Two‐sample inference for high‐dimensional Markov networks

Byol Kim, Song Liu and Mladen Kolar

Journal of the Royal Statistical Society Series B, 2021, vol. 83, issue 5, 939-962

Abstract: Markov networks are frequently used in sciences to represent conditional independence relationships underlying observed variables arising from a complex system. It is often of interest to understand how an underlying network differs between two conditions. In this paper, we develop methods for comparing a pair of high‐dimensional Markov networks where we allow the number of observed variables to increase with the sample sizes. By taking the density ratio approach, we are able to learn the network difference directly and avoid estimating the individual graphs. Our methods are thus applicable even when the individual networks are dense as long as their difference is sparse. We prove finite‐sample Gaussian approximation error bounds for the estimator we construct under significantly weaker assumptions than are typically required for model selection consistency. Furthermore, we propose bootstrap procedures for estimating quantiles of a max‐type statistics based on our estimator, and show how they can be used to test the equality of two Markov networks or construct simultaneous confidence intervals. The performance of our methods is demonstrated through extensive simulations. The scientific usefulness is illustrated with an analysis of a new fMRI data set.

Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/rssb.12446

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:83:y:2021:i:5:p:939-962

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().