Failures of the One-Step Learning Algorithm
Failures of the One-Step Learning Algorithm
复制标题
一步学习算法的失败
DOI：
--
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
D. MacKay
中科院分区：
文献类型：
--
作者：
D. MacKay
Hinton网络（Hinton, 2001, personal communication）是从可观测空间x到能量函数E（x; w）的确定性映射，由参数w参数化。能量偏离的概率P(xjw) = exp(iE(x; w))=Z(w)。该密度模型的最大似然学习算法采取步骤¢/ihgi 0 + hgi 1，其中hgi 0是在数据密度x处的梯度g = @E=@w的平均值，hgi 1是从P（xjw）绘制的点x的平均梯度。如果T是x空间中的马尔可夫链，其唯一不变密度为P（xjw）那么我们可以通过取数据点x，用T对每个点进行I次撞击来近似hgi 1，其中I是一个大整数。在Hinton（2001）的一步学习算法中，我们将I设为1。在本文中，我给出了模型E（x; w）和马尔可夫链T的例子，其中真似然在参数中是单峰的，但一步算法不一定收敛到最大似然参数。希望这些反例有助于确定一步算法是正确收敛算法的条件。Hinton网络（Hinton, 2001, personal communication）是从可观测空间x维到能量函数E（x;w）的确定性映射，由参数w参数化。能量衰减为概率
The Hinton network (Hinton, 2001, personal communication) is a deterministic mapping from an observable space x to an energy function E(x; w), parameterized by parameters w. The energy deflnes a probability P(xjw) = exp(iE(x; w))=Z(w). A maximum likelihood learning algorithm for this density model takes steps ¢w/ihgi 0 + hgi 1 where hgi 0 is the average of the gradient g = @E=@w evaluated at points x drawn from the data density, and hgi 1 is the average gradient for points x drawn from P(xjw). If T is a Markov chain in x-space that has P(xjw) as its unique invariant density then we can approximate hgi 1 by taking the data points x and hitting each of them I times with T, where I is a large integer. In the one-step learning algorithm of Hinton (2001), we set I to 1. In this paper I give examples of models E(x; w) and Markov chains T for which the true likelihood is unimodal in the parameters, but the one-step algorithm does not necessarily converge to the maximum likelihood parameters. It is hoped that these negative examples will help pin down the conditions for the one-step algorithm to be a correctly convergent algorithm. The Hinton network (Hinton, 2001, personal communication) is a deterministic mapping from anobservablespace xofdimension Dtoanenergyfunction E(x;w),parameterizedbyparameters w. The energy deflnesa probability