Hypotheses testing on infinite random graphs
This work addresses foundational statistical challenges for researchers in graph theory and machine learning, though it appears incremental as it builds on existing formalism for stationarity.
The paper tackles the problem of statistical testing and learning on infinite random graphs by establishing a criterion for consistent hypothesis testing, generalizing results from time series, and demonstrates its application to testing the Markov property and estimating memory in trees.
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.