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Relevance vector machine

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Inmathematics, aRelevance Vector Machine (RVM) is amachine learning technique that usesBayesian inference to obtainparsimonious solutions forregression andprobabilistic classification.^[1] A greedy optimisation procedure and thus fast version were subsequently developed.^[2]^[3]The RVM has an identical functional form to thesupport vector machine, but provides probabilistic classification.

It is actually equivalent to aGaussian process model withcovariance 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 thekernel 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 thetraining set.^[4]

Compared to that ofsupport 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 anexpectation maximization (EM)-like learning method and are therefore at risk of local minima. This is unlike the standardsequential minimal optimization (SMO)-based algorithms employed bySVMs, which are guaranteed to find a global optimum (of the convex problem).

The relevance vector machine waspatented in the United States byMicrosoft (patent expired September 4, 2019).^[5]

References

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^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. Retrieved21 November 2024.
^Faul, Anita; Tipping, Michael (2001)."Analysis of Sparse Bayesian Learning"(PDF).Advances in Neural Information Processing Systems. Retrieved21 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. RetrievedApril 22, 2016.
^US 6633857, Michael E. Tipping, "Relevance vector machine"

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