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

arXiv: https://arxiv.org/abs/2301.03655 · HTML: https://mlsanity.com/paper/2301.03655/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 48 references that are in the map.
- First posted on arXiv 9 Jan 2023.

## Builds on (most cited first, 6 of 6)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Bayesian Tensor Regression](https://mlsanity.com/paper/1509.06490/) (2015)
- [ISLET: Fast and Optimal Low-rank Tensor Regression via Importance Sketching](https://mlsanity.com/paper/1911.03804/) (2019)
- [Probabilistic PARAFAC2](https://mlsanity.com/paper/1806.08195/) (2018)
- [Soft Tensor Regression](https://mlsanity.com/paper/1910.09699/) (2019)
- [Variational Inference for Additive Main and Multiplicative Interaction Effects Models](https://mlsanity.com/paper/2207.00011/) (2022)

## Abstract (arXiv)

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.