Variational Inference for Additive Main and Multiplicative Interaction Effects Models

TL;DR

This paper introduces a variational inference method for AMMI models in plant breeding, enabling faster computation of GxE interactions while maintaining accuracy, especially useful for high-dimensional data.

Contribution

It develops a variational inference framework for AMMI models, offering a computationally efficient alternative to MCMC with comparable predictive performance.

Findings

Variational inference is approximately twice as fast as MCMC.

The method maintains similar predictive accuracy to traditional MCMC.

Effective for high-dimensional GxE interaction modeling.

Abstract

In plant breeding the presence of a genotype by environment (GxE) interaction has a strong impact on cultivation decision making and the introduction of new crop cultivars. The combination of linear and bilinear terms has been shown to be very useful in modelling this type of data. A widely-used approach to identify GxE is the Additive Main Effects and Multiplicative Interaction Effects (AMMI) model. However, as data frequently can be high-dimensional, Markov chain Monte Carlo (MCMC) approaches can be computationally infeasible. In this article, we consider a variational inference approach for such a model. We derive variational approximations for estimating the parameters and we compare the approximations to MCMC using both simulated and real data. The new inferential framework we propose is on average two times faster whilst maintaining the same predictive performance as MCMC.