Video Lectures

Existing generative models are typically based on explicit representations of probability distributions (e.g., autoregressive or VAEs) or implicit sampling procedures (e.g., GANs). We propose an alternative approach based on modeling directly the...

Given a Lipschitz map, it is often useful to chop the domain into pieces on which the map has simple behavior. For example, depending on the dimensions of source and target, one may ask for pieces on which the map behaves like a bi-Lipschitz...

Distributed learning protocols are designed to train on distributed data without gathering it all on a single centralized machine, thus contributing to the efficiency of the system and enhancing its privacy. We study a central problem in distributed...

In randomized experiments, such as a medical trials, we randomly assign the treatment, such as a drug or a placebo, that each experimental subject receives. Randomization can help us accurately estimate the difference in treatment effects with high...

In this talk, I will address a geometric inverse problem from contact geometry: is it possible to recognize whether all orbits of a given Reeb flow are closed from the knowledge of the action spectrum? Borrowing the terminology from Riemannian...

Establishing the conjectured analytic properties of triple product L-functions is a crucial case of Langlands functoriality. However, little is known. I will present work in progress on the case of triples of automorphic representations on GL_3; in...

A possible high level description of statistical learning is that it aims to learn about some unknown probability distribution ("environment”) from samples it generates ("training data”). In its most general form, assuming no prior knowledge and...

We study boosting algorithms under the assumption that the given weak learner outputs hypotheses from a class of bounded capacity. This assumption is inspired by the common convention that weak hypotheses are “rules-of-thumbs” from an “easy-to-learn...

Proof Complexity studies the length of proofs of propositional tautologies in various restricted proof systems. One of the most well-studied is the Cutting Planes proof system, which captures reasoning which can be expressed using linear...

We show that a topologically mixing C^\infty Anosov flow on a 3 dimensional compact manifold is exponential mixing with respect to any equilibrium measure with Holder potential. This is a joint work with Masato Tsujii.