Integrating Neural Encoders in Bayesian Generalized Linear Mixed Models for Multimodal Data
2026-07-06 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a scalable method to analyze complex longitudinal data that includes images or text, not just simple tables. They use neural networks to turn high-dimensional data into simpler forms that work with a statistical model called a generalized linear mixed model (GLMM). Their approach combines learning from data with measuring uncertainty in predictions for groups and individuals. Tests showed their method matches traditional full-data approaches in accuracy and uncertainty estimates, and it works well on health data about glaucoma and mental health. This lets researchers understand how different types of data contribute to outcomes without losing prediction quality.
Bayesian inferenceGeneralized linear mixed modelsNeural encodersStochastic gradient MCMCLongitudinal dataPosterior uncertaintyRepresentation learningRandom effectsPredictive calibrationMultimodal data
Authors
Yuankang Zhao, Youngsoo Baek, Felipe A. Medeiros, Samuel Berchuck, Matthew M. Engelhard
Abstract
Scalable Bayesian inference for generalized linear mixed models (GLMMs) provides uncertainty-aware analysis of correlated longitudinal data, but existing scalable approaches largely assume low-dimensional tabular predictors and do not directly accommodate high-dimensional modalities such as images and text. We address this limitation by learning one or more modality-specific neural encoders jointly with a GLMM objective, then performing variance-corrected stochasticgradient MCMC for the GLMM parameters conditional on the learned representation. This conditional-Bayes design combines supervised representation learning with posterior uncertainty quantification for population-level effects, subjectspecific heterogeneity, and modality-level random slopes. The resulting model preserves interpretable fixed and random effects for structured covariates and learned modalities while scaling gracefully to large longitudinal datasets. In simulation studies, our method recovers posterior means and variance estimates from full-data MCMC benchmarks after covariance correction. We further evaluate uncertainty through parameter-level interval coverage in simulations and predictive calibration on held-out data. Applications to glaucoma progression and adolescent mental health demonstrate that the framework allows nuanced assessment of the relative importance of each modality on both individual and population levels without sacrificing predictive performance.