Drawing meaningful conclusions on the way complex real life phenomena work and being able to predict the behavior of systems of interest requires developing accurate and highly interpretable mathematical models whose parameters need to be estimated from data. In modern applications of data modeling, however, we are often challenged with the lack of such models, and even when these are available they are too computational demanding to be suitable for standard parameter optimization/inference. Deep learning techniques have become extremely popular to tackle such challenges in an effective way, but they do not offer satisfactory performance in applications where quantification of uncertainty is of primary interest. Bayesian Deep Learning techniques have been proposed to combine the representational power of deep learning techniques with the ability to accurately quantify uncertainty thanks to their probabilistic treatment. While attractive from a theoretical standpoint, the application of Bayesian Deep Learning techniques poses huge computational and statistical challenges that arguably hinder their wide adoption. In this talk, I will present new trends in Bayesian Deep Learning, with particular emphasis on practical and scalable inference techniques and applications.
