pyreml: a general-purpose, GPU-accelerated mixed model solver in Python

Linear mixed models (LMM) are widely used in bioinformatics and other scientific fields for modeling and inference. To accurately estimate variance components, LMMs require restricted maximum likelihood (REML) fitting, which is a computationally demanding process. Currently, there is no Python library that offers complete LMM functionalities, such as the ability to specify spatial and genomic variance structures, multivariate analyses, random regression, factors, and heteroscedastic residuals.

To address this gap, we introduce pyreml, an LMM solver written in Python. This new solver provides a user-centered interface and significantly speeds up calculations by leveraging GPU acceleration. Our research demonstrates that pyreml can fit a genomic best linear unbiased prediction (GBLUP) model more than 12 times faster than the current state-of-the-art closed source REML software.

In addition, pyreml is capable of estimating complex latent factor-analytic variance structures, a feature that is currently missing from all open source REML solutions.

We also illustrate the versatility of pyreml by showing its application in analyzing longitudinal data and performing spatial analysis. To ensure the reliability of our solver, we have anchored pyreml with over 500 functional tests that compare its outputs to those from reference software (lme4, rrBLUP, and BLUPF90). These tests confirm that pyreml is a performant, reliable, and open-source solution that caters to the needs of academic, research, and industrial users working with linear mixed models.