arXiv subjects

Fred A. van Eeuwijk

Publications and source records attributed to Fred A. van Eeuwijk.

5 recordsLinked to original sources

arXiv2026

A hybrid GPU/CPU implementation of the average information restricted maximum likelihood algorithm for fitting multivariate linear mixed models

The multivariate linear mixed model combined with restricted maximum likelihood estimation of (co)variance components and solving the mixed model equations is widely used for the analysis of plant breeding data. Several algorithms for restricted maximum likelihood estimation have been proposed, with the average information algorithm being widely used for its computational efficiency, quadratic rate of convergence, and ability to handle large amounts of parameters. A key reason for the scalability of linear mixed models is the exploitation of sparse matrix techniques. Recently, decreasing costs of high-throughput data collection have led to high-dimensional sets of features characterizing genotypes and environments. A convenient way of using these features is through the use of kernel-based covariance structures. However, while convenient, these kernels typically have dense inverses meaning optimizations based on sparse matrix techniques are not always applicable. For these settings, the introduction of general-purpose computing on graphics processing units brought significant computational advantages for dense linear algebra operations. We present a hybrid GPU/CPU implementation of the average information restricted maximum likelihood algorithm. We eliminate sparse equations using supernodal Cholesky factorization and rely on CUDA GPU acceleration to solve the resulting reduced dense system. We show the significant computational advantages of this approach for fully dense problems, as well as problems with a mix of dense and sparse equations.

stat.CO↗

arXiv2026

REML implementations of kernel-based genomic prediction models for genotype x environment x management interactions

High-throughput pheno-, geno-, and envirotyping allows characterization of plant genotypes and the trials they are evaluated in, producing different types of data. These different data modalities can be integrated into statistical or machine learning models for genomic prediction in several ways. One commonly used approach within the analysis of multi-environment trial data in plant breeding is to create linear or nonlinear kernels which are subsequently used in linear mixed models (LMMs) to model genotype by environment (G$\times$E) interactions. Current implementations of these kernel-based LMMs present a number of opportunities in terms of methodological extensions. Here we show how these models can be implemented in standard software, allowing direct restricted maximum likelihood (REML) estimation of all parameters. We also further extend the models by combining the kernels with unstructured covariance matrices for three-way interactions in genotype by environment by management (G$\times$E$\times$M) datasets, while simultaneously allowing for environment-specific genetic variances. We show how the models incorporating nonlinear kernels and heterogeneous variances maximize the amount of genetic variance captured by environmental covariables and perform best in prediction settings. We discuss the opportunities regarding models with multiple kernels or kernels obtained after environmental feature selection, as well as the similarities to models regressing phenotypes on latent and observed environmental covariables. Finally, we discuss the flexibility provided by our implementation in terms of modeling complex plant breeding datasets, allowing for straightforward integration of phenomics, enviromics, and genomics.

stat.ME↗

arXiv2026

A latent factor approach to hyperspectral time series data for multivariate genomic prediction of grain yield in wheat

High-dimensional time series phenotypic data is becoming increasingly common within plant breeding programmes. However, analysing and integrating such data for genetic analysis and genomic prediction remains difficult. Here we show how factor analysis with Procrustes rotation on the genetic correlation matrix of hyperspectral secondary phenotype data can help in extracting relevant features for within-trial prediction. We use a subset of Centro Internacional de Mejoramiento de Maíz y Trigo (CIMMYT) elite yield wheat trial of 2014-2015, consisting of 1,033 genotypes. These were measured across three irrigation treatments at several timepoints during the season, using manned airplane flights with hyperspectral sensors capturing 62 bands in the spectrum of 385-850 nm. We perform multivariate genomic prediction using latent variables to improve within-trial genomic predictive ability (PA) of wheat grain yield within three distinct watering treatments. By integrating latent variables of the hyperspectral data in a multivariate genomic prediction model, we are able to achieve an absolute gain of .1 to .3 (on the correlation scale) in PA compared to univariate genomic prediction. Furthermore, we show which timepoints within a trial are important and how these relate to plant growth stages. This paper showcases how domain knowledge and data-driven approaches can be combined to increase PA and gain new insights from sensor data of high-throughput phenotyping platforms.

stat.AP↗

arXiv2025

Improving Genomic Prediction using High-dimensional Secondary Phenotypes: the Genetic Latent Factor Approach

Decreasing costs and new technologies have led to an increase in the amount of data available to plant breeding programs. High-throughput phenotyping (HTP) platforms routinely generate high-dimensional datasets of secondary features that may be used to improve genomic prediction accuracy. However, integration of these data comes with challenges such as multicollinearity, parameter estimation in $p > n$ settings, and the computational complexity of many standard approaches. Several methods have emerged to analyze such data, but interpretation of model parameters often remains challenging. We propose genetic latent factor best linear unbiased prediction (glfBLUP), a prediction pipeline that reduces the dimensionality of the original secondary HTP data using generative factor analysis. In short, glfBLUP uses redundancy filtered and regularized genetic and residual correlation matrices to fit a maximum likelihood factor model and estimate genetic latent factor scores. These latent factors are subsequently used in multi-trait genomic prediction. Our approach performs better than alternatives in extensive simulations and a real-world application, while producing easily interpretable and biologically relevant parameters. We discuss several possible extensions and highlight glfBLUP as the basis for a flexible and modular multi-trait genomic prediction framework.

stat.ME↗

arXiv2016

Spatial Models for Field Trials

An important aim of the analysis of agricultural field trials is to obtain good predictions for genotypic performance, by correcting for spatial effects. In practice these corrections turn out to be complicated, since there can be different types of spatial effects; those due to management interventions applied to the field plots and those due to various kinds of erratic spatial trends. This paper presents models for field trials in which the random spatial component consists of tensor product Penalized splines (P-splines). A special ANOVA-type reformulation leads to five smooth additive spatial components, which form the basis of a mixed model with five unknown variance components. On top of this spatial field, effects of genotypes, blocks, replicates, and/or other sources of spatial variation are described by a mixed model in a standard way. We show the relation between several definitions of heritability and the effective dimension or the effective degrees of freedom associated to the genetic component. The approach is illustrated with large-scale field trial experiments. An R-package is provided.

stat.ME↗