114 research outputs found
Complete Graphical Characterization and Construction of Adjustment Sets in Markov Equivalence Classes of Ancestral Graphs
We present a graphical criterion for covariate adjustment that is sound and
complete