@Inproceedings (Conference){ensemble-learning-in-bayesian-neural-networks,
author = {Barber, D. and Bishop, Christopher},
title = {Ensemble learning in Bayesian neural networks},
booktitle = {Generalization in Neural Networks and Machine Learning},
year = {1998},
month = {January},
abstract = {
Bayesian treatments of learning in neural networks are typically based either on a local Gaussian approximation to a mode of the posterior weight distribution, or on Markov chain Monte Carlo simulations. A third approach, called `ensemble learning', was introduced by Hinton (1993). It aims to approximate the posterior distribution by minimizing the Kullback-Leibler divergence between the true posterior and a parametric approximating distribution. The original derivation of a deterministic algorithm relied on the use of a Gaussian approximating distribution with a diagonal covariance matrix and hence was unable to capture the posterior correlations between parameters. In this chapter 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 hyperparameters, leading to a simple re-estimation procedure. One of the benefits of our approach is that it yields a strict lower bound on the marginal likelihood, in contrast to other approximate procedures.
},
publisher = {Springer Verlag},
url = {https://www.microsoft.com/en-us/research/publication/ensemble-learning-in-bayesian-neural-networks/},
pages = {215-237},
edition = {Generalization in Neural Networks and Machine Learning},
}