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SUMMARY:Characterizing and identifying separable graphical models - Christ
 opher Meek (University of Washington)
DTSTART:20260306T133000Z
DTEND:20260306T141500Z
UID:TALK244423@talks.cam.ac.uk
DESCRIPTION:We study a broad class of graphical models whose independencie
 s correspond to vertex separation in mixed graphs with directed\, undirect
 ed\, and bidirected edges\, that are capable of encoding independence stru
 ctures arising from feedback\, latent and selection mechanisms. We introdu
 ce separable graphs\, in which each missing edge implies the existence of 
 a separating set for its endpoints\, and essentially separable graphs\, th
 ose graphs separation equivalent to a separable graph. We provide characte
 rizations of separable graphs and essentially separable graphs and show th
 at essentially separable graphs are essentially acyclic graphs\, that is\,
  they are separation equivalent to an acyclic graph. We provide two charac
 terizations of the separation equivalence of separable graphs. The first i
 s a direct generalizations of previous characterizations for subfamilies o
 f separable graphs. This characterization requires both adjacency and orie
 ntation information about the graphs. The second characterization\, howeve
 r\, only depends on adjacency and separation properties of the graphs. In 
 particular\, we use separation properties to define arrowhead inducing pai
 rs of vertices. Such pairs of vertices guarantee the existence of an arrow
 head on any edge between them. Our characterization is then given in terms
  of adjacency and edges with arrowhead inducing endpoints. We use arrowhea
 d inducing pairs of vertices to provide a representation of the equivalenc
 e classes of essentially separable graphs and to develop an algorithm that
 \, under suitable assumptions\, identifies the equivalence class of any es
 sentially separable graphical model.\nThis talk is based on the manuscript
  ``Characterizing and identifying separable graphical models'' by Christop
 her Meek and Kayvan Sadeghi.
LOCATION:Seminar Room 1\, Newton Institute
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