# 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.

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 alsoEdit

- Kernel trick
- Platt scaling: turns an SVM into a probability model

## ReferencesEdit

**^**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"

## SoftwareEdit

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