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] 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), $\alpha_j$ 's as 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.^[2]

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 is patented in the United States by Microsoft.^[3]

References

↑ Tipping, Michael E. (2001). "Sparse Bayesian Learning and the Relevance Vector Machine". Journal of Machine Learning Research 1: 211–244.
↑ 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"

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Relevance vector machine

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References

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