# Mean-Field Methods For A Special Class Of Belief Networks

Chiranjib  Bhattacharyya Dept. of Computer Science & Automation, Indian Institute of Science, Bangalore, Karnataka , India 560012 S. Sathiya Keerthi Dept. of Mechanical and Production Engineering, National University of Singapore, Singapore CB CHIRU @CSA . I SC . ERNET . IN
MP ESSK @ GUP PY .MPE .NUS .EDU .SG

## Abstract

The chief aim of this paper is to propose mean-field approximations for a broad class of Belief networks, of which sigmoid and noisy-or networks can be seen as special cases.

The approximations are based on a powerful mean-field theory suggested by Plefka. We show that Saul, Jaakkola, and Jordan's approach is the first order approximation in Plefka's approach, via a variational derivation. The application of Plefka's theory to belief networks is not comput ationally tractable. To tackle this problem we propose new approximations based on Taylor series. Small scale experiments show that the proposed schemes are attractive.

## 1. Introduction

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