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Learning Bayesian Networks with Heterogeneous Agronomic Data Sets via Mixed-Effect Models and Hierarchical Clustering

Abstract

Maize is a major crop providing vital calories in sub-Saharan Africa, Asia and Latin America, with a global cultivation area of 197 million hectares in 2021. Therefore, many statistical models (such as mixed-effect and random coefficients models) and machine learning models (such as random forests and deep learning architectures) have been developed to predict maize yield and how it is affected by genotype, environment and genotype-environment interaction factors, including field management. However, these models do not fully leverage the network of causal relationships between these factors and the hierarchical structure of the agronomic data arising from data collection. Bayesian networks (BNs) provide a powerful framework for modelling causal and probabilistic relationships using directed acyclic graphs to illustrate the connections between variables. This study introduces a novel approach that integrates random effects into BN learning. Rooted in the linear mixed-effects models framework, it is particularly well-suited to hierarchical data. Results from a real-world agronomic trial suggest that the proposed approach enhances BN learning, leading to a more interpretable model and discovering new causal connections. At the same time, the error rate of maize yield prediction is reduced from 28% to 17%. Therefore, we argue that BNs should be the tool of choice to construct practical decision support tools for hierarchical agronomic data that allow for causal inference.

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