Bayesian Additive Main Effects and Multiplicative Interaction Models using Tensor Regression for Multi-environmental Trials

TL;DR

This paper introduces a Bayesian tensor regression model for multi-environmental trials that effectively captures complex interactions and identifies relevant factors, outperforming existing methods in simulations and real-world wheat production data.

Contribution

It presents a novel Bayesian tensor regression approach with spike-and-slab priors for variable selection, addressing identifiability and interaction relevance in multi-factor phenotype prediction.

Findings

Outperforms previous models and machine learning algorithms in simulations.

Achieves competitive results on real-world wheat production data.

Provides visual tools for interpreting tensor effects and interactions.

Abstract

We propose a Bayesian tensor regression model to accommodate the effect of multiple factors on phenotype prediction. We adopt a set of prior distributions that resolve identifiability issues that may arise between the parameters in the model. Further, we incorporate a spike-and-slab structure that identifies which interactions are relevant for inclusion in the linear predictor, even when they form a subset of the available variables. Simulation experiments show that our method outperforms previous related models and machine learning algorithms under different sample sizes and degrees of complexity. We further explore the applicability of our model by analysing real-world data related to wheat production across Ireland from 2010 to 2019. Our model performs competitively and overcomes key limitations found in other analogous approaches. Finally, we adapt a set of visualisations for the posterior distribution of the tensor effects that facilitate the identification of optimal interactions between the tensor variables, whilst accounting for the uncertainty in the posterior distribution.