Machine Learning and Data Science (ML) is starting to take the place in industry that “Information Technology” had in the late 1990s: businesses of all sizes and in all sectors, are recognizing how necessary it has become to develop predictive capabilities for continued profitability of their core competencies. To be …
Optimal mass transport (OMT) is a rich area of research with applications to numerous disciplines including econometrics, physics, signal processing, systems and controls, data science and so on. In this talk, I will give a brief introduction to OMT and then focus on its recent developments in algorithms and applications. …
Quadratic assignment is a very general problem in theoretical computer science. It includes graph matching, the traveling salesman problem, and the Gromov-Hausdorff distance between finite metric spaces as particular cases. Quadratic assignment is in general NP-hard and even hard to approximate, but in fact the problem can be tractable for …
Although half a decade has passed since Frank Rosenblatt’s original work on multi- layer perceptrons, modern artificial neural networks are still surprisingly similar to his original ideas. In this talk I will question one of their most fundamental design aspects. As networks have become much deeper than had been possible …
What do interstellar navigation and protein shape reconstruction have in common? They both require us to solve the quintessential distance geometry problem: find a set a points which realizes an observed set of distances. Though stars, spaceships and proteins all tend to move, however, the textbook version of the distance …
This paper investigates asymptotic behaviors of gradient descent algorithms (particularly stochastic gradient descent and accelerated gradient descent) in the context of stochastic optimization arose in statistics and machine learning where objective functions are estimated from available data. We show that these algorithms can be modeled by continuous-time ordinary or stochastic …
In this talk, we will explore the implicit bias of generic optimization methods and its connection to generalization in ill-posed optimization problems. We will specifically study optimizing underdetermined linear regression or separable linear classification problems using common optimization methods including, mirror descent, natural gradient descent and steepest descent with respect …
In subset selection we search for the best linear predictor that involves a small subset of variables. Due to the vast applicability of this model, many approaches have been proposed by different communities, including enumeration, greedy algorithms, branch and bound, and convex relaxations. Our point of departure is to understand …
Machine teaching provides a rigorous formalism for a number of real-world applications including personalized educational systems, adversarial attacks, and program synthesis by examples. In this talk, I will discuss research questions in the context of two societal applications: (i) teaching participants of citizen science projects for biodiversity monitoring, and (ii) …
We present a mathematical analysis of a non-convex energy landscape for Robust Subspace Recovery. Under a deterministic condition, the only stationary point in a large neighborhood of an underlying subspace is the subspace itself. The same deterministic condition implies that a geodesic gradient descent method can exactly recover the underlying …