ISyE Seminar - Jason Lee

Event Details
  • Date/Time:
    • Wednesday September 6, 2017
      3:00 pm - 4:00 pm
  • Location: Groseclose 402
  • Phone:
  • URL:
  • Email:
  • Fee(s):
    N/A
  • Extras:
Contact
No contact information submitted.
Summaries

Summary Sentence: ISyE Seminar - Jason Lee

Full Summary: No summary paragraph submitted.

TITLE: Matrix Completion, Saddlepoints, and Gradient Descent

ABSTRACT:

Matrix completion is a fundamental machine learning problem with wide applications in collaborative filtering and recommender systems. Typically, matrix completion are solved by non-convex optimization procedures, which are empirically extremely successful. We prove that the symmetric matrix completion problem has no spurious local minima, meaning all local minima are also global. Thus the matrix completion objective has only saddlepoints an global minima.  Next, we show that saddlepoints are easy to avoid for even Gradient Descent -- arguably the simplest optimization procedure. We prove that with probability 1, randomly initialized Gradient Descent converges to a local minimizer. The same result holds for a large class of optimization algorithms including proximal point, mirror descent, and coordinate descent.

BIO: Jason Lee is an assistant professor in Data Sciences and Operations at the University of Southern California. Prior to that, he was a postdoctoral researcher at UC Berkeley working with Michael Jordan. Jason received his PhD at Stanford University advised by Trevor Hastie and Jonathan Taylor. His research interests are in statistics, machine learning, and optimization. Lately, he has worked on high dimensional statistical inference, analysis of non-convex optimization algorithms, and theory for deep learning.

Additional Information

In Campus Calendar
No
Groups

H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

Invited Audience
Faculty/Staff, Public, Undergraduate students
Categories
No categories were selected.
Keywords
No keywords were submitted.
Status
  • Created By: nhendricks6
  • Workflow Status: Published
  • Created On: Aug 23, 2017 - 4:49pm
  • Last Updated: Aug 24, 2017 - 1:14pm