Smoothed Bagging with Kernel Bandwidth Selectors

Abstract

Recently, a combined approach of bagging (bootstrap aggregating) and noise addition was proposed and shown to result in a significantly improved generalization performance. But, the level of noise introduced, a crucial factor, was determined by trial and error. The procedure is not only ad hoc but also time consuming since bagging involves training a committee of networks. Here we propose a principled procedure of computing the level of noise, which is also computationally less expensive. The idea comes from kernel density estimation (KDE), a non-parametric probability density estimation method where appropriate kernel functions such as Gaussian are imposed on data. The kernel bandwidth selector is a numerical method for finding the width of a kernel function (called bandwidth). The computed bandwidth can be used as the variance of added noise. The proposed approach makes the trial and error procedure unnecessary, and thus provides a much faster way of finding an appropriate level of noise. In addition, experimental results show that the proposed approach results in an improved performance over bagging, particularly for noisy data.