Probabilistic Deep Learning via Hierarchical Stochastic Partial Differential Equations

Deep learning, using either artificial neural networks or probabilistic deep Gaussian processes, is a popular machine learning technique with a strong optimization-based engineering tradition that has obtained its popularity through the ever-increasing computational power. In this project, we developed a novel family of hierarchical stochastic partial differential equation models and methods which can be used to replace deep GPs as scalable fully probabilistic alternatives to the problem of deep learning. This leads to computational advantages and clear statistical interpretation of all the random fields and parameters.