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| In [[mathematics]], a '''relevance vector machine (RVM)''' is a [[machine learning]] technique that uses [[Bayesian inference]] to obtain [[Parsimony|parsimonious]] solutions for [[Regression analysis|regression]] and [[Statistical classification|classification]].<ref>{{cite journal | last=Tipping | first=Michael E. |title=Sparse Bayesian Learning and the Relevance Vector Machine |year=2001 |journal = [[Journal of Machine Learning Research]] |volume=1 |pages=211–244 |url=http://jmlr.csail.mit.edu/papers/v1/tipping01a.html }}</ref>
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| The RVM has an identical functional form to the [[support vector machine]], but provides probabilistic classification.
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| It is actually equivalent to a [[Gaussian process]] model with [[covariance function]]:
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| :<math>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) </math>
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| where <math>\varphi</math> is the [[kernel function]] (usually Gaussian), and <math>\mathbf{x}_1,\ldots,\mathbf{x}_N</math> are the input vectors of the [[training set]].{{Citation needed|date=February 2010}} | |
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| Compared to that of [[support vector machine]]s (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 [[Support vector machine|SVM]]s, which are guaranteed to find a global optimum (of the convex problem).
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| The relevance vector machine is [[Software patents under United States patent law|patented in the United States]] by [[Microsoft]].<ref>{{cite patent
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| |country = US
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| |number = 6633857
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| |title = Relevance vector machine
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| |inventor = Michael E. Tipping
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| }}</ref>
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| == See also ==
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| * [[Kernel trick]]
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| == References ==
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| {{reflist}}
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| == Software ==
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| * [http://dlib.net dlib C++ Library]
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| * [http://www.terborg.net/research/kml/ The Kernel-Machine Library]
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| * [http://www.maths.bris.ac.uk/R/web/packages/rvmbinary/index.html rvmbinary:R package for binary classification]
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| ==External links==
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| *[http://www.relevancevector.com Tipping's webpage on Sparse Bayesian Models and the RVM]
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| *[http://www.tristanfletcher.co.uk/RVM%20Explained.pdf A Tutorial on RVM by Tristan Fletcher]
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| [[Category:Classification algorithms]]
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| [[Category:Kernel methods for machine learning]]
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| [[Category:Non-parametric Bayesian methods]]
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