Gregory A. Ross

Github repositiory: Langevin neural nets
I find Bayesian inference very appealing because it forces us to confront what we know and do not know about the phenomena we are trying to model. Fortunately for me there is a one-to-one correspondence between molecular dynamics simulations and Bayesian inference. The same computational methods that are used to sample molecular configurations can be directly applied to sample the parameters of Bayesian models.

Neural networks are very flexible function approximators and, when combined with Bayesian methods, offer the possiblity of performing robust inference on almost any problem. Like molecular simulations, neural nets can have an extremely large number of parameters that can be difficult to infer. This project is about applying the kinds of sampling methods I'm used to developing and using on molecular dynamics to neural nets.

Github repositiory: Deep marginal likelihoods
When attempting to create quantitative and predictive models of data, one seldom has a single model in mind. At some point, one inevitably has to select aspects of the model like the functional form and the number of parameters. The formal approach to this choice is known as model selection, which can be an immensely complex and difficult task to do rigorously. The singular interest of this project is model selection in a Bayesian context, whose framework naturally admits a quantity - the marginal likelihood or marginal evidence - through which all models can be judged and compared.

In this project, I've derived an upper bound to the marginal likelihood that can be computed with deep learning methods. Bayesian analysis and machine learning are often (wrongly) considered to be distinct approaches, and, in this project, it's been fun to make to connect the two fields so explicitly. My prototyped codes provides validation of my analytical results.

A huge part of my research centers around free energy calculations in molecular simulations, which has a direct correspondence with Bayesian model seletion. This project draws on some of this experience.