On the Markov equivalence of maximal ancestral graphs

2005 ◽  
Vol 48 (4) ◽  
pp. 548 ◽  
Author(s):  
Hui ZHAO
Keyword(s):  
Markov Equivalence ◽  
Maximal Ancestral Graphs

Characterizing the Minimal Essential Graphs of Maximal Ancestral Graphs

2019 ◽  
Vol 34 (04) ◽  
pp. 2059009
Author(s):  
Yanying Li
Keyword(s):  
Sufficient Conditions ◽  
Compact Representation ◽  
Theory Analysis ◽  
Minimum Number ◽  
Np Hard Problem ◽  
Graph Theory Analysis ◽  
Necessary And Sufficient ◽  
Markov Equivalence ◽  
Ancestral Graph ◽  
Maximal Ancestral Graphs

Learning ancestor graph is a typical NP-hard problem. We consider the problem to represent a Markov equivalence class of ancestral graphs with a compact representation. Firstly, the minimal essential graph is defined to represent the equivalent class of maximal ancestral graphs with the minimum number of invariant arrowheads. Then, an algorithm is proposed to learn the minimal essential graph of ancestral graphs based on the detection of minimal collider paths. It is the first algorithm to use necessary and sufficient conditions for Markov equivalence as a base to seek essential graphs. Finally, a set of orientation rules is presented to orient edge marks of a minimal essential graph. Theory analysis shows our algorithm is sound, and complete in the sense of recognizing all minimal collider paths in a given ancestral graph. And the experiment results show we can discover all invariant marks by these orientation rules.

scholarly journals Markov equivalence for ancestral graphs

2009 ◽  
Vol 37 (5B) ◽  
pp. 2808-2837 ◽  
Author(s):  
R. Ayesha Ali ◽  
Thomas S. Richardson ◽  
Peter Spirtes
Keyword(s):  
Markov Equivalence

On scoring Maximal Ancestral Graphs with the Max–Min Hill Climbing algorithm

2018 ◽  
Vol 102 ◽  
pp. 74-85 ◽  
Author(s):  
Konstantinos Tsirlis ◽  
Vincenzo Lagani ◽  
Sofia Triantafillou ◽  
Ioannis Tsamardinos
Keyword(s):  
Hill Climbing ◽  
Hill Climbing Algorithm ◽  
Maximal Ancestral Graphs

scholarly journals Markov measures determine the zeta function

1987 ◽  
Vol 7 (2) ◽  
pp. 303-311 ◽  
Author(s):  
Selim Tuncel
Keyword(s):  
Zeta Function ◽  
Finite Type ◽  
Periodic Orbits ◽  
Point Of View ◽  
Subshifts Of Finite Type ◽  
Markov Measures ◽  
Markov Equivalence

AbstractWith the purpose of understanding when two subshifts of finite type are equivalent from the point of view of their spaces of Markov measures we propose the notion of Markov equivalence. We show that a Markov equivalence must respect the cycles (periodic orbits) of the subshifts. In particular, Markov equivalent subshifts of finite type have the same zeta function.

scholarly journals A simple interpretation of undirected edges in essential graphs is wrong

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249415
Author(s):  
Erich Kummerfeld
Keyword(s):  
Artificial Intelligence ◽  
Directed Acyclic Graphs ◽  
Equivalence Classes ◽  
The Other ◽  
Causal Discovery ◽  
Simple Interpretation ◽  
Acyclic Graphs ◽  
Dutch Books ◽  
Markov Equivalence ◽  
Causal Directionality

Artificial intelligence for causal discovery frequently uses Markov equivalence classes of directed acyclic graphs, graphically represented as essential graphs, as a way of representing uncertainty in causal directionality. There has been confusion regarding how to interpret undirected edges in essential graphs, however. In particular, experts and non-experts both have difficulty quantifying the likelihood of uncertain causal arrows being pointed in one direction or another. A simple interpretation of undirected edges treats them as having equal odds of being oriented in either direction, but I show in this paper that any agent interpreting undirected edges in this simple way can be Dutch booked. In other words, I can construct a set of bets that appears rational for the users of the simple interpretation to accept, but for which in all possible outcomes they lose money. I put forward another interpretation, prove this interpretation leads to a bet-taking strategy that is sufficient to avoid all Dutch books of this kind, and conjecture that this strategy is also necessary for avoiding such Dutch books. Finally, I demonstrate that undirected edges that are more likely to be oriented in one direction than the other are common in graphs with 4 nodes and 3 edges.

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