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).
^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"
Tipping's webpage on Sparse Bayesian Models and the RVM
Applied tutorial on RVM
Comparison of RVM and SVM
January 01, 1970
relevance, vector, machine, mathematics, relevance, vector, machine, machine, learning, technique, that, uses, bayesian, inference, obtain, parsimonious, solutions, regression, probabilistic, classification, identical, functional, form, support, vector, machin. 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 x x j 1 N 1 a j f x x j f x x j displaystyle 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 f displaystyle varphi is the kernel function usually Gaussian a j displaystyle alpha j are the variances of the prior on the weight vector w N 0 a 1 I displaystyle w sim N 0 alpha 1 I and x 1 x N displaystyle 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 was patented in the United States by Microsoft patent expired September 4 2019 3 Contents 1 See also 2 References 3 Software 4 External linksSee also editKernel trick Platt scaling turns an SVM into a probability modelReferences edit Tipping Michael E 2001 Sparse Bayesian Learning and the Relevance Vector Machine Journal of Machine Learning Research 1 211 244 Candela Joaquin Quinonero 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 Software editdlib C Library The Kernel Machine Library rvmbinary R package for binary classification scikit rvm fast scikit rvm rvm tutorialExternal links editTipping s webpage on Sparse Bayesian Models and the RVM A Tutorial on RVM by Tristan Fletcher Applied tutorial on RVM Comparison of RVM and SVM Retrieved from https en wikipedia org w index php title Relevance vector machine amp oldid 1072269200, wikipedia, wiki, book, books, library,
