Geometric Ideas in Machine Learning: From Deep Learning to Incremental Optimization

Friday, September 28, 2018, 11:00 am - 12:00 pm PDTiCal
6th floor large conference room
This event is open to the public.
AI Seminar - Interview talk
Ashkan Panahi, NCSU
Video Recording:

Geometry is one of the oldest and richest areas of study in mathematics, which still dominates our mathematical intuition in a wide array of problems in data sciences. In this talk, we discuss novel ideas from geometry to expand our understanding about the recent remarkable machine learning (ML) breakthroughs and further improve the existing methods. We discuss two major topics in ML, namely deep learning and mathematical optimization. In the context of deep learning, we develop a geometric framework for functional analysis that leads to an algorithmic scheme for deep learning, being heavily tied to the conventional deep neural network technique. We present theoretical evidences demonstrating that this geometric framework reveals new theoretical aspects of the existing deep learning approaches and at the same time has a great potential to improve them.  In the second part of this talk, we revisit incremental optimization methods, which have received considerable attention for their appealing numerical properties. In particular, we extend the so-called variance reduction techniques to non-smooth, constrained optimization problems and present a novel study of these methods based on the geometry of constraints. We present the application of this technique in a number of standard applications, such as vector clustering and bi-clustering, optimal transport, optimal assignment and etc. with theoretical guarantees.


Ashkan Panahi received his PhD degree in 2015 from the Signal Processing group, Electrical Engineering department at Chalmers University of Technology, Sweden. During 2015 and 2016, he held a postdoctoral research position at the machine Learning, Algorithms and computational Biology (LAB) group, Computer Science and Engineering department at Chalmers. Since 2016, he has held a U.S. National Research Council (NRC) research associate position at U.S. Research Army Office at Research Triangle Park, NC and the Electrical and Computer Engineering department at North Carolina State University, Raleigh, NC. Dr. Panahi’s research interest spans a wide range of data processing topics from both areas of information theory and computing science. He is currently involved in developing various machine learning tools, mainly for computer vision and image processing, based on studying large-scale optimization methods.

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