Approximate inference of the bandwidth in multivariate kernel density estimation
Maurizio Filippone and Guido Sanguinetti
Computational Statistics & Data Analysis
Kernel density estimation is a popular and widely used non-parametric method for data-driven density estimation. Its appeal lies in its simplicity and ease of implementation, as well as strong asymptotic results on its convergence to the true data distribution. However, a major difficulty is the setting of the bandwidth, particularly in high dimensions and with limited amount of data. Here we propose an approximate Bayesian method based on the Expectation-Propagation algorithm with a likelihood obtained from a leave-one-out cross validation approach. We study how to use the results of the approximate method to select the structure of the bandwidth and perform online learning. Through extensive experimental validation, we also show that the proposed method is competitive in terms of performance with state-of-the-art plug-in methods.