For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria.

Matrix representations and independencies in directed acyclic graphs / G. Marchetti; N. Wermuth. - In: ANNALS OF STATISTICS. - ISSN 0090-5364. - STAMPA. - 37:(2009), pp. 961-978. [10.1214/08-AOS594]

Matrix representations and independencies in directed acyclic graphs

MARCHETTI, GIOVANNI MARIA;
2009

Abstract

For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria.
2009
37
961
978
G. Marchetti; N. Wermuth
File in questo prodotto:
File Dimensione Formato  
Marchetti_Wermuth_AOS_2009.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 193.16 kB
Formato Adobe PDF
193.16 kB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/322528
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 7
social impact