Relevance vector machine

In today's article we will delve into the fascinating world of Relevance vector machine. Since its inception, Relevance vector machine has been the subject of interest and study, capturing the attention of those seeking to further understand its nuances and complexities. Throughout history, Relevance vector machine has been the protagonist of countless debates, discussions and reflections, being a topic that encompasses a wide range of perspectives and approaches. With so much to discover and analyze, it is evident that Relevance vector machine continues to be a topic of relevance today, sparking the interest of academics, enthusiasts and the curious alike. In this article, we will explore the highlights of Relevance vector machine, diving into its history, evolution, and its impact on various areas of society.

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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. 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(\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 $\varphi$ is the kernel function (usually Gaussian), $\alpha _{j}$ are the variances of the prior on the weight vector $w\sim N(0,\alpha ^{-1}I)$ , and $\mathbf {x} _{1},\ldots ,\mathbf {x} _{N}$ are the input vectors of the training set.

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).

References

^ 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"

Software

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

Relevance vector machine

See also

References

Software

External links

Wikious

Boobota

Sagapedia