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DY: Fachverband Dynamik und Statistische Physik

DY 1: Tutorial: Statistical Physics Methods for Data Science in Physics (joint SOE/DY/CPP/BP/jDPG) (joint session SOE/TUT/DY)

DY 1.1: Tutorium

Sonntag, 31. März 2019, 16:00–16:50, H3

Statistical network inference and community detection — •Tiago Peixoto — University of Bath, UK

Network structures are shaped by evolutionary mechanisms and determine the central aspects of how a system functions. However, differently from systems that are naturally embedded in space, we cannot simply “look” at network in order to extract its most important structural patterns. Instead, we must rely on well-founded algorithmic methods to extract this information from data in an interpretable way. In this tutorial, we review a principled approach to this problem based on the elaboration of probabilistic models of network structure, and their statistical inference from empirical data. We focus in particular on the detection of modules (or “communities”) in networks.

We aim to cover the following topics: 1. The stochastic block model (SBM) and its variants (degree correction, overlapping groups, etc.); 2. Bayesian inference and model selection: Distinguishing structure from noise; 3. Generalizing from data: Prediction of missing and spurious links; 4. Model extensions: Layered, dynamic SBMs, and generalized models on continuous latent spaces; 5 Fundamental limits of inference, and the undetectability phase transition; 6. Efficient inference algorithms; 7. Network reconstruction from noisy or indirect data.