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Generalized Permutohedra from Probabilistic Graphical Models [article]

Fatemeh Mohammadi, Caroline Uhler, Charles Wang, Josephine Yu
2017 arXiv   pre-print
A graphical model encodes conditional independence relations via the Markov properties.  ...  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  ...  On the other hand, the CI relations corresponding to graphical models in this list all correspond to generalized permutohedra arising as MSMP.  ... 
arXiv:1606.01814v3 fatcat:btm2gkrgefbghos5q2fcihrwqi

Convex Rank Tests and Semigraphoids

Jason Morton, Lior Pachter, Anne Shiu, Bernd Sturmfels, Oliver Wienand
2009 SIAM Journal on Discrete Mathematics  
Of particular interest are graphical tests, which correspond to both graphical models and to graph associahedra.  ...  We establish a bijection between convex rank tests and probabilistic conditional independence structures known as semigraphoids.  ...  Graphical tests. We have seen that semigraphoids are equivalent to convex rank tests. We now explore the connection to graphical models.  ... 
doi:10.1137/080715822 fatcat:tly74ogbqbbpznjwr2oaadbpxy

Root system chip-firing I: Interval-firing [article]

Pavel Galashin, Sam Hopkins, Thomas McConville, Alexander Postnikov
2018 arXiv   pre-print
We prove that these interval-firing processes are always confluent, from any initial weight.  ...  Hopkins, McConville, and Propp showed that this process is confluent from some (but not all) initial configurations of chips.  ...  probabilistic abacus.  ... 
arXiv:1708.04850v3 fatcat:afd72hit7zedvj7qw5t3fckid4

Conditional independence structures over four discrete random variables revisited: conditional Ingleton inequalities [article]

Milan Studeny
2022 arXiv   pre-print
Acknowledgements The research of the author is supported from GA ČR project 19-04579S.  ...  This concept has a key theoretical role in probabilistic reasoning [27] and graphical statistical models [12] .  ...  The same class of polytopes is also known as the class of generalized permutohedra [29] .  ... 
arXiv:2012.04092v3 fatcat:6etaaeb5jndxjiaiq5nauhrh2y

Ordering-Based Causal Structure Learning in the Presence of Latent Variables [article]

Daniel Irving Bernstein, Basil Saeed, Chandler Squires, Caroline Uhler
2020 arXiv   pre-print
We consider the task of learning a causal graph in the presence of latent confounders given i.i.d. samples from the model.  ...  This motivates the Sparsest Poset formulation - that posets can be mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs is Markov equivalent to the true model.  ...  Graphical Models, volume 17. Clarendon Press, 1996. F. Mohammadi, C. Uhler, C. Wang, and J. Yu. Gen- eralized permutohedra from probabilistic graphical models.  ... 
arXiv:1910.09014v2 fatcat:mbphnu7nl5am5fgrkum2juspjm