Hypotheses testing on infinite random graphs

TL;DR

This paper develops statistical testing methods for infinite random graphs, extending concepts from time series analysis, and demonstrates how to test for properties like the Markov property in trees.

Contribution

It introduces a criterion for consistent hypothesis testing on infinite random graphs, generalizing existing time series results, and applies it to test Markov properties in trees.

Findings

Criterion for consistent tests on infinite graphs

Method to test Markov property in trees

Extension of time series hypothesis testing

Abstract

Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a criterion for the existence of a consistent test for complex hypotheses is presented, generalizing the corresponding results on time series. As an application, it is shown how one can test that a tree has the Markov property, or, more generally, to estimate its memory.