In many domains in science, medicine, and engineering, computational methods for simulation, uncertainty quantification, and experimental design are becoming increasingly important. However, a key challenge in these domains is dealing with computationally expensive methods. In some problems, massive and high-dimensional data require algorithms that can scale to those settings. In other problems, accurate models for complex systems are expensive to evaluate, such as an expensive physical simulation, or observations may be expensive to gather.
I am developing computational methods with the goal of accelerating and improving the performance of approximate Bayesian inference methods and methods for decision making under uncertainty. Some current research directions include:
- Developing multi-fidelity methods for MCMC with expensive target densities and online Bayesian changepoint detection with expensive observations
- Developing general-purpose reparameterization gradient approaches that allow for, e.g., variational Bayesian inference with more flexible model families or sensitivity analysis of a posterior functional
- Developing methods for data approximation, such as count sketching and random projections