Local conditional and marginal approach to parameter estimation in discrete graphical models

Hélène Massam and Nanwei Wang

Journal of Multivariate Analysis, 2018, vol. 164, issue C, 1-21

Abstract: Discrete graphical models are an essential tool in the identification of the relationship between variables in complex high-dimensional problems. When the number of variables p is large, computing the maximum likelihood estimate (henceforth abbreviated MLE) of the parameter is difficult. A popular approach is to estimate the composite MLE (abbreviated MCLE) rather than the MLE, i.e., the value of the parameter that maximizes the product of local conditional or local marginal likelihoods, centered around each vertex v of the graph underlying the model. The purpose of this paper is to first show that, when all the neighbors of v are linked to other nodes in the graph, the estimates obtained through local conditional and marginal likelihoods are identical. Thus the two MCLE are usually very close. Second, we study the asymptotic properties of the composite MLE obtained by averaging of the estimates from the local conditional likelihoods: this is done under the double asymptotic regime when both p and N go to infinity.

Keywords: Discrete graphical models; Distributed estimation; Local conditional; Local marginal; Maximum composite likelihood estimate; “Large p, large N” asymptotics (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X17306139
Full text for ScienceDirect subscribers only

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:eee:jmvana:v:164:y:2018:i:c:p:1-21

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2017.10.003

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().