# The Structure of Neural Network Posteriors

Neil D. Lawrence, University of Sheffield
Mehdi Azzouzi

#### Abstract

Exact inference in Bayesian neural networks is non analytic to compute and as a result approximate approaches such as the evidence procedure, Monte-Carlo sampling and variational inference have been proposed. In this paper we explore the structure of the posterior distributions in such a model through a new approximating distribution based on mixtures of Gaussian distributions and show how it may be implemented.

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 %T The Structure of Neural Network Posteriors %A Neil D. Lawrence and Mehdi Azzouzi %B %D %F lawrence-structure01 %P -- %R %U http://inverseprobability.com/publications/lawrence-structure01.html %X Exact inference in Bayesian neural networks is non analytic to compute and as a result approximate approaches such as the evidence procedure, Monte-Carlo sampling and variational inference have been proposed. In this paper we explore the structure of the posterior distributions in such a model through a new approximating distribution based on *mixtures* of Gaussian distributions and show how it may be implemented. 
 TY - CPAPER TI - The Structure of Neural Network Posteriors AU - Neil D. Lawrence AU - Mehdi Azzouzi PY - 2001/01/01 DA - 2001/01/01 ID - lawrence-structure01 SP - EP - L1 - http://www.thelawrences.net/neil/mixture.pdf UR - http://inverseprobability.com/publications/lawrence-structure01.html AB - Exact inference in Bayesian neural networks is non analytic to compute and as a result approximate approaches such as the evidence procedure, Monte-Carlo sampling and variational inference have been proposed. In this paper we explore the structure of the posterior distributions in such a model through a new approximating distribution based on *mixtures* of Gaussian distributions and show how it may be implemented. ER - 
 Lawrence, N.D. & Azzouzi, M.. (2001). The Structure of Neural Network Posteriors.:-