Inference for Stationary Processes: Optimal Transport and Generalized Bayesian Approaches

This project will address the problem of making inferences about sequences of observations that exhibit dependence arising from physical or other interactions. Observations of this sort occur in many fields, including finance, ecology, natural language processing, and biology. We will explore ways to fit a sequence of observations to a family of statistical models using ideas from the theory of optimal transport.

Informally, we will identify models in the family into which the generating mechanism of the observations can be transformed with the least overall cost. We will address both the theory and efficient computation of these transformation costs, and will consider applications to biomedicine and computer science. The project will involve collaborations with graduate students and more senior researchers working in genomics and bioinformatics.

Both undergraduate and graduate students will receive training through involvement in supported research projects.

On a more technical level, this project will address inference for stochastic processes, in particular, how to fit a family of stationary processes to an observed ergodic process, revealed sequentially. Research will focus on the use and extension of ideas from optimal transport, including stationary couplings of stationary processes and related variational quantities, with a focus on methods development and supporting theory.

The research has two primary aims. The first aim is to investigate minimum divergence estimation based on joinings, including the use and properties of entropy regularization. The second aim is to investigate the efficient computation of optimal transition couplings of Markov chains, with applications to graph distances, graph alignment, and hidden Markov models.

The project will involve collaborations with graduate students and more senior researchers working in genomics and bioinformatics. Both undergraduate and graduate students will receive training through involvement in supported research projects.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.