Neighborhood Selection Methods

Authored by: Marloes Maathuis , Mathias Drton , Steffen Lauritzen , Martin Wainwright

Handbook of Graphical Models

Print publication date:  November  2018
Online publication date:  November  2018

Print ISBN: 9781498788625
eBook ISBN: 9780429463976
Adobe ISBN:

10.1201/9780429463976-12

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Abstract

In this chapter, we discuss the problem of edge estimation in undirected graphical models, also known as Markov networks. Given observations from a joint distribution, the goal is to construct an estimate of the edge set of the underlying graph. Since the edges encode conditional independence relationships between individual random variables given all other variables, it is natural to expect that jointly observed vectors reveal information about the unknown edge structure. Applications are widespread in numerous scientific fields, including computer vision, political science, epidemiology, neuroscience, and genetics, where it may be desirable to infer the connectivity between individual pixels, people, organisms, neurons, or genes. We are particularly interested in situations where the number of nodes exceeds the number of observations, and sparse edge structure of the underlying graph may be leveraged to perform edge recovery based on a relatively small sample size.

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