Seminars and Colloquia by Series

Thursday, October 19, 2017 - 15:05 , Location: Skiles 006 , Yao Xie , ISyE, Georgia Institute of Technology , Organizer: Mayya Zhilova
We present a unified framework for sequential low-rank matrix completion and estimation, address the joint goals of uncertainty quantification (UQ) and statistical design. The first goal of UQ aims to provide a measure of uncertainty of estimated entries in the unknown low-rank matrix X, while the second goal of statistical design provides an informed sampling or measurement scheme for observing the entries in X. For UQ, we adopt a Bayesian approach and assume a singular matrix-variate Gaussian prior the low-rank matrix X which enjoys conjugacy. For design, we explore deterministic design from information-theoretic coding theory. The effectiveness of our proposed methodology is then illustrated on applications to collaborative filtering.
Thursday, October 5, 2017 - 15:05 , Location: Skiles 006 , Subhabrata Sen , MIT / Microsoft , ssen90@stanford.edu , Organizer: Michael Damron
  The study of graph-partition problems such as Maxcut, max-bisection and min-bisection have a long and rich history in combinatorics and theoretical computer science. A recent line of work studies these problems on sparse random graphs, via a connection with mean field spin glasses. In this talk, we will look at this general direction, and derive sharp comparison inequalities between cut-sizes on sparse Erdös-Rényi and random regular graphs. Based on joint work with Aukosh Jagannath. 
Thursday, September 21, 2017 - 15:05 , Location: Skiles 006 , Edgar Dobriban , University of Pennsylvania, Wharton School , dobriban@wharton.upenn.edu , Organizer: Mayya Zhilova
We consider the $\textit{linearly transformed spiked model}$, where observations $Y_i$ are noisy linear transforms of unobserved signals of interest $X_i$: $$Y_i = A_i X_i + \varepsilon_i,$$ for $i=1,\ldots,n$. The transform matrices $A_i$ are also observed. We model $X_i$ as random vectors lying on an unknown low-dimensional space. How should we predict the unobserved signals (regression coefficients) $X_i$? The naive approach of performing regression for each observation separately is inaccurate due to the large noise. Instead, we develop optimal linear empirical Bayes methods for predicting $X_i$ by "borrowing strength'' across the different samples. Our methods are applicable to large datasets and rely on weak moment assumptions. The analysis is based on random matrix theory. We discuss applications to signal processing, deconvolution, cryo-electron microscopy, and missing data in the high-noise regime. For missing data, we show in simulations that our methods are faster, more robust to noise and to unequal sampling than well-known matrix completion methods. This is joint work with William Leeb and Amit Singer from Princeton, available as a preprint at arxiv.org/abs/1709.03393.
Thursday, September 14, 2017 - 15:05 , Location: Skiles 006 , Gerandy Brito , Georgia Institute of Technology , gerandy@uw.edu , Organizer: Michael Damron
This talk concerns to spectral gap of random regular graphs. First, we prove that almost all bipartite biregular graphs are almost Ramanujan by providing a tight upper bound for the non trivial eigenvalues of its adjacency operator, proving Alon's Conjecture for this family of graphs. Also, we use a spectral algorithm to recover hidden communities in a random network model we call regular stochastic block model. Our proofs rely on a technique introduced recently by Massoullie, which we developed for random regular graphs.    
Thursday, September 7, 2017 - 15:05 , Location: Skiles 006 , Michael Damron , Georgia Institute of Technology , mdamron6@gatech.edu , Organizer: Michael Damron
On the two-dimensional square lattice, assign i.i.d. nonnegative weights to the edges with common distribution F. For which F is there an infinite self-avoiding path with finite total weight? This question arises in first-passage percolation, the study of the random metric space Z^2 with the induced random graph metric coming from the above edge-weights. It has long been known that there is no such infinite path when F(0)<1/2 (there are only finite paths of zero-weight edges), and there is one when F(0)>1/2 (there is an infinite path of zero-weight edges). The critical case, F(0)=1/2, is considerably more difficult due to the presence of finite paths of zero-weight edges on all scales. I will discuss work with W.-K. Lam and X. Wang in which we give necessary and sufficient conditions on F for the existence of an infinite finite-weight path. The methods involve comparing the model to another one, invasion percolation, and showing that geodesics in first-passage percolation have the same first order travel time as optimal paths in an embedded invasion cluster. 
