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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:
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 was patented in the United States by Microsoft (patent expired September 4, 2019). [3]
Part of a series on |
Machine learning and data mining |
---|
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 was patented in the United States by Microsoft (patent expired September 4, 2019). [3]