Abstract

Abstract: When labelled training data is plentiful, discriminative techniques are widely used since they give excellent classification results. However, hand-labelling of data can get expensive, and there is considerable interest in semi-supervised techniques based on generative models. Although the generalisation performance of generative models can often be improved by `training them discriminatively’, they can then no longer make use of unlabelled data. In an attempt to exploit the benefits of both generative and discriminative approaches, methods have been proposed which interpolate between these two extremes by taking a convex combination of the generative and discriminative objective functions. In this article, we consider that there is only one correct way to train a given model, and that a `discriminatively trained’ generative model is fundamentally a new model. From this viewpoint, generative and discriminative models correspond to specific choices for the prior over parameters, which opens the door to principled ways of interpolating between generative and discriminative extremes through alternative choices of prior. We illustrate this framework on semi- supervised learning.