Nonparametric Bayesian Statistics

Bayesian nonparametrics provides modeling solutions by replacing the finite-dimensional prior distributions of classical Bayesian analysis with infinite-dimensional stochastic processes.

Causal inference algebraic statistics gene regulatory networks

Causal inference and applications to learning gene regulatory networks

Causal inference: Geometry of conditional independence structures for 3-node directed Gaussian graphical models.

Combinatorial learning submodular functions

Combinatorial learning with set functions

Learning problems that involve combinatorial objects are ubiquitous - they include the prediction of graphs, assignments, rankings, trees, groups of discrete labels or preferred sets of a user; the expression of prior structural knowledge for regularization, the identification of sets of important variables, or inference in discrete probabilistic models.

Online Learning

In this line of research, we develop strategies to optimize utility in dynamic environments in an optimal and efficient fashion.

Statistical and Computational Tradeoffs

Statistical and Computational Tradeoffs

Computational limitations of statistical problems have largely been ignored or simply overcome by ad hoc relaxations techniques.