An Analysis of Relevance Vector Machine Regression

The relevance vector machine (RVM) is a Bayesian framework for learning sparse regression models and classifiers. Despite of its popularity and practical success, no thorough analysis of its functionality exists. In this paper we consider the RVM in the case of regression models and present two kinds of analysis results: we derive a full characterization of the behavior of the RVM analytically when the columns of the regression matrix are orthogonal and give some results concerning scale and rotation invariance of the RVM. We also consider the practical implications of our results and present a scenario in which our results can be used to detect potential weakness in the RVM framework.