Sparse Bayesian Regression Modeling via the Relevance Vector Machine

• Activity Number: 356
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Kazuki Matsuda*+ and Sadanori Konishi
• Companies: and Chuo University
• Keywords: Bayesian predictive distributions ; Information criterion ; Nonlinear regression ; Sparse Bayesian learning

Abstract

The relevance vector machine (Tipping, 2001) has emerged as a useful tool for constructing sparse regression models and classifiers, which sets many weights to zero in the estimated models. This attractive feature relies on appropriate choice of basis functions and tuning parameters, which essentially control the model complexity. Choosing the optimal model from a predictive point of view by applying cross-validation can result in computational difficulties and often yields unstable model estimates. We introduce model selection criteria for evaluating models constructed by the relevance vector machine for regression. We also propose nonlinear regression modeling based on multi-overlapping basis functions via the RVM. Monte Carlo experiments are conducted to examine the properties of our sparse Bayesian regression modeling.