Variational Relevance Vector Machines

TL;DR

This paper introduces a Bayesian formulation of the Relevance Vector Machine using variational inference, enabling full posterior distributions over parameters and hyperparameters, and demonstrating its effectiveness on synthetic and real data.

Contribution

It presents the first fully Bayesian variational approach to the RVM, improving uncertainty quantification and model sparsity over previous methods.

Findings

The variational RVM provides comparable accuracy to SVMs.

It yields a full predictive distribution, unlike traditional SVMs.

The approach is effective on both synthetic and real-world datasets.

Abstract

The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions centred on a subset of the training data, known as support vectors. Despite its widespread success, the SVM suffers from some important limitations, one of the most significant being that it makes point predictions rather than generating predictive distributions. Recently Tipping (1999) has formulated the Relevance Vector Machine (RVM), a probabilistic model whose functional form is equivalent to the SVM. It achieves comparable recognition accuracy to the SVM, yet provides a full predictive distribution, and also requires substantially fewer kernel functions. The original treatment of the RVM relied on the use of type II maximum likelihood (the `evidence framework') to provide point estimates of the hyperparameters which govern model sparsity. In this paper we show how the RVM can be formulated and solved within a completely Bayesian paradigm through the use of variational inference, thereby giving a posterior distribution over both parameters and hyperparameters. We demonstrate the practicality and performance of the variational RVM using both synthetic and real world examples.