[Sds-seminars] S&DS Seminar via Zoom: John N. Wright, 10/25 @4pm-5pm, "Deep Networks and the Multiple Manifold Problem"

[elizavette.torres at yale.edu]

   <https://statistics.yale.edu/> Department of Statistics and Data Science


You are invited to a scheduled Zoom Seminar


JOHN N. WRIGHT, Columbia University


Monday, October 25, 2021

4:00PM to 5:00PM

Zoom:
https://yale.zoom.us/j/99169700816?pwd=SWEvWHI5d3dPNVdHMkZMZURMWWJPUT09

Password: 24

 <https://www.ee.columbia.edu/content/john-n-wright> Website







Title: Deep Networks and the Multiple Manifold Problem



Information and Abstract:

Data with low-dimensional nonlinear structure are ubiquitous in engineering
and scientific problems. We study a model problem with such structure-a
binary classification task that uses a deep fully-connected neural network
to classify data drawn from two disjoint smooth curves on the unit sphere.
Aside from mild regularity conditions, we place no restrictions on the
configuration of the curves. We prove that when (i) the network depth is
large relative to certain geometric properties that set the difficulty of
the problem and (ii) the network width and number of samples is polynomial
in the depth, randomly-initialized gradient descent quickly learns to
correctly classify all points on the two curves with high probability. To
our knowledge, this is the first generalization guarantee for deep networks
with nonlinear data that depends only on intrinsic data properties. Our
analysis draws on ideas from harmonic analysis and martingale concentration
for handling statistical dependencies in the initial (random) network. We
sketch applications to invariant vision, and to gravitational wave
astronomy, where leveraging low-dimensional structure leads to statistically
optimal tests for identifying signals in noise.  Joint work with Sam
Buchanan, Dar Gilboa, Tim Wang, Jingkai Yan

Speaker Bio: John Wright is an associate professor in Electrical Engineering
at Columbia University. He is also affiliated with the Department of Applied
Physics and Applied Mathematics and Columbia’s Data Science Institute. He
received his PhD in Electrical Engineering from the University of Illinois
at Urbana Champaign in 2009. Before joining Columbia he was with Microsoft
Research Asia from 2009-2011. His research interests include sparse and
low-dimensional models for high-dimensional data, optimization (convex and
otherwise), and applications in imaging and vision.

You are invited to a scheduled Zoom meeting. Zoom is Yale’s audio and
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Topic: Yale S&DS Department Seminar

Time: 4:00pm - 5:00pm

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