# Difference between revisions of "Probability Seminar"

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Abstract: I will talk about a random geometric graph model, where connections between vertices depend on distances between latent d-dimensional labels; we are particularly interested in the high-dimensional case when d is large. Upon observing a graph, we want to tell if it was generated from this geometric model, or from an Erdos-Renyi random graph. We show that there exists a computationally efficient procedure to do this which is almost optimal (in an information-theoretic sense). The key insight is based on a new statistic which we call "signed triangles". To prove optimality we use a bound on the total variation distance between Wishart matrices and the Gaussian Orthogonal Ensemble. This is joint work with Sebastien Bubeck, Jian Ding, and Ronen Eldan. | Abstract: I will talk about a random geometric graph model, where connections between vertices depend on distances between latent d-dimensional labels; we are particularly interested in the high-dimensional case when d is large. Upon observing a graph, we want to tell if it was generated from this geometric model, or from an Erdos-Renyi random graph. We show that there exists a computationally efficient procedure to do this which is almost optimal (in an information-theoretic sense). The key insight is based on a new statistic which we call "signed triangles". To prove optimality we use a bound on the total variation distance between Wishart matrices and the Gaussian Orthogonal Ensemble. This is joint work with Sebastien Bubeck, Jian Ding, and Ronen Eldan. | ||

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== Thursday, January 29, [http://www.math.umn.edu/~arnab/ Arnab Sen], [http://www.math.umn.edu/ University of Minnesota] == | == Thursday, January 29, [http://www.math.umn.edu/~arnab/ Arnab Sen], [http://www.math.umn.edu/ University of Minnesota] == |

## Revision as of 11:18, 20 January 2015

# Spring 2015

**Thursdays in 901 Van Vleck Hall at 2:25 PM**, unless otherwise noted.

**
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu.
**

## Thursday, January 15, Miklos Racz, UC-Berkeley Stats

Title: Testing for high-dimensional geometry in random graphs

Abstract: I will talk about a random geometric graph model, where connections between vertices depend on distances between latent d-dimensional labels; we are particularly interested in the high-dimensional case when d is large. Upon observing a graph, we want to tell if it was generated from this geometric model, or from an Erdos-Renyi random graph. We show that there exists a computationally efficient procedure to do this which is almost optimal (in an information-theoretic sense). The key insight is based on a new statistic which we call "signed triangles". To prove optimality we use a bound on the total variation distance between Wishart matrices and the Gaussian Orthogonal Ensemble. This is joint work with Sebastien Bubeck, Jian Ding, and Ronen Eldan.

## Thursday, January 22, No Seminar

## Thursday, January 29, Arnab Sen, University of Minnesota

Title: TBA

Abstract:

## Thursday, February 5, TBA

Title: TBA

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## Thursday, February 12, TBA

Title: TBA

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## Thursday, February 19, TBA

Title: TBA

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## Thursday, February 26, Dan Crisan, Imperial College London

Title: TBA

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## Thursday, March 5, TBA

Title: TBA

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## Thursday, March 12, TBA

Title: TBA

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## Thursday, March 19, TBA

Title: TBA

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## Thursday, March 26, Elnur Emrah, UW-Madison

Title: TBA

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