Simge Küçükyavuz is Chair and David A. and Karen Richards Sachs Professor in the Industrial Engineering and Management Sciences Department at Northwestern University. She is an expert in mixed-integer, large-scale, and stochastic optimization and their applications across numerous domains, including social networks, computing and energy infrastructure, statistical learning, and logistics. She is an INFORMS Fellow, and the recipient of the NSF CAREER Award and the INFORMS Computing Society (ICS) Prize. She is the past chair of ICS and serves on the editorial boards of Mathematics of Operations Research, Mathematical Programming, Operations Research, SIAM Journal on Optimization, and MOS-SIAM Optimization Book Series. She received her Ph.D. in Industrial Engineering and Operations Research from the University of California, Berkeley.

Abstract:
Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in casual discovery. We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The central problem can be modeled as a mixed-integer program with an objective function composed of a convex loss function and a regularization penalty subject to linear constraints. The optimal solution to this mathematical program is known to have desirable statistical properties under certain conditions. However, the state-of-the-art optimization solvers are not able to obtain provably optimal solutions to the existing mathematical formulations for medium-size problems within reasonable computational times. To address this difficulty, we tackle the problem from both computational and statistical perspectives. On the one hand, we propose a concrete early stopping criterion to terminate the branch-and-bound process in order to obtain a near-optimal solution to the mixed-integer program, and establish the consistency of this approximate solution. On the other hand, we improve the existing formulations by replacing the linear big-M constraints that represent the relationship between the continuous and binary indicator variables with second-order conic constraints. Our numerical results demonstrate the effectiveness of the proposed approaches. This is joint work with Tong Xu, Armeen Taeb, Ali Shojaie.