Relevance vector machine

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.

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

where is the kernel function (usually Gaussian), are the variances of the prior on the weight vector , and 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 (patent expired September 4, 2019).[3]

See also
  • Kernel trick
  • Platt scaling: turns an SVM into a probability model

References
  1. Tipping, Michael E. (2001). "Sparse Bayesian Learning and the Relevance Vector Machine". Journal of Machine Learning Research. 1: 211–244.
  2. 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.
  3. US 6633857, Michael E. Tipping, "Relevance vector machine"

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