Basic models and questions in statistical network analysis

Summer 2016


Basic info

Lecturer: Miklos Racz
Course co-designed with: Sébastien Bubeck

Lecture dates, times, and locations at University of Washington:
Lecture dates, times, and locations at the XX Brazilian School of Probability:

Abstract

Extracting information from large graphs has become an important statistical problem since network data is now common in various fields. In this minicourse we will investigate the most natural statistical questions for three canonical probabilistic models of networks: (i) community detection in the stochastic block model, (ii) finding the embedding of a random geometric graph, and (iii) finding the original vertex in a preferential attachment tree. Along the way we will cover many interesting topics in probability theory such as Polya urns, large deviation theory, concentration of measure in high dimension, entropic central limit theorems, and more.

Outline

Lecture 1: A primer on exact recovery in the general stochastic block model.
Lecture 2: Estimating the dimension of a random geometric graph on a high-dimensional sphere.
Lecture 3: Introduction to entropic central limit theorems and a proof of the fundamental limits of dimension estimation in random geometric graphs.
Lectures 4 & 5: Confidence sets for the root in uniform and preferential attachment trees.

Lecture notes

Lecture notes are available here and on the arxiv.

Blog posts

A series of blog posts on Sébastien Bubeck's blog also capture the minicourse. These blog posts are essentially a transcript of the lecture notes, slightly shortened and modified.



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