Networked interactions, graphical models and econometrics perspectives in data analysis

This thesis is composed of two independent parts. In Part I, we study higher-order interactions in both graphical models and networks, i.e., interactions between more than two nodes. In the graphical model setting, we do not assume that interactions are known and our goal is to recover the structure of the graph. Our main contribution is an algebraic criterion that enables us to determine whether a set of observed variables have a single cause or multiple causes. We also prove that this criterion holds in the presence of confounders, i.e., when the causes are hidden. In the network setting, we assume that the structure of the graph is known. Our objective is then to identify what kind of information about data can be learned from the analysis of higher-order interactions. More precisely, using the generalization of the normalized Laplacian and random walks on graphs to simplicial complexes, we study a simplicial notion of PageRank centrality as defined in [Schaub et al., 2018].

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Institute for Data, Systems, and Society

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Seby, Jean-Baptiste.

Advisor dc:contributor.advisor

• Chintan Vaishnav and John Tsitsiklis.

• Institute for Data, Systems, and Society.
• Technology and Policy Program.
• Electrical Engineering and Computer Science.

Statement dc:rights

• MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/129081

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/129081