Stochastic Variational Inference for Latent Gaussian Models

• Applicants: Professor Dr. Thomas Kneib; Dr. Johannes Söding
• Subject Area: Statistics and Econometrics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 527917760

In this project, we will develop a generic and versatile stochastic variational inference (SVI) approach for approximate Bayesian inference for different types of Latent Gaussian Models (LGMs). Focusing on LGMs as the underlying model class will enable us to develop approaches that are specific enough to achieve efficiency gains compared to Bayesian inference based on Markov chain Monte Carlo (MCMC) simulations while at the same time maintaining enough flexibility with respect to the variational family such as in generic black box variational inference. Multivariate distributional LGMs and Bayesian sparse regression will be considered as special cases for the application in challenging case studies. Stochastic variational inference in multivariate distributional regression will allow us to perform analyses of multidimensional malnutrition and poverty risks as well as multivariate health outcomes based on large medical data sets. Bayesian sparse linear regression requires a binary latent inclusion variable for each of the covariate effects. The discreteness of the problem renders it inefficient not only for MCMC-based methods but also for state-of-the-art SVI. We will develop a novel estimator that is applicable to discrete variables and apply this estimator in human genetics to predict expression quantitative trait locus (eQTL) genetic variants.

• DFG Programme: Research Grants