Variational Relevance Vector Machines
This work addresses the need for probabilistic predictions in pattern recognition, offering a more informative alternative to SVMs for practitioners in machine learning, though it is incremental as it builds on the existing RVM framework.
The paper tackled the limitation of Support Vector Machines (SVMs) in providing only point predictions by formulating a Bayesian version of the Relevance Vector Machine (RVM) using variational inference, which yields predictive distributions and requires fewer kernel functions while maintaining comparable accuracy.
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.