Approximate inference of the bandwidth in multivariate kernel density estimation

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 its strong asymptotic results regarding 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. An approximate Bayesian method is proposed, based on the Expectation–Propagation algorithm with a likelihood obtained from a leave-one-out cross validation approach. The proposed method yields an iterative procedure to approximate the posterior distribution of the inverse bandwidth. The approximate posterior can be used to estimate the model evidence for selecting the structure of the bandwidth and approach online learning. Extensive experimental validation shows that the proposed method is competitive in terms of performance with state-of-the-art plug-in methods.

► We study the problem of inferring of the bandwidth in multivariate KDE.
► An approximate inference method is proposed, based on Expectation Propagation.
► We study model selection and online learning with the approximate method.
► Results show that this is a fast alternative to MCMC for Bayesian KDE.
► Performances are comparable to those of other bandwidth selectors.