Estimation of Third-Order Correlations within Mean Field Approximation.
Toshiyuki Tanaka · 1998
Linear response theorem provides a means of estimating correlations for Boltzmann machines within the framework of mean eld approximation. I present an extension of the linear response theorem which allows us to estimate third-order correlations for higher-order Boltzmann machines. KEYWORDS: Boltzmann machine, mean eld approximation, linear response 1. INTRODUCTION Use of Boltzmann machines[1] in general requires an enormous amount of computation in evaluating expectations from their parameters. Mean eld approximation[2] has been frequently used as a means to practically circumvent the diculty. It has the advantage that it is considerably faster than conventional methods, but at the expense of losing accuracy, since it ignores eects of higher-order statistics such as correlations. Kappen and Rodrguez[3, 4] proposed a method of estimating second-order correlations within the framework of mean eld approximation by the use of the linear response theorem[7]. I give an extension o...