Georgia Institute of Technology College of Sciences

Several new results on asymptotic normality and other asymptotic properties of sample covariance operators for Gaussian observations in a high-dimensional setting will be discussed. Such asymptotics are of importance in various problems of high-dimensional statistics (in particular, related to principal component analysis). The proofs of these results rely on Gaussian concentration inequality. This is a joint work with Karim Lounici.

Hypergeometric functions have played an important role in mathematics and physics in the last centuries. Multivariate extensions of the classical hypergeometric functions have appeared recently in different applications. I will discuss research problems which relate these functions to the representation theory of Lie algebras and quantum superintegrable systems.

Dynamical processes, such as information diffusion in social networks, gene regulation in biological systems and functional collaborations between brain regions, generate a large volume of high dimensional “asynchronous” and “interdependent” time-stamped event data. This type of timing information is rather different from traditional iid. data and discrete-time temporal data, which calls for new models and scalable algorithms for learning, analyzing and utilizing them. In this talk, I will present methods based on multivariate point processes, high dimensional sparse recovery, and randomized algorithms for addressing a sequence of problems arising from this context. As a concrete example, I will also present experimental results on learning and optimizing information cascades in web logs, including estimating hidden diffusion networks and influence maximization with the learned networks. With both careful model and algorithm design, the framework is able to handle millions of events and millions of networked entities.