Thursday, August 31, 2017 - 15:05 , Location: Skiles 006 , Po-Ling Loh , University of Wisconsin-Madison , Organizer: Mayya Zhilova
We discuss two recent results concerning disease modeling on networks. The infection is assumed to spread via contagion (e.g., transmission over the edges of an underlying network). In the first scenario, we observe the infection status of individuals at a particular time instance and the goal is to identify a confidence set of nodes that contain the source of the infection with high probability. We show that when the underlying graph is a tree with certain regularity properties and the structure of the graph is known, confidence sets may be constructed with cardinality independent of the size of the infection set. In the scenario, the goal is to infer the network structure of the underlying graph based on knowledge of the infected individuals. We develop a hypothesis test based on permutation testing, and describe a sufficient condition for the validity of the hypothesis test based on automorphism groups of the graphs involved in the hypothesis test. This is joint work with Justin Khim (UPenn).
Thursday, April 20, 2017 - 15:05 , Location: Skiles 006 , Lutz Warnke , School of Mathematics, GaTech , Organizer: Christian Houdre
We consider rooted subgraph extension counts, such as (a) the number of triangles containinga given vertex, or (b) the number of paths of length three connecting two given vertices. In 1989 Spencer gave sufficient conditions for the event that whp all roots of the binomial random graph G(n,p) have the same asymptotic number of extensions, i.e., (1 \pm \epsilon) times their expected number. Perhaps surprisingly, the question whether these conditions are necessary has remained open. In this talk we briefly discuss our qualitative solution of this problem for the `strictly balanced' case, and mention several intriguing questions that remain open (which lie at the intersection of probability theory + discrete mathematics, and are of concentration inequality type).   Based on joint work in progress with Matas Sileikis
Thursday, April 13, 2017 - 15:05 , Location: Skiles 006 , Christian Houdré , School of Mathematics, Georgia Institute of Technology , Organizer: Christian Houdre
I will revisit the classical Stein's method, for normal random variables, as well as its version for Poisson random variables and show how both (as well as many other examples) can be incorporated in a single framework. 
Friday, April 7, 2017 - 13:05 , Location: Skiles 270 , David Herzog , Iowa State University , dherzog@iastate.edu , Organizer: Michael Damron
We discuss scaling methods which can be used to solve low mode control problems for nonlinear partial differential equations.  These methods lead naturally to a infinite-dimensional generalization of the notion of saturation, originally due to Jurdjevic and Kupka in the finite-dimensional setting of ODEs.  The methods will be highlighted by applying them to specific equations, including reaction-diffusion equations, the 2d/3d Euler/Navier-Stokes equations and the 2d Boussinesq equations.  Applications to support properties of the laws solving randomly-forced versions of each of these equations will be noted.
Thursday, April 6, 2017 - 15:05 , Location: Skiles 006 , Zhou Fan , Stanford University , Organizer: Christian Houdre
Spectral algorithms are a powerful method for detecting low-rank structure in dense random matrices and random graphs. However, in certain problems involving sparse random graphs with bounded average vertex degree, a naive spectral analysis of the graph adjacency matrix fails to detect this structure. In this talk, I will discuss a semidefinite programming (SDP) approach to address this problem, which may be viewed both as imposing a delocalization constraint on the maximum eigenvalue problem and as a natural convex relaxation of minimum graph bisection. I will discuss probabilistic results that bound the value of this SDP for sparse Erdos-Renyi random graphs with fixed average vertex degree, as well as an extension of the lower bound to the two-group stochastic block model. Our upper bound uses a dual witness construction that is related to the non-backtracking matrix of the graph. Our lower bounds analyze the behavior of local algorithms, and in particular imply that such algorithms can approximately solve the SDP in the Erdos-Renyi setting. This is joint work with Andrea Montanari.

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