Sparse regularized local regression

Authors:
Diego Vidaurre;Concha Bielza;Pedro LarrañAga
Affiliations:
Oxford Centre for Human Brain Activity, Warneford Hospital, Department of Psychiatry, University of Oxford, UK;Computational Intelligence Group, Departamento de Inteligencia Artificial, Universidad Politécnica de Madrid, Spain;Computational Intelligence Group, Departamento de Inteligencia Artificial, Universidad Politécnica de Madrid, Spain
Venue:
Computational Statistics & Data Analysis
Year:
2013

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Abstract

The intention is to provide a Bayesian formulation of regularized local linear regression, combined with techniques for optimal bandwidth selection. This approach arises from the idea that only those covariates that are found to be relevant for the regression function should be considered by the kernel function used to define the neighborhood of the point of interest. However, the regression function itself depends on the kernel function. A maximum posterior joint estimation of the regression parameters is given. Also, an alternative algorithm based on sampling techniques is developed for finding both the regression parameter distribution and the predictive distribution.