On boosting kernel density methods for multivariate data: density estimation and classification

Statistical learning is emerging as a promising field where a number of algorithms from machine learning are interpreted as statistical methods and vice–versa. Due to good practical performance, boosting is one of the most studied machine learning techniques. We propose algorithms for multivariate density estimation and classification. They are generated by using the traditional kernel techniques as weak learners in boosting algorithms. Our algorithms take the form of multistep estimators, whose first step is a standard kernel method. Some strategies for bandwidth selection are also discussed with regard both to the standard kernel density classification problem, and to our ‘boosted’ kernel methods. Extensive experiments, using real and simulated data, show an encouraging practical relevance of the findings. Standard kernel methods are often outperformed by the first boosting iterations and in correspondence of several bandwidth values. In addition, the practical effectiveness of our classification algorithm is confirmed by a comparative study on two real datasets, the competitors being trees including AdaBoosting with trees.