EPGLM

R codes for efficient expectation propagation for generalized linear models under Gaussian prior.

Authors: Niccolò Anceschi, Augusto Fasano, Beatrice Franzolini, and Giovanni Rebaudo.

Overview

This repository is associated with the article Anceschi, Fasano, Franzolini, and Rebaudo (2024+) Scalable expectation propagation for generalized linear models.

The key contribution of the paper is outlined below.

[...] We [...] deriv[e] a novel efficient formulation of \ep for \textsc{glm}s, whose cost scales linearly in the number of covariates p, and reducing the state-of-the-art O(p²n) per-iteration computational cost of the \ep routine for GLMs to O(p n min{p,n}), with n being the sample size. We also show that, for binary models and log-linear GLMs approximate predictive means can be obtained at no additional cost. To preserve efficient moment matching for count data, we propose employing a combination of log-normal Laplace transform approximations, avoiding numerical integration. These novel results open the possibility of employing EP in settings that were believed to be practically impossible.

More precisely, we provide the R code to implement Algorithms 1 and 2 in Anceschi, Fasano, Franzolini, and Rebaudo (2024+) and replicate the results of their Illustration.

The repository contains the following:

1. EPGLM_illustrationProbit.R code to reproduce the results in Section 5.1;
2. EPGLM_illustrationPoisson.R code to reproduce the results in Section 5.2;
3. EPGLM_fcts.R functions needed to run the main code;
4. Data-and-Results folder with data and results of the analyses.