Bayesian Relational Generative Model for Scalable Multi-modal Learning

The study of complex systems requires the integration of multiple heterogeneous and high-dimensional data types (e.g. multi-omics). However, previous generative approaches for multi-modal inputs suffer from two shortcomings. First, they are not stochastic processes, leading to poor uncertainty estimations over their predictions. This is mostly due to the computationally intensive nature of traditional stochastic processes, such as Gaussian Processes (GPs), that makes their applicability limited in multi-modal learning frameworks. Second, they are not able to effectively approximate the joint posterior distribution of multi-modal data types with various missing patterns. More precisely, their model assumptions result in miscalibrated precisions and/or computational cost of sub-sampling procedure. In this paper, we propose a class of stochastic processes that learns a graph of dependencies between samples across multi-modal data types through adopting priors over the relational structure of the given data modalities. The dependency graph in our method, multi-modal Relational Neural Process (mRNP), not only posits distributions over the functions and naturally enables rapid adaptation to new observations by its predictive distribution, but also makes mRNP scalable to large datasets through mini-batch optimization. We also introduce mixture-of-graphs (MoG) in our model construction and show that it can address the aforementioned limitations in joint posterior approximation. Experiments on both toy regression and classification tasks using real-world datasets demonstrate the potential of mRNP for offering higher prediction accuracies as well as more robust uncertainty estimates compared to existing baselines and state-of-the-art methods.