Seminars and Colloquia by Series

TBA by Song Mei

Series
Stochastics Seminar
Time
Thursday, November 12, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
Online (link TBA)
Speaker
Song MeiUC Berkeley

Higher-order fluctuations in dense random graph models (note the unusual time: 5pm)

Series
Stochastics Seminar
Time
Thursday, October 22, 2020 - 17:00 for 1 hour (actually 50 minutes)
Location
Bluejeans (tbA)
Speaker
Adrian RoellinNational University of Singapore

Dense graph limit theory is essentially a first-order limit theory analogous to the classical Law of Large Numbers. Is there a corresponding central limit theorem? We believe so. Using the language of Gaussian Hilbert Spaces and the comprehensive theory of generalised U-statistics developed by Svante Janson in the 90s, we identify a collection of Gaussian measures (aka white noise processes) that describes the fluctuations of all orders of magnitude for a broad family of random graphs. We complement the theory with error bounds using a new variant of Stein’s method for multivariate normal approximation, which allows us to also generalise Janson’s theory in some important aspects. This is joint work with Gursharn Kaur.

Please note the unusual time: 5pm

Coalescence estimates for the corner growth model with exponential weights

Series
Stochastics Seminar
Time
Thursday, October 15, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
Bluejeans (link to be sent)
Speaker
Xiao ShenUniversity of Wisconsin

(Joint work with Timo Seppäläinen) We establish estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model with i.i.d. exponential weights. There are four estimates: upper and lower bounds on the probabilities of both fast and slow coalescence on the correct spatial scale with exponent 3/2. Our proofs utilize a geodesic duality introduced by Pimentel and properties of the increment-stationary last-passage percolation process. For fast coalescence our bounds are new and they have matching optimal exponential order of magnitude. For slow coalescence, we reproduce bounds proved earlier with integrable probability inputs, except that our upper bound misses the optimal order by a logarithmic factor.

A precise high-dimensional theory for Boosting

Series
Stochastics Seminar
Time
Thursday, October 1, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/276389634
Speaker
Pragya SurHarvard University

This talk will introduce a precise high-dimensional asymptotic theory for Boosting (AdaBoost) on separable data, taking both statistical and computational perspectives. We will consider the common modern setting where the number of features p and the sample size n are both large and comparable, and in particular, look at scenarios where the data is asymptotically separable. Under a class of statistical models, we will provide an (asymptotically) exact analysis of the generalization error of AdaBoost, when the algorithm interpolates the training data and maximizes an empirical L1 margin. On the computational front, we will provide a sharp analysis of the stopping time when boosting approximately maximizes the empirical L1 margin. Our theory provides several insights into properties of Boosting; for instance, the larger the dimensionality ratio p/n, the faster the optimization reaches interpolation. At the heart of our theory lies an in-depth study of the maximum L1-margin, which can be accurately described by a new system of non-linear equations; we analyze this margin and the properties of this system, using Gaussian comparison techniques and a novel uniform deviation argument. Time permitting, I will present analogous results for a new class of boosting algorithms that correspond to Lq geometry, for q>1. This is based on joint work with Tengyuan Liang.

Statistical Inference in Popularity Adjusted Stochastic Block Model

Series
Stochastics Seminar
Time
Thursday, September 24, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
https://ucf.zoom.us/j/92646603521?pwd=TnRGSVo1WXo2bjE4Y3JEVGRPSmNWQT09
Speaker
Marianna PenskyUniversity of Central Florida

The talk considers the Popularity Adjusted Block model (PABM) introduced by Sengupta and Chen (2018). We argue that the main appeal of the PABM is the flexibility of the spectral properties of the graph which makes the PABM an attractive choice for modeling networks that appear in, for example, biological sciences. In addition, to the best of our knowledge, the PABM is the only stochastic block model that allows to treat the network sparsity as the structural sparsity that describes community patterns, rather than being an attribute of the network as a whole.

Link to Zoom meeting: https://ucf.zoom.us/j/92646603521?pwd=TnRGSVo1WXo2bjE4Y3JEVGRPSmNWQT09

Couplings of Markov chain Monte Carlo and their uses

Series
Stochastics Seminar
Time
Thursday, September 10, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/83378796301
Speaker
Pierre JacobHarvard University

Markov chain Monte Carlo (MCMC) methods are state-of-the-art techniques for numerical integration. MCMC methods yield estimators that converge to integrals of interest in the limit of the number of iterations, obtained from Markov chains that converge to stationarity. This iterative asymptotic justification is not ideal. Indeed the literature offers little practical guidance on how many iterations should be performed, despite decades of research on the topic. This talk will describe a computational approach to address some of these issues. The key idea, pioneered by Glynn and Rhee in 2014, is to generate couplings of Markov chains, whereby pairs of chains contract, coalesce or even "meet" after a random number of iterations; we will see that these meeting times, which can be simulated in many practical settings, contain useful information about the finite-time marginal distributions of the chains. This talk will provide an overview of this line of research, joint work with John O'Leary, Yves Atchadé and various collaborators.
The main reference is available here: https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/rssb.12336

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