epkde

Bayesian Bandwidth Selection for Multivariate KDE via Expectation Propagation

epkde implements the approximate Bayesian method for bandwidth selection in multivariate kernel density estimation (KDE) from Filippone & Sanguinetti (2011). The method uses the Expectation Propagation (EP) algorithm to approximate the posterior distribution of the kernel precision matrix under a leave-one-out cross-validated likelihood.

Three covariance structures are supported:

• Isotropic — scalar precision (fastest)
• Diagonal — per-dimension precisions
• Full — unconstrained precision matrix

An online variant is also provided for the isotropic case, allowing incremental updates as new data arrive.

Installation

# From GitHub
# devtools::install_github("mauriziofilippone/epkde")
install.packages("epkde", repos = c('https://mauriziofilippone.r-universe.dev', 'https://cloud.r-project.org'))

Quick start

library(epkde)
set.seed(1)

# Fit isotropic EP bandwidth to bivariate data
x <- matrix(rnorm(200 * 2), ncol = 2)
fit <- ep_kde_isotropic(x, prior_shape = 1, prior_rate = 1)

# Posterior mean precision
lambda_hat <- fit$post_shape / fit$post_rate
cat("Posterior mean precision:", lambda_hat, "\n")
cat("Log model evidence:", fit$log_evidence, "\n")

# Evaluate the KDE at test points
x_test <- matrix(c(0, 0, 1, 1), ncol = 2)
Lambda  <- lambda_hat * diag(2)
p_hat   <- kde_predict(x_test, x, Lambda)

# Compare models via Bayes factors
fit_diag <- ep_kde_diagonal(x, prior_shape = rep(1, 2), prior_rate = rep(1, 2))
cat("Log BF (diagonal vs isotropic):",
    model_evidence(fit_diag) - model_evidence(fit), "\n")

Functions

Function	Description
ep_kde_isotropic()	EP for scalar (isotropic) precision
ep_kde_diagonal()	EP for diagonal precision matrix
ep_kde_full()	EP for full precision matrix
ep_kde_online()	Online EP update for isotropic precision
kde_predict()	Evaluate the KDE at test points
model_evidence()	Extract log model evidence for model comparison

Reference

Filippone, M. & Sanguinetti, G. (2011). Approximate inference of the bandwidth in multivariate kernel density estimation. Computational Statistics & Data Analysis, 55(12), 3104–3122. https://doi.org/10.1016/j.csda.2011.05.023

License

GPL-3 © Maurizio Filippone