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LANS Seminar
May 10, 2023 @ 10:30 - 11:30 CDT
Seminar Title: Generalization and Sampling from the Dynamics Perspective
Speaker: Nisha Chandramoorthy, Assistant Professor, Georgia Tech
Date/Time: May 10, 2023 / 10:30 AM – 11:30 AM
Location: See meeting URL on the cels-seminars website (requires Argonne login)
Host: Emil Constantinescu
Description: In this talk, we obtain new computational insights into two classical areas of statistics: generalization and sampling. In the first part, we study generalization: the performance of a learning algorithm on unseen data. We define a notion of generalization for non-converging learning algorithms via the stability of loss statistics. This notion yields generalization bounds in a similar manner to classical algorithmic stability. Then, we show that spectral information from the training dynamics provides clues to generalization performance. In the second part, we discuss a new construction of a solution to the measure transport problem. The new construction arises from an infinite-dimensional generalization of a Newton method to find the zero of a “score operator”. We define such a score operator that gives the difference of the score — gradient of logarithm of density — of a transported distribution from the target score. The new construction is iterative, enjoys fast convergence under smoothness assumptions, and does not make a parametric ansatz on the transport map. It is appropriate for the variational inference setting, where the score is known, and for sampling certain chaotic dynamical systems, where a conditional score can be calculated even in the absence of a statistical model for the target.
Bio: Nisha Chandramoorthy is an Assistant Professor in the School of Computational Science and Engineering at Georgia Tech. Her research aims at developing mathematically rigorous numerical methods for computing with and understanding complex dynamical systems. She received her PhD in Computational Science and Engineering at MIT.
Please note that the meeting URL for this event can be seen on the cels-seminars website, which requires an Argonne login.