Ensemble Learning for Multi-Layer Networks
David Barber, Chris Bishop · 1997
Bayesian treatments of learning in neural networks are typically based either on local Gaussian approximations to a mode of the posterior weight distribution, or on Markov chain Monte Carlo simulations. A third approach, called ensemble learning, was in-troduced by Hinton and van Camp (1993). It aims to approximate the posterior distribution by minimizing the Kullback-Leibler di-vergence between the true posterior and a parametric approximat-ing distribution. However, the derivation of a deterministic algo-rithm relied on the use of a Gaussian approximating distribution with a diagonal covariance matrix and so was unable to capture the posterior correlations between parameters. In this paper, we show how the ensemble learning approach can be extended to full-covariance Gaussian distributions while remaining computationally tractable. We also extend the framework to deal with hyperparam-eters, leading to a simple re-estimation procedure. Initial results from a standard benchmark problem are encouraging. 1