Testing for directed information graphs

In this paper, we study a hypothesis test to determine the underlying directed graph structure of nodes in a network, where the nodes represent random processes and the direction of the links indicate a causal relationship between said processes. Specifically, a k-th order Markov structure is consid...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-08
Main Authors: Molavipour, Sina, Bassi, Germán, Skoglund, Mikael
Format: Article
Language:English
Subjects:
False alarms
Graph theory
Hypotheses
Nodes
Random processes
Transition probabilities
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we study a hypothesis test to determine the underlying directed graph structure of nodes in a network, where the nodes represent random processes and the direction of the links indicate a causal relationship between said processes. Specifically, a k-th order Markov structure is considered for them, and the chosen metric to determine a connection between nodes is the directed information. The hypothesis test is based on the empirically calculated transition probabilities which are used to estimate the directed information. For a single edge, it is proven that the detection probability can be chosen arbitrarily close to one, while the false alarm probability remains negligible. When the test is performed on the whole graph, we derive bounds for the false alarm and detection probabilities, which show that the test is asymptotically optimal by properly setting the threshold test and using a large number of samples. Furthermore, we study how the convergence of the measures relies on the existence of links in the true graph.
ISSN:2331-8422
DOI:10.48550/arxiv.2108.11074