Bayesian Neural Networks and Density Networks

This paper reviews the Bayesian approach to learning in neural networks, then introduces a new adaptive model, the density network. This is a neural network for which target outputs are provided, but the inputs are unspecied. When a probability distribution is placed on the unknown inputs, a latent variable model is dened that is capable of discovering the underlying dimensionality of a data set. A Bayesian learning algorithm for these networks is derived and demonstrated. 1 Introduction to the Bayesian view of learning A binary classier is a parameterized mapping from an input x to an output y 2 [0; 1]); when its parameters w are specied, the classier states the probability that an input x belongs to class t = 1, rather than the alternative t = 0. Consider a binary classier which models the probability as a sigmoid function of x: P (t = 1jx; w;H) = y(x; w;H) = 1 1 + e wx (1) This form of model is known to statisticians as a linear logistic model, and in the neural networks ..