DeepAI AI Chat
Log In Sign Up

Testing for directed information graphs

by   Sina Molavipour, et al.
KTH Royal Institute of Technology

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.


page 1

page 2

page 3

page 4


A Bayesian Approach to Directed Acyclic Graphs with a Candidate Graph

Directed acyclic graphs represent the dependence structure among multipl...

Asymptotics for Outlier Hypothesis Testing

We revisit the outlier hypothesis testing framework of Li et al. (TIT 20...

Bipartitioning of directed and mixed random graphs

We show that an intricate relation of cluster properties and optimal bip...

Bernoulli honeywords

Decoy passwords, or “honeywords,” planted in a credential database can a...

Causal motifs and existence of endogenous cascades in directed networks with application to company defaults

Motivated by detection of cascades of defaults in economy, we developed ...

Testing correlation of unlabeled random graphs

We study the problem of detecting the edge correlation between two rando...

Heterogeneous Dense Subhypergraph Detection

We study the problem of testing the existence of a heterogeneous dense s...