# Variational Inference for Additive Main and Multiplicative Interaction Effects Models

arXiv: https://arxiv.org/abs/2207.00011 · HTML: https://mlsanity.com/paper/2207.00011/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 43 references that are in the map.
- First posted on arXiv 29 Jun 2022.

## Builds on (most cited first, 2 of 2)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Good Initializations of Variational Bayes for Deep Models](https://mlsanity.com/paper/1810.08083/) (2018)

## Built on by (most cited first, 1 of 1)

- [Bayesian Additive Main Effects and Multiplicative Interaction Models using Tensor Regression for Multi-environmental Trials](https://mlsanity.com/paper/2301.03655/) (2023)

## Abstract (arXiv)

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.