scholarly journals Learning Markov Equivalence Classes of Directed Acyclic Graphs: An Objective Bayes Approach

2018 ◽  
Vol 13 (4) ◽  
pp. 1235-1260 ◽  
Author(s):  
Federico Castelletti ◽  
Guido Consonni ◽  
Marco L. Della Vedova ◽  
Stefano Peluso
Keyword(s):  
Directed Acyclic Graphs ◽  
Equivalence Classes ◽  
Objective Bayes ◽  
Acyclic Graphs ◽  
Markov Equivalence ◽  
Bayes Approach

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.

scholarly journals Consistency Guarantees for Greedy Permutation-Based Causal Inference Algorithms

Biometrika ◽  
2021 ◽  
Author(s):  
L Solus ◽  
Y Wang ◽  
C Uhler
Keyword(s):  
Graphical Models ◽  
Directed Acyclic Graph ◽  
Real Data ◽  
Directed Acyclic Graphs ◽  
Equivalence Classes ◽  
Acyclic Graph ◽  
Basic Task ◽  
Acyclic Graphs ◽  
Edge Graph ◽  
Markov Equivalence

Abstract Directed acyclic graphical models are widely used to represent complex causal systems. Since the basic task of learning such a model from data is NP-hard, a standard approach is greedy search over the space of directed acyclic graphs or Markov equivalence classes of directed acyclic graphs. As the space of directed acyclic graphs on p nodes and the associated space of Markov equivalence classes are both much larger than the space of permutations, it is desirable to consider permutation-based greedy searches. Here, we provide the first consistency guarantees, both uniform and high-dimensional, of a greedy permutation-based search. This search corresponds to a simplex-like algorithm operating over the edge-graph of a subpolytope of the permutohedron, called a directed acyclic graph associahedron. Every vertex in this polytope is associated with a directed acyclic graph, and hence with a collection of permutations that are consistent with the directed acyclic graph ordering. A walk is performed on the edges of the polytope maximizing the sparsity of the associated directed acyclic graphs. We show via simulated and real data that this permutation search is competitive with current approaches.

scholarly journals Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables

2015 ◽  
Vol 3 (2) ◽  
pp. 189-205 ◽  
Author(s):  
Elizabeth S. Allman ◽  
John A. Rhodes ◽  
Elena Stanghellini ◽  
Marco Valtorta
Keyword(s):  
Bayesian Networks ◽  
Hidden Variables ◽  
Directed Acyclic Graphs ◽  
Essential Property ◽  
State Spaces ◽  
Parameter Identifiability ◽  
Acyclic Graphs ◽  
Finite State ◽  
Hidden States ◽  
Markov Equivalence

AbstractIdentifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of finite state spaces, we give algebraic arguments establishing identifiability of some special models on small directed acyclic graphs (DAGs). We also establish that, for fixed state spaces, generic identifiability of parameters depends only on the Markov equivalence class of the DAG. To illustrate the use of these results, we investigate identifiability for all binary Bayesian networks with up to five variables, one of which is hidden and parental to all observable ones. Surprisingly, some of these models have parameterizations that are generically 4-to-one, and not 2-to-one as label swapping of the hidden states would suggest. This leads to interesting conflict in interpreting causal effects.

scholarly journals Directed acyclic graphs: An under-utilized tool for child maltreatment research

2019 ◽  
Vol 91 ◽  
pp. 78-87 ◽  
Author(s):  
Anna E. Austin ◽  
Tania A. Desrosiers ◽  
Meghan E. Shanahan
Keyword(s):  
Child Maltreatment ◽  
Directed Acyclic Graphs ◽  
Acyclic Graphs
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