Imputing relative abundances via Gaussian random fields
Longitudinal studies with human participants frequently face the challenge of missing samples, which lead to incomplete trajectories of participant biomarkers and a reduction in data size. Existing approaches focus on single-variable imputation or model features one at a time, while neural networks typically require a large number of parameters and substantial training data. To address these challenges, we present an explainable model for multiple imputation of compositional samples based on a Gaussian random field (GRF). The model is specifically designed for longitudinal data: it incorporates participant-specific information and accounts for both temporal dependence across repeated observations and within-sample correlations, while using a moderate number of parameters. By coupling the GRF with sparse activation functions, the framework outputs sum-constrained compositions and explicitly models zero inflation. Under the Aitchison and Jensen--Shannon distances, our framework achieves imputation accuracy comparable to that of an observation-carrying baseline, while overcoming its static nature by modeling temporal trajectories and multivariate correlations. The resulting multiple imputations allow us to reconstruct complete datasets for downstream analysis and uncertainty quantification. We demonstrate the practical utility of our framework on gut microbiome datasets, restoring incomplete time series and achieving a balanced accuracy of 0.72 in predicting food allergy in infants (sensitivity 0.8) and of 0.64 in forecasting postpartum depression.