# 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),'s as the variances of the prior on the weight vector ,and are the input vectors of the training set.^{[citation needed]}

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.^{[2]}

## Contents

## See also

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

## References

- ↑ Tipping, Michael E. (2001). "Sparse Bayesian Learning and the Relevance Vector Machine".
*Journal of Machine Learning Research*.**1**: 211–244.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ US 6633857, Michael E. Tipping, "Relevance vector machine"

## Software

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