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 Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics

2020 ◽  
Vol 58 (4) ◽  
pp. 1129-1179
Author(s):  
Guido W. Imbens
Keyword(s):  
Directed Acyclic Graph ◽  
Empirical Work ◽  
Directed Acyclic Graphs ◽  
Potential Outcome ◽  
Acyclic Graph ◽  
Acyclic Graphs ◽  
Outcome Framework ◽  
Outcome Perspective

In this essay I discuss potential outcome and graphical approaches to causality, and their relevance for empirical work in economics. I review some of the work on directed acyclic graphs, including the recent The Book of Why (Pearl and Mackenzie 2018). I also discuss the potential outcome framework developed by Rubin and coauthors (e.g., Rubin 2006), building on work by Neyman (1990 [1923]). I then discuss the relative merits of these approaches for empirical work in economics, focusing on the questions each framework answers well, and why much of the the work in economics is closer in spirit to the potential outcome perspective. (JEL C31, C36, I26)

MINIMIZATION OF PLANAR DIRECTED ACYCLIC GRAPH ALGEBRAS

2013 ◽  
Vol 24 (04) ◽  
pp. 519-531
Author(s):  
ANTONIOS KALAMPAKAS ◽  
OLYMPIA LOUSCOU-BOZAPALIDOU
Keyword(s):  
Directed Acyclic Graph ◽  
Directed Acyclic Graphs ◽  
Graph Algebras ◽  
Minimization Method ◽  
Nondeterministic Automaton ◽  
Acyclic Graph ◽  
Acyclic Graphs

We introduce planar directed acyclic graph algebras and present an explicit minimization method. The minimal simulation of a nondeterministic automaton on planar directed acyclic graphs is constructed.

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 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

Structural Intervention Distance for Evaluating Causal Graphs

2015 ◽  
Vol 27 (3) ◽  
pp. 771-799 ◽  
Author(s):  
Jonas Peters ◽  
Peter Bühlmann
Keyword(s):  
Causal Inference ◽  
Directed Acyclic Graph ◽  
Hamming Distance ◽  
Equivalence Classes ◽  
Additional Measure ◽  
Structural Intervention ◽  
Acyclic Graph ◽  
Causal Graphs ◽  
Software Code ◽  
Markov Equivalence

Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-)metric between DAGs, the structural intervention distance (SID). The SID is based on a graphical criterion only and quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. It is therefore well suited for evaluating graphs that are used for computing interventions. Instead of DAGs, it is also possible to compare CPDAGs, completed partially DAGs that represent Markov equivalence classes. The SID differs significantly from the widely used structural Hamming distance and therefore constitutes a valuable additional measure. We discuss properties of this distance and provide a (reasonably) efficient implementation with software code available on the first author’s home page.

scholarly journals Improvement of layered directed acyclic graph layout in CourseViewer

2019 ◽  
Author(s):  
Geovana Marinello Palomo ◽  
Celmar Guimaraes da Silva
Keyword(s):  
Directed Acyclic Graph ◽  
Directed Acyclic Graphs ◽  
Graph Layout ◽  
Acyclic Graph ◽  
Interactive Diagrams ◽  
Edge Crossing ◽  
Acyclic Graphs ◽  
Edge Bundling ◽  
Crossing Minimization

CourseViewer is a software that uses interactive diagrams to assist students, teachers, and course coordinators in analyzing information related to academic transcripts and course curriculum, which are represented as layered directed acyclic graphs of subjects and prerequisites. Recent improvements in the layout of these graphs included edge crossing minimization and better horizontal positioning of nodes. This work continues this list of improvements by means of researching edge bundling techniques that group edges of layered directed acyclic graphs, in order to simplify graph understanding. We selected and implemented an edge bundling technique in CourseViewer. We also exemplify course curricula in which we applied this technique.

Propagating Distributions Up Directed Acyclic Graphs

1999 ◽  
Vol 11 (1) ◽  
pp. 215-227 ◽  
Author(s):  
Eric B. Baum ◽  
Warren D. Smith
Keyword(s):  
Graphical Models ◽  
Directed Acyclic Graph ◽  
Search Tree ◽  
Directed Acyclic Graphs ◽  
Game Tree ◽  
Worst Case ◽  
Exponential Time ◽  
Acyclic Graphs ◽  
Game Trees ◽  
Directed Growth

In a previous article, we considered game trees as graphical models. Adopting an evaluation function that returned a probability distribution over values likely to be taken at a given position, we described how to build a model of uncertainty and use it for utility-directed growth of the search tree and for deciding on a move after search was completed. In some games, such as chess and Othello, the same position can occur more than once, collapsing the game tree to a directed acyclic graph (DAG). This induces correlations among the distributions at sibling nodes. This article discusses some issues that arise in extending our algorithms to a DAG. We give a simply described algorithm for correctly propagating distributions up a game DAG, taking account of dependencies induced by the DAG structure. This algorithm is exponential time in the worst case. We prove that it is #P complete to propagate distributions up a game DAG correctly. We suggest how our exact propagation algorithm can yield a fast but inexact heuristic.

scholarly journals A directed acyclic graph for interactions

2020 ◽  
Author(s):  
Anton Nilsson ◽  
Carl Bonander ◽  
Ulf Strömberg ◽  
Jonas Björk
Keyword(s):  
Directed Acyclic Graph ◽  
Causal Effect ◽  
Target Population ◽  
Directed Acyclic Graphs ◽  
Indirect Interaction ◽  
Causal Relationships ◽  
Fundamental Feature ◽  
Acyclic Graph ◽  
Acyclic Graphs ◽  
New Type

Abstract Background Directed acyclic graphs (DAGs) are of great help when researchers try to understand the nature of causal relationships and the consequences of conditioning on different variables. One fundamental feature of causal relations that has not been incorporated into the standard DAG framework is interaction, i.e. when the effect of one variable (on a chosen scale) depends on the value that another variable is set to. In this paper, we propose a new type of DAG—the interaction DAG (IDAG), which can be used to understand this phenomenon. Methods The IDAG works like any DAG but instead of including a node for the outcome, it includes a node for a causal effect. We introduce concepts such as confounded interaction and total, direct and indirect interaction, showing that these can be depicted in ways analogous to how similar concepts are depicted in standard DAGs. This also allows for conclusions on which treatment interactions to account for empirically. Moreover, since generalizability can be compromised in the presence of underlying interactions, the framework can be used to illustrate threats to generalizability and to identify variables to account for in order to make results valid for the target population. Conclusions The IDAG allows for a both intuitive and stringent way of illustrating interactions. It helps to distinguish between causal and non-causal mechanisms behind effect variation. Conclusions about how to empirically estimate interactions can be drawn—as well as conclusions about how to achieve generalizability in contexts where interest lies in estimating an overall effect.

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