I will discuss the influence of the seed in models of randomly growing trees; in particular, I will focus on the preferential attachment and uniform attachment models. In both of these models, perhaps surprisingly, different seeds lead to different distributions of limiting trees from a total variation point of view. …
Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the issue of the model selection phase has often been ignored in the literature. In fact, in theoretical works …
In many optimization problems the set of feasible solutions can be described or approximated through a polyhedron. In this talk, I will focus on the polyhedral structure of specific classes of polytopes. First, I will introduce the fractional stable set polytope, that arises from the edge formulation of the stable …
We talk a lot in this seminar about random graphs, and by this we often mean random graphs in the Erdos – Renyi sense. In recent years, the theory of graph limits or graphons has been developed; this gives us a very nice analytic way of describing various Erdos-Renyi-like graphs. …
In motion planning, one often encounters high-dimensional state spaces that describe the configuration of things, be it the state of a robot(s), the planning necessary to autonomously drive a car or fly a drone. Many times these state spaces are difficult to come to terms with. There are however some …
I’m going to talk about some of our recent and ongoing work on topics that touch on machine learning and optimization. I’ll focus mainly on our work on model inversion attacks. Consider a machine learning model f that takes features x_1,…,x_t and produces from them a prediction y. In many …
Optimality condition for mixed-integer convex minimization problems will be discussed and the concept of center-points, a generalization of the median from the one dimensional space to vector spaces. Through the theory of center-points, I will show how to extend the general cutting plane scheme from the continuous setting to the …
Note: This seminar consisted of two half-hour student talks. Information Theory in Network Coding Ting-Ting Nan Network coding has been used in many applications. However, one of the basic problems, finding the coding capacity of most networks, is still unsolved. The entropy region is central to computing network coding capacities, …
We consider the problem of clustering a collection of N unlabeled data points assumed to lie near a union of k lower dimensional planes. This assumption works in certain computer vision applications such as face recognition and image segmentation. Elhamifar and Vidal have proposed “Sparse Subspace Clustering (SSC)” algorithm to …
The optimal power flow (OPF) problem is a nonconvex quadratically constrained continuous optimization problem that is a key problem in the area of electrical power systems operations. The theme of our work is to design algorithmic techniques for finding globally optimal solutions of OPF. We begin by presenting a new …