Heterogeneity and complexity of biomedical data are a crucial pitfall for modeling neurodegeneration in clinical studies. Modern analysis approaches are required to account for measurements' uncertainty and variability, as well as for the typical large dimensionality of biomedical information. Moreover, model interpretability is an imperative requirement for the clinical translation of automated analysis methods. This project addresses these challenges through three major research axes. The first axis concerns the investigation of novel approaches for the probabilistic modeling of spatio-temporal variations in biomedical data. This research leverages on the extension of non-parametric learning methods, such as Gaussian process (GP) regression, to account for high-dimensional and spatio-temporally correlated signals. Furthermore, it introduces a consistent framework for modeling and inference of the dynamical systems describing the potential bio-mechanical properties governing biological data. The second axis contributes to the definition of learning algorithms for modeling the joint variation between heterogeneous information, such as imaging, clinical, and biological data. Firstly, by defining novel validation strategies for multivariate models applied to high-dimensional brain imaging-genetics and cardiac data. Secondly, by introducing novel formulations of probabilistic latent variable models, where latent representations issued from multiple data views (or channels) are constrained to match a common target latent distribution. The last axis represents a novel direction of investigation aimed at reformulating inference in probabilistic models to cope with the constraint of data privacy and security in multi-centric studies. This research direction addresses an important societal problem, for biomedical data hosted in hospitals usually cannot be shared due to privacy and legal issues. This problem is here tackled by extending variational inference in Bayesian models to the setting of federated learning.