Seminar Abstract:
In myriad statistical applications, data is collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. Is it possible to recover the shared and source-specific factors? We show that under appropriate conditions on the alignment of source-specific factors, the problem is well-defined, and both shared and source-specific factors are identifiable under a constrained matrix factorization objective. To solve this objective, we propose a new class of matrix factorization algorithms called heterogeneous matrix factorization. HMF is easy to implement, enjoys local linear convergence under suitable assumptions, and is intrinsically distributed. Through a variety of empirical studies, we showcase the advantageous properties of HMF and its potential application in feature extraction and anomaly detection. We also show HMF's capabilities in handling large noise and missing entries.


Presenter Bio:
Naichen Shi is a Ph.D. candidate from the department of industrial and operations engineering at the University of Michigan, where he is advised by Dr. Raed Al Kontar. His research focuses on data analytics and optimization and their applications in manufacturing systems. In particular, he is interested in applying efficient optimization algorithms to understand the intrinsic patterns of complex systems. Naichen is an active member of his communities and has served as a reviewer for multiple journals and conferences, including Technometrics, NeurIPS, and AISTATS. See his personal website (https://sites.google.com/umich.edu/ncs/home) for more detailed information about him.