Systems | Information | Learning | Optimization
 

Optimization over nonconvex constraints & Gradient Coding via Sparse Random Graphs

Many problems in modern statistics can be formulated as an optimization problem with structured constraints, where the constraints often exhibit nonconvexity such as sparsity or low rank. However, working with nonconvex constraints presents challenges from both a theoretical and practical point of view. In this talk, we discuss a convergence …

Causal discovery with high dimensional non-Gaussian data & Scalable Generalized Linear Bandits: Online Computation and Hashing

In this talk, we will consider linear structural equation models which correspond to directed acyclic graphs (DAGs). These models assume that each observed variable is a linear function of the other variables and some error term. It has been previously shown for DAGs, when the error terms in a SEM …

Trace Test

Numerical algebraic geometry uses numerical algorithms to study algebraic varieties, which are sets defined by polynomial equations. It is becoming a core tool in applications of algebraic geometry outside of mathematics. Its fundamental concept is a witness set which gives a representation of a variety that may be manipulated on …

Breaking computational barriers: using data to enable extreme-scale simulations for uncertainty quantification and design

As physics-based simulation has played an increasingly important role in science and engineering, greater demands are being placed on model fidelity. This high fidelity necessitates fine spatiotemporal resolution, which can lead to extreme-scale models whose simulations consume months on thousands of computing cores. Further, most practical decision-making scenarios (e.g., uncertainty …

A geometric analysis of algorithms for phase retrieval and other single-index models with even link functions

Mathematical phase retrieval is the problem of solving systems of quadratic equations. In the first half of this talk, I will discuss recent approaches to this problem, focusing on stochastic gradient methods. In the second half, I will discuss how these algorithms can be extended and generalized. The first extension …

New Approximate Solution Approaches for Multi-Stage Stochastic Optimization

Multi-stage stochastic optimization can be used to model dynamic decision-making environments in which a sequence of decisions are to be made in response to a sequence of random events. Such problems arise in many applications, such as unit commitment and economic dispatch in power systems and inventory and production management. …