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October 2016

Matrix estimation by Universal Singular Value Thresholding

October 28, 2016 @ 11:00 am

Consider the problem of estimating the entries of a large matrix, when the observed entries are noisy versions of a small random fraction of the original entries. This problem has received widespread attention in recent times. I will describe a simple estimation procedure, called Universal Singular Value Thresholding (USVT), that works for any matrix that has "a little bit of structure". Surprisingly, this simple estimator achieves the minimax error rate up to a constant factor. The method is applied to…

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November 2016

Information Session: Minor in Statistics and Data Science

November 4, 2016 @ 1:00 pm

Learn about the new new Minor in Statistics and Data Science.

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Interpretable prediction models for network-linked data

November 18, 2016 @ 11:00 am

Prediction problems typically assume the training data are independent samples, but in many modern applications samples come from individuals connected by a network. For example, in adolescent health studies of risk-taking behaviors, information on the subjects’ social networks is often available and plays an important role through network cohesion, the empirically observed phenomenon of friends behaving similarly. Taking cohesion into account should allow us to improve prediction. Here we propose a regression-based framework with a network penalty on individual node…

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December 2016

Shotgun Assembly of Graphs

December 2, 2016 @ 11:00 am

We will present some results and some open problems related to shotgun assembly of graphs for random generating models.Shotgun assembly of graphs is the problem of recovering a random graph or a randomly labelled graphs from small pieces. This problem generalizes the theoretically elegant and practically important problem of shotgun assembly of DNA sequences. The general problem of shotgun assembly presents novel problems in random graphs, percolation, and random constraint satisfaction problems. Based on joint works with Nathan Ross, with…

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Special Stochastics and Statistics Seminar – John Cunningham

December 16, 2016 @ 4:00 pm
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February 2017

Non-classical Berry-Esseen inequality and accuracy of the weighted bootstrap.

February 3 @ 11:00 am

In this talk, we will study higher-order accuracy of the weighted bootstrap procedure for estimation of a distribution of a sum of independent random vectors with bounded fourth moments, on the set of all Euclidean balls. Our approach is based on Berry-Esseen type inequality which extends the classical normal approximation bound. These results justify in non-asymptotic setting that the weighted bootstrap can outperform Gaussian (or chi-squared) approximation in accuracy w.r.t. dimension and sample size. In addition, the presented results lead…

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Slope meets Lasso in sparse linear regression

February 10 @ 11:00 am

We will present results in sparse linear regression on two convex regularizedestimators, the Lasso and the recently introduced Slope estimator, in the high-dimensional setting where the number of covariates p is larger than the number of observations n. The estimation and prediction performance of these estimators will be presented, as well as a comparative study of the assumptions on the design matrix.

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Causal Discovery in Systems with Feedback Cycles

February 17 @ 11:00 am

While causal relations are generally considered to be anti-symmetric, we often find that over time there are feedback systems such that a variable can have a causal effect on itself. Such "cyclic" causal systems pose significant challenges for causal analysis, both in terms of the appropriate representation of the system under investigation, and for the development of algorithms that attempt to infer as much as possible about the underlying causal system from statistical data. This talk will aim to provide…

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Estimating the number of connected components of large graphs based on subgraph sampling

February 24 @ 11:00 am

Learning properties of large graphs from samples is an important problem in statistical network analysis, dating back to the early work of Goodman and Frank. We revisit the problem formulated by Frank (1978) of estimating the numbers of connected components in a graph of N vertices based on the subgraph sampling model, where we observe the subgraph induced by n vertices drawn uniformly at random. The key question is whether it is possible to achieve accurate estimation, i.e., vanishing normalized…

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March 2017

Computing partition functions by interpolation

March 3 @ 11:00 am

Partition functions are just multivariate polynomials with great many monomials enumerating combinatorial structures of a particular typeand their efficient computation (approximation) are of interest for combinatorics, statistics, physics and computational complexity. I’ll present a general principle: the partition function can be efficiently approximated in a domain if it has no complex zeros in a slightly larger domain, and illustrate it on the examples of the permanent of a matrix, the independence polynomial of a graph and, time permitting, the graph…

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