Georgia Institute of Technology College of Sciences

(The talk will be at 1-2pm, then it follows by a discussion session from 2 pm to 2:45 pm.)

Powerful AI systems, which are driven by machine learning, are increasingly controlling various aspects of modern society: from social interactions (e.g., Facebook, Twitter, Google, YouTube), economics (e.g., Uber, Airbnb, Banking), learning (e.g., Wikipedia, MOOCs), governance (Judgements, Policing, Voting), to autonomous vehicles and weapons. These systems have a tremendous potential to change our lives for the better, but, via the ability to mimic and nudge human behavior, they also have the potential to be discriminatory, reinforce societal prejudices, and polarize opinions. Moreover, recent studies have demonstrated that these systems can be quite brittle and generally lack the required robustness to be deployed in various civil/military situations. The reason being that considerations such as fairness, robustness, stability, explainability, accountability etc. have largely been an afterthought in the development of AI systems. In this talk, I will discuss the opportunities that lie ahead in a principled and thoughtful development of AI systems.

Nisheeth Vishnoi is a Professor of Computer Science at Yale University. He received a B.Tech in Computer Science and Engineering from IIT Bombay in 1999 and a Ph.D. in Algorithms, Combinatorics and Optimization from Georgia Tech in 2004. His research spans several areas of theoretical computer science: from approximability of NP-hard problems, to combinatorial, convex and non-convex optimization, to tackling algorithmic questions involving dynamical systems, stochastic processes and polynomials. He is also broadly interested in understanding and addressing some of the key questions that arise in nature and society from the viewpoint of theoretical computer science. Here, his current focus is on natural algorithms, emergence of intelligence, and questions at the interface of AI, ethics, and society. He was the recipient of the Best Paper Award at FOCS in 2005, the IBM Research Pat Goldberg Memorial Award in 2006, the Indian National Science Academy Young Scientist Award in 2011, and the IIT Bombay Young Alumni Achievers Award in 2016.

We discuss a problem of asymptotically efficient (that is, asymptotically normal with minimax optimal limit variance) estimation of functionals of the form $\langle f(\Sigma), B\rangle$ of unknown covariance $\Sigma$ based on i.i.d.mean zero Gaussian observations $X_1,\dots, X_n\in {\mathbb R}^d$ with covariance $$\Sigma$. Under the assumptions that the dimension $d\leq n^{\alpha}$ for some $\alpha\in (0,1)$ and $f:{\mathbb R}\mapsto {\mathbb R}$ is of smoothness $s>\frac{1}{1-\alpha},$ we show how to construct an asymptotically efficient estimator of such functionals (the smoothness threshold $\frac{1}{1-\alpha}$ is known to be optimal for a simpler problem of estimation of smooth functionals of unknown mean of normal distribution).

The proof of this result relies on a variety of probabilistic and analytic tools including Gaussian concentration, bounds on the remainders of Taylor expansions of operator functions and bounds on finite differences of smooth functions along certain Markov chains in the spaces of positively semi-definite matrices.

Constriction of blood vessels in the extremities due to traumatic injury to halt excessive blood loss or resulting from pathologic occlusion can cause considerable damage to the surrounding tissues with significant morbidity and mortality. Optimal healing of damaged tissue relies on the precise balance of pro-inflammatory and pro-healing processes of innate inflammation. In this talk, we will present a discrete multiscale mathematical model that spans the tissue and intracellular scales, and captures the consequences of targeting various regulatory components. We take advantage of the canalization properties of some of the functions, which is a type of hierarchical clustering of the inputs, and use it as control to steer the system away from a faulty attractor and understand better the regulatory relations that govern the system dynamics.EDIT: CANCELLED

We shall survey a variety of results, some recent, some going back a long time, where combinatorial methods are used to prove or disprove the existence of orthogonal exponential bases and Gabor bases. The classical Erdos distance problem and the Erdos Integer Distance Principle play a key role in our discussion.