Integrating Neural Encoders in Bayesian Generalized Linear Mixed Models for Multimodal Data
For researchers analyzing longitudinal data with mixed structured and high-dimensional modalities, this provides a scalable Bayesian framework with interpretable fixed/random effects and uncertainty quantification, though it is an incremental extension of existing GLMM and neural encoder methods.
This work integrates neural encoders into Bayesian GLMMs to handle high-dimensional multimodal data (e.g., images, text) alongside structured covariates, enabling uncertainty-aware analysis of longitudinal data. The method recovers posterior means and variance estimates comparable to full-data MCMC benchmarks in simulations and demonstrates utility in glaucoma and mental health applications.
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.