Relevance vector machine

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In mathematics, a Relevance Vector Machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and probabilistic classification.^[1] A greedy optimisation procedure and thus fast version were subsequently developed.^[2]^[3] The RVM has an identical functional form to the support vector machine, but provides probabilistic classification.

It is actually equivalent to a Gaussian process model with covariance function:

k(\mathbf {x} ,\mathbf {x'} )=\sum _{j=1}^{N}{\frac {1}{\alpha _{j}}}\varphi (\mathbf {x} ,\mathbf {x} _{j})\varphi (\mathbf {x} ',\mathbf {x} _{j})

where $\varphi$ is the kernel function (usually Gaussian), $\alpha _{j}$ are the variances of the prior on the weight vector $w\sim N(0,\alpha ^{-1}I)$ , and $\mathbf {x} _{1},\ldots ,\mathbf {x} _{N}$ are the input vectors of the training set.^[4]

Compared to that of support vector machines (SVM), the Bayesian formulation of the RVM avoids the set of free parameters of the SVM (that usually require cross-validation-based post-optimizations). However RVMs use an expectation maximization (EM)-like learning method and are therefore at risk of local minima. This is unlike the standard sequential minimal optimization (SMO)-based algorithms employed by SVMs, which are guaranteed to find a global optimum (of the convex problem).

The relevance vector machine was patented in the United States by Microsoft (patent expired September 4, 2019).^[5]

References

^ Tipping, Michael E. (2001). "Sparse Bayesian Learning and the Relevance Vector Machine". Journal of Machine Learning Research. 1: 211–244.
^ Tipping, Michael; Faul, Anita (2003). "Fast Marginal Likelihood Maximisation for Sparse Bayesian Models". Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics: 276–283. Retrieved 21 November 2024.
^ Faul, Anita; Tipping, Michael (2001). "Analysis of Sparse Bayesian Learning" (PDF). Advances in Neural Information Processing Systems. Retrieved 21 November 2024.
^ Candela, Joaquin Quiñonero (2004). "Sparse Probabilistic Linear Models and the RVM". Learning with Uncertainty - Gaussian Processes and Relevance Vector Machines (PDF) (Ph.D.). Technical University of Denmark. Retrieved April 22, 2016.
^ US 6633857, Michael E. Tipping, "Relevance vector machine"

Software

dlib C++ Library
The Kernel-Machine Library
rvmbinary: R package for binary classification
scikit-rvm
fast-scikit-rvm, rvm tutorial

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