound the maximal and the expected Kullback-Leibler approximation errors of DBNs from above depending on the number of hidden layers and units that they contain.