Past Events

Random high-dimensional cost functions and random probability distributions arise in a number of applied fields. For instance, in high-dimensional statistics, an M-estimator is the solution of a random optimization problem (the randomness being...

Sampling is a fundamental and widespread algorithmic primitive that lies at the heart of Bayesian inference and scientific computing, among other disciplines. Recent years have seen a flood of works aimed at laying down the theoretical underpinnings...

Curvature is one of the fundamental ingredients in differential geometry. People are increasingly interested in whether it is possible to think of combinatorial graphs as manifolds and a number of different notions of curvature have been proposed. I...

What are the optimal algorithms for learning from data? Have we found them already, or are better ones out there to be discovered? Making these questions precise, and answering them, requires taking on the mathematically deep interplay between...

In this talk, we will first review the concept of inverse-closedness for a pair of algebras and its connection with an important property of groups known as being Hermitian (or symmetric). This property appears when one considers inverse-closedness...

We consider the problem of learning an unknown function f from given data about f. The learning problem is to give an approximation fˆ to f that predicts the values of f away from the data. There are numerous settings for this learning problem...

Topology is the branch of mathematics concerned with shapes and their spatial properties. In this talk I’ll show how several ideas from classic algebraic topology – like cohomology, classifying spaces and vector bundles – can be used in machine...

About 100 years ago, William Henry Young and Felix Hausdorff provedthat, for a periodic L_p-integrable function, the sequence of its Fourier coefficients necessarily lies in the discrete \ell_{p'} space provided that p' is the conjugate of p and 1

Graphs are ubiquitous in modern applications---including some very large graphs. This leads one to wonder, "How can we understand such large graphs?" One prevalent idea is to observe them locally: to count how many times certain substructures appear...

Determining information about the state of a complex physical system from observations of its behavior is a fundamental problem in scientific inference and engineering design. Often, this can be formulated as the stochastic inverse problem of...