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:
- June 6, Monday, 2 - 3 pm, CSE 403 -- note location change
- June 7, Tuesday, 11 am - 12 pm, CSE 305
- June 8, Wednesday, 2 - 3 pm, CSE 305
- June 9, Thursday, 2 - 3 pm, CSE 403
- June 10, Friday, 2 - 3 pm, CSE 403 -- note location change
- July 4 - 8, Monday - Friday.
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.
- A primer on exact recovery in the general stochastic block model
- Estimating the dimension of a random geometric graph on a high-dimensional sphere
- The fundamental limits of dimension estimation in random geometric graphs
- Entropic central limit theorems and a proof of the fundamental limits of dimension estimation
- Confidence sets for the root in uniform and preferential attachment trees
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