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Universal Approximation Depth and Errors of Narrow Belief Networks with Discrete Units
Deep belief network restricted Boltzmann machine universal approxima-tion representational power Kullback-Leibler divergence,q-ary variable
2013/4/28
We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily ...
Uncertainty quantification and weak approximation of an elliptic inverse problem
Uncertainty quantification weak approximation elliptic inverse problem
2011/3/18
We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a lin...
A new method for obtaining sharp compound Poisson approximation error estimates for sums of locally dependent random variables
compound Poisson approximation coupling inequality law of small numbers
2010/10/19
Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the...
Multivariate normal approximation using exchangeable pairs
Stein's method exchangeable pairs normal approximation random matrices
2009/6/12
The aim of this article is to fill this void.We present three abstract normal approximation theorems using exchangeable pairs in multivariate contexts,one for situations in which the underlying symmet...