Generalized Permutohedra from Probabilistic Graphical Models
Name
16m107894x.pdf
Description
Published version
Size
13.87 MB
Format
Adobe PDF
Checksum (MD5)
3b73530c687df29b07f1db10ffdc7153
Author(s)
Mohammadi, Fatemeh
Uhler, Caroline
Wang, Charles
Yu, Josephine
Date Issued
2018
Journal
SIAM Journal on Discrete Mathematics
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
© 2018 Society for Industrial and Applied Mathematics. A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be constructed as a Minkowski sum of standard simplices. There is an analogous polytope for conditional independence relations coming from a regular Gaussian model, and it can be defined using multiinformation or relative entropy. For directed acyclic graphical models and also for mixed graphical models containing undirected, directed, and bidirected edges, we give a construction of this polytope, up to equivalence of normal fans, as a Minkowski sum of matroid polytopes. Finally, we apply this geometric insight to construct a new ordering-based search algorithm for causal inference via directed acyclic graphical models.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/16M107894X
