论文标题
深度信念网络的定量通用近似范围
Quantitative Universal Approximation Bounds for Deep Belief Networks
论文作者
论文摘要
我们表明，具有二进制隐藏单元的深度信念网络可以在非常轻微的可见性要求下近似任何多元概率密度在可见节点的父母密度上。近似值以$ l^q $ -norm为$ q \ in [1，\ infty] $（$ q = \ infty $，对应于上述规范）和kullback-leibler Divergence。此外，我们根据隐藏单元数量在近似误差上建立了尖锐的定量界限。
We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density of the visible nodes. The approximation is measured in the $L^q$-norm for $q\in[1,\infty]$ ($q=\infty$ corresponding to the supremum norm) and in Kullback-Leibler divergence. Furthermore, we establish sharp quantitative bounds on the approximation error in terms of the number of hidden units.
