Expressive Power of Conditional Restricted Boltzmann Machines
Expressive Power of Conditional Restricted Boltzmann Machines
复制标题
条件受限玻尔兹曼机的表达能力
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Keyan Ghazi
中科院分区：
文献类型：
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作者：
Guido Montúfar;N. Ay;Keyan Ghazi
条件受限玻尔兹曼机是一种无向随机神经网络，其中一层输入和输出单元双部分地连接到一层隐藏单元。这些网络根据输入单元的状态定义输出单元状态的条件概率分布模型，并通过交互权重和偏差参数化。我们讨论了这些模型的表示能力，证明了条件概率分布的最小大小的全称逼近器，确定性函数的最小大小的全称逼近器，最大的模型逼近误差，以及可表示条件分布集的维数。我们为研究条件模型提供了新的工具，并获得了可以直接从限制玻尔兹曼机器概率模型的现有工作中得到的结果的重大改进。
Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability distributions on the states of the output units given the states of the input units, parametrized by interaction weights and biases. We address the representational power of these models, proving results on the minimal size of universal approximators of conditional probability distributions, the minimal size of universal approximators of deterministic functions, the maximal model approximation errors, and on the dimension of the set of representable conditional distributions. We contribute new tools for investigating conditional models and obtain significant improvements over the results that can be derived directly from existing work on restricted Boltzmann machine probability models.