Unifying Markov properties for graphical models

Steffen L. Lauritzen; Kayvan Sadeghi Sadeghi

doi:10.1214/17-aos1618

Unifying Markov properties for graphical models

Steffen L. Lauritzen, Kayvan Sadeghi Sadeghi

Institut for Matematiske Fag

10 Citationer (Scopus)

31 Downloads (Pure)

Abstract

Several types of graphs with different conditional independence interpretations—also known as Markov properties—have been proposed and used in graphical models. In this paper, we unify these Markov properties by introducing a class of graphs with four types of edges—lines, arrows, arcs and dotted lines—and a single separation criterion. We show that independence structures defined by this class specialize to each of the previously defined cases, when suitable subclasses of graphs are considered. In addition, we define a pairwise Markov property for the subclass of chain mixed graphs, which includes chain graphs with the LWF interpretation, as well as summary graphs (and consequently ancestral graphs). We prove the equivalence of this pairwise Markov property to the global Markov property for compositional graphoid independence models.

Originalsprog	Engelsk
Tidsskrift	Annals of Statistics
Vol/bind	46
Udgave nummer	5
Sider (fra-til)	2251-2278
ISSN	0090-5364
DOI	https://doi.org/10.1214/17-aos1618
Status	Udgivet - okt. 2018

Adgang til dokumentet

10.1214/17-aos1618

AOS1618Forlagets udgivne version, 271 KB
17-AOS1618.pdfForlagets udgivne version, 271 KB

Citationsformater

@article{a9db63319a174bbb87d695722ef15422,

title = "Unifying Markov properties for graphical models",

abstract = "Several types of graphs with different conditional independence interpretations—also known as Markov properties—have been proposed and used in graphical models. In this paper, we unify these Markov properties by introducing a class of graphs with four types of edges—lines, arrows, arcs and dotted lines—and a single separation criterion. We show that independence structures defined by this class specialize to each of the previously defined cases, when suitable subclasses of graphs are considered. In addition, we define a pairwise Markov property for the subclass of chain mixed graphs, which includes chain graphs with the LWF interpretation, as well as summary graphs (and consequently ancestral graphs). We prove the equivalence of this pairwise Markov property to the global Markov property for compositional graphoid independence models.",

author = "Lauritzen, {Steffen L.} and Sadeghi, {Kayvan Sadeghi}",

year = "2018",

month = oct,

doi = "10.1214/17-aos1618",

language = "English",

volume = "46",

pages = "2251--2278",

journal = "Annals of Statistics",

issn = "0090-5364",

publisher = "Institute of Mathematical Statistics",

number = "5",

}

TY - JOUR

T1 - Unifying Markov properties for graphical models

AU - Lauritzen, Steffen L.

AU - Sadeghi, Kayvan Sadeghi

PY - 2018/10

Y1 - 2018/10

N2 - Several types of graphs with different conditional independence interpretations—also known as Markov properties—have been proposed and used in graphical models. In this paper, we unify these Markov properties by introducing a class of graphs with four types of edges—lines, arrows, arcs and dotted lines—and a single separation criterion. We show that independence structures defined by this class specialize to each of the previously defined cases, when suitable subclasses of graphs are considered. In addition, we define a pairwise Markov property for the subclass of chain mixed graphs, which includes chain graphs with the LWF interpretation, as well as summary graphs (and consequently ancestral graphs). We prove the equivalence of this pairwise Markov property to the global Markov property for compositional graphoid independence models.

AB - Several types of graphs with different conditional independence interpretations—also known as Markov properties—have been proposed and used in graphical models. In this paper, we unify these Markov properties by introducing a class of graphs with four types of edges—lines, arrows, arcs and dotted lines—and a single separation criterion. We show that independence structures defined by this class specialize to each of the previously defined cases, when suitable subclasses of graphs are considered. In addition, we define a pairwise Markov property for the subclass of chain mixed graphs, which includes chain graphs with the LWF interpretation, as well as summary graphs (and consequently ancestral graphs). We prove the equivalence of this pairwise Markov property to the global Markov property for compositional graphoid independence models.

U2 - 10.1214/17-aos1618

DO - 10.1214/17-aos1618

M3 - Journal article

SN - 0090-5364

VL - 46

SP - 2251

EP - 2278

JO - Annals of Statistics

JF - Annals of Statistics

IS - 5

ER -

Unifying Markov properties for graphical models

Abstract

Adgang til dokumentet

Fingeraftryk

Citationsformater