Seminars and Colloquia by Series

Thursday, November 29, 2018 - 15:05 , Location: Skiles 006 , Rachel Kuske , School of Mathematics, GaTech , Organizer: Christian Houdre
Heavy tailed distributions have been shown to be consistent with data in a variety of systems with multiple time scales.  Recently, increasing attention has appeared in different phenomena related to climate.  For example,  correlated additive and multiplicative (CAM) Gaussian noise, with infinite variance or heavy tails in certain parameter regimes,  has received increased attention in the context of atmosphere and ocean dynamics.  We discuss how CAM noise can appear generically in many reduced models. Then we show how reduced models for systems driven by fast linear CAM noise processes can be connected with the stochastic averaging for multiple scales systems driven by alpha-stable processes.   We identify the conditions under which the approximation of a CAM noise process is valid in the averaged system, and illustrate methods using effectively equivalent fast, infinite-variance processes.   These applications motivate new stochastic averaging results for systems with fast processes driven by heavy-tailed noise.  We develop these results for the case of alpha-stable noise, and discuss open problems for identifying appropriate heavy tailed distributions for these multiple scale systems. This is joint work with Prof. Adam Monahan (U Victoria) and Dr. Will Thompson (UBC/NMi Metrology and Gaming).
Thursday, November 15, 2018 - 15:05 , Location: Skiles 006 , Geronimo Uribe , UNAM , geronimo@matem.unam.mx , Organizer: Gerandy Brito
Thursday, November 8, 2018 - 15:05 , Location: Skiles 006 , Galyna Livshyts , School of Mathematics, GaTech , Organizer: Christian Houdre
Thursday, November 1, 2018 - 15:05 , Location: Skiles 006 , Christian Houdré , Georgia Institute of Technology , Organizer: Christian Houdre
Thursday, October 25, 2018 - 15:05 , Location: Skiles 006 , Eviatar Procaccia , Texas A&M , procaccia@math.tamu.edu , Organizer: Michael Damron
Thursday, October 11, 2018 - 15:05 , Location: Skiles 006 , Michael Damron , Georgia Institute of Technology , mdamron6@gatech.edu , Organizer: Michael Damron
Thursday, September 20, 2018 - 15:05 , Location: Skiles 006 , TBA , TBA , Organizer: Christian Houdre
Thursday, September 13, 2018 - 15:05 , Location: Skiles 006 , Konstantin Tikhomirov , School of Mathematics, GaTech , Organizer: Christian Houdre
Let (A_n) be a sequence of random matrices, such that for every n, A_n is n by n with i.i.d. entries, and each entry is of the form b*x, where b is a Bernoulli random variable with probability of success p_n, and x is an independent random variable of unit variance. We show that, as long as n*p_n converges to infinity, the appropriately rescaled spectral distribution of A_n converges to the uniform measure on the unit disc of complex plane. Based on joint work with Mark Rudelson.
Thursday, September 6, 2018 - 15:05 , Location: Skiles 006 , Sara van de Geer , ETH Zurich , Organizer: Mayya Zhilova
The seminar will be the third lecture of the TRIAD Distinguished Lecture Series by Prof. Sara van de Geer. For further information please see http://math.gatech.edu/events/triad-distinguished-lecture-series-sara-van-de-geer-0
Thursday, August 30, 2018 - 15:05 , Location: Skiles 006 , Andrew Nobel , University of North Carolina, Chapel Hill , Organizer: Mayya Zhilova
This talk concerns the description and analysis of a variational framework for empirical risk minimization. In its most general form the framework concerns a two-stage estimation procedure in which (i) the trajectory of an observed (but unknown) dynamical system is fit to a trajectory from a known reference dynamical system by minimizing average per-state loss, and (ii) a parameter estimate is obtained from the initial state of the best fit reference trajectory. I will show that the empirical risk of the best fit trajectory converges almost surely to a constant that can be expressed in variational form as the minimal expected loss over dynamically invariant couplings (joinings) of the observed and reference systems. Moreover, the family of joinings minimizing the expected loss fully characterizes the asymptotic behavior of the estimated parameters. I will illustrate the breadth of the variational framework through applications to the well-studied problems of maximum likelihood estimation and non-linear regression, as well as the analysis of system identification from quantized trajectories subject to noise, a problem in which the models themselves exhibit dynamical behavior across time. 

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