Class of ’27 Lecture Series

The Class of ’27 Lecture Series is a special lecture held each year. It was established in 1960 to honor the first chair of the Math Sciences Department, Professor Edwin Allen. The three members of the class of 1927 who established this series are Issac Arnold, Alexander Hassan, and Isadore Fixman.

Class of '27 Lecture I - "Nonlocal PDEs and Quantum Optics"

John C. Schotland from Department of Mathematics - Yale University

Abstract: Quantum optics is the quantum theory of the interaction of light and matter. This talk will present a survey of recent results on a real-space formulation of quantum electrodynamics and its relation to nonlocal partial differential equations. This talk is intended for a general mathematical audience.

Class of '27 Lecture II - "Inverse Problems in Quantum Optics"

John C. Schotland from Yale University

Abstract: We consider the quantum electrodynamics of a system of two-level atoms. We show that it is possible to uniquely determine the density of atoms from measurements of the source to solution map for a system of nonlocal partial differential equations, which describe the scattering of a two-photon state from the atoms. The required measurements involve correlating the outputs of a point detector with an integrating detector, thereby exploiting information about the entanglement of the photons.

Class of '27 Lecture II - "Classical Analysis for Some Machine Learning Problems"

Lexing Ying from Stanford University

Abstract: Machine learning has increasingly influenced the development of scientific computing. In this talk, I will share some recent experiences on how classical analysis can help understand machine learning algorithms. The first example is online learning, where ODEs and SDEs can help explain the optimal regret bounds concisely. In the second example, a perturbative analysis clarifies why sometimes line spectrum estimation algorithms exhibit a super-convergence phenomenon.

 

Class of '27 Lecture I - "Eigenmatrix for Unstructured Sparse Recovery"

Lexing Ying from Stanford University

Abstract: This talk considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. We propose the eigenmatrix as a unified solution for these sparse recovery problems. The key is a data-driven construction with desired approximate eigenvalues and eigenvectors. We also discuss its multidimensional version and applications in free deconvolution.

 

Class of '27 Lecture II-"Convergence Analysis of Stochastic Optimization Methods via Martingales"

Katya Scheinberg from Lehigh University
Abstract:  We will present a very general framework for unconstrained stochastic optimization which encompasses standard frameworks such as line search and trust region using random models. In particular this framework retains the desirable practical features such step acceptance criterion, trust region adjustment and ability to utilize of second order models. The framework is based on bounding the expected stopping time of a stochastic process, which satisfies certain assumptions...

Class of '27 Lecture I-"Gradient Decent Without Gradients"

Katya Scheinberg from Lehigh University
Abstract: The core of continuous optimization lies in using information from first and second order derivatives to produce steps that improve objective function value. Classical methods such as gradient decent and Newton method rely on this information. The recently popular method in machine learning - Stochastic Gradient Decent - does not require the gradient itself, but still requires its unbiased estimate. However, in many applications either derivatives or their unbiased estimates are not available.

Class of ’27 Lecture : Coordinate Descent Methods

Stephen J. Wright from University of Wisconsin
Coordinate descent is an approach for minimizing functions in which only a subset of the variables are allowed to change at each iteration, while the remaining variables are held fixed. This approach has been popular in applications since the earliest days of optimization, because it is intuitive and because the low-dimensional searches that take place at each iteration are inexpensive in many applications. In recent years, the popularity of coordinate descent methods has grown further because of their usefulness in data analysis.

Class of ’27 Lecture: Fundamental Optimization Methods in Data Analysis

Stephen Wright from University of Wisconsin
Optimization formulations and algorithms are vital tools for solving problems in data analysis. There has been particular interest in some fundamental, elementary, optimization algorithms that were previously thought to have only niche appeal. Stochastic gradient, coordinate descent, and accelerated first-order methods are three examples. We outline applications in which these approaches are useful, discuss the basic properties of these methods, and survey some recent developments in the analysis of their convergence behavior.
Mathematical Sciences

Amos Eaton 301

110 8th Street

Troy, NY 12180

(518) 276-6345

Amos Eaton Hall
Contact Us
Back to top