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Learning in graphical models
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Bayesian parameter estimation via variational methods
Statistics and Computing
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Neural Computation
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MLDM'05 Proceedings of the 4th international conference on Machine Learning and Data Mining in Pattern Recognition
An anomaly detection method for spacecraft using relevance vector learning
PAKDD'05 Proceedings of the 9th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining
Expert Systems with Applications: An International Journal
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AI'06 Proceedings of the 19th Australian joint conference on Artificial Intelligence: advances in Artificial Intelligence
MCS'10 Proceedings of the 9th international conference on Multiple Classifier Systems
PRIB'12 Proceedings of the 7th IAPR international conference on Pattern Recognition in Bioinformatics
Mean field variational Bayesian inference for support vector machine classification
Computational Statistics & Data Analysis
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The Support Vector Machine (SVM) of Vapnik [9] 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 [8] 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.