Seminars and Colloquia by Series

Thursday, October 27, 2011 - 15:05 , Location: Skyles 006 , Xi Luo , The Wharton School, Department of Statistics, University of Pennsylvania , xiluo@wharton.upenn.edu , Organizer: Karim Lounici
We consider the problem of estimating the covariance matrix. Factormodels and random effect models have been shown to provide goodapproximations in modeling multivariate observations in many settings. These models motivate us to consider a general framework of covariancestructures, which contains sparse and low rank components. We propose aconvex optimization criterion, and the resulting estimator is shown torecover exactly the rank and support of the low rank and sparsecomponents respectively. The convergence rates are also presented. Tosolve the optimization problem, we propose an iterative algorithm basedon Nesterov's method, and it converges to the optimal with order 1/t2for any finite t iterations. Numerical performance is demonstratedusing simulated data and stock portfolio selection on S&P 100.(This is joint work with T. Tony Cai.)
Thursday, October 20, 2011 - 15:05 , Location: Skiles 006 , Don Richards , Penn State, Department of Statistics , Organizer: Karim Lounici
In work on the Riemann zeta function, it is of interest to evaluate certain integrals involving the characteristic polynomials of N x N unitary matrices and to derive asymptotic expansions of these integrals as N -> \infty. In this talk, I will obtain exact formulas for several of these integrals, and relate these results to conjectures about the distribution of the zeros of the Riemann zeta function on the critical line. I will also explain how these results are related to multivariate statistical analysis and to the hypergeometric functions of Hermitian matrix argument.
Thursday, October 6, 2011 - 15:05 , Location: Skiles 006 , Haiyan Cai , Department of Mathematics and Computer Science, University of Missouri , Organizer: Liang Peng
I will talk briefly some of my recent research on random networks. In the first part of the talk, we will focus on the connectivity of a random network. The network is formed from a set of randomly located points and their connections depend on the distance between the points. It is clear that the probability of connection depends on the density of the points. We will explore some properties of this probability as a function of the point density. In the second part, I will discuss a possible approach in the study correlation structure of a large number of random variables. We will focus mainly on Gaussian distribution and distributions which are "similar" to Gaussian distributions. The idea is to use a single number to quantify the strength of correlation among all the random variables. Such a quantity can be derived from a latent cluster structure within a Markovian random network setting.
Thursday, September 29, 2011 - 15:05 , Location: Skiles 006 , David Goldberg , ISyE, Georgia Tech , Organizer:
In this talk, we resolve several questions related to a certain heavy traffic scaling regime (Halfin-Whitt) for parallel server queues, a family of stochastic models which arise in the analysis of service systems.  In particular, we show that the steady-state queue length scales like $O(\sqrt{n})$, and bound the large deviations behavior of the limiting steady-state queue length.  We prove that our bounds are tight for the case of Poisson arrivals.  We also derive the first non-trivial bounds for the steady-state probability that an arriving customer has to wait for service under this scaling.  Our bounds are of a structural nature, hold for all $n$ and all times $t \geq 0$, and have intuitive closed-form representations as the suprema of certain natural processes.  Our upper and lower bounds also exhibit a certain duality relationship, and exemplify a general methodology which may be useful for analyzing a variety of stochastic models.  The first part of the talk is joint work with David Gamarnik.
Thursday, September 22, 2011 - 15:05 , Location: Skiles 006 , Yuri Bakhtin , School of Mathematics, Georgia institute of Technology , Organizer: Karim Lounici
The Burgers equation is a nonlinear PDE and one of the basic hydrodynamic models. The ergodic theory of the Burgers turbulence began with the work of E, Khanin, Mazel, Sinai (Ann. Math. 2000). In their paper and in subsequent papers by Khanin and his coauthors, the compact case (Burgers on a circle or torus) was studied. In this talk, I will discuss the noncompact case. The main object is optimal paths through clouds of Poissonian points.
Thursday, September 15, 2011 - 15:05 , Location: Skiles 006 , Shannon L. Starr , University of Rochester , sstarr@math.rochester.edu , Organizer: Karim Lounici
The Potts antiferromagnet on a random graph is a model problem from disordered systems, statistical mechanics with random Hamiltonians. Bayati, Gamarnik and Tetali showed that the free energy exists in the thermodynamic limit, and demonstrated the applicability of an interpolation method similar to one used by Guerra and Toninelli, and Franz and Leone for spin glasses. With Contucci, Dommers and Giardina, we applied interpolation to find one-sided bounds for the free energy using the physicists' ``replica symmetric ansatz.'' We also showed that for sufficiently high temperatures, this ansatz is correct. I will describe these results and some open questions which may also be susceptible to the interpolation method.
Thursday, September 8, 2011 - 15:05 , Location: Skyles 006 , Christian houdre , School of mathematics, Georgia institute of Technology , Organizer: Karim Lounici
Given a random word of size n whose letters are drawn independently from an ordered alphabet of size m, the fluctuations of the shape of the associated random RSK Young tableaux are investigated, when n and m converge together to infinity. If m does not grow too fast and if the draws are uniform, then the limiting shape is the same as the limiting spectrum of the GUE. In the non-uniform case, a control of both highest probabilities will ensure the convergence of the first row of the tableau, i.e. of the length of the longest increasing subsequence of the word, towards the Tracy?Widom distribution.
Thursday, September 1, 2011 - 15:05 , Location: Skiles 006 , Joseph Salmon , Electrical and Computer Engineering, Duke University , joseph.salmon@duke.edu , Organizer: Karim Lounici
We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing onthe exponentially weighted aggregate, we prove a PAC-Bayesian type inequality that leads tosharp oracle inequalities in discrete but also in continuous settings. The framework is general enough to cover the combinations of various procedures such as least square regression,kernel ridge regression, shrinking estimators and many other estimators used in the literatureon statistical inverse problems. As a consequence, we show that the proposed aggregate provides an adaptive estimator in the exact minimax sense without neither discretizing the rangeof tuning parameters nor splitting the set of observations. We also illustrate numerically thegood performance achieved by the exponentially weighted aggregate. (This is a joint work with Arnak Dalalyan.)
Thursday, May 12, 2011 - 15:05 , Location: Skiles 005 , Jean-Christophe Breton , Universite de Rennes , Organizer: Christian Houdre
We consider weighted random ball model driven by a Poisson random measure on \Bbb{R}^d\times \Bbb{R}^+\times \Bbb{R} with product heavy tailed intensity and we are interested in the functional describing the contribution of the model in some configurations of \Bbb{R}^d. The fluctuations of such functionals are investigated under different types of scaling and the talk will discuss the possible limits. Such models arise in communication network to represent the transmission of information emitted by stations distributed according to the Poisson measure.
Thursday, April 21, 2011 - 15:05 , Location: Skiles 005 , Wlodek Bryc , University of Cincinnati , Organizer: Christian Houdre

Hosted by Christian Houdre and Liang Peng.

In this talk I will discuss random matrices that are matricial analogs of the well known binomial, Poisson, and negative binomial random variables. The common thread is the conditional variance of X given S = X+X', which is a quadratic polynomial in S and in the univariate case describes the family of six Meixner laws that will be described in the talk. The Laplace transform of a general n by n Meixner matrix ensemble satisfies a system of PDEs which is explicitly solvable for n = 2. The solutions lead to a family of six non-trivial 2 by 2 Meixner matrix ensembles. Constructions for the "elliptic cases" generalize to n by n matrices. The talk is based on joint work with Gerard Letac.

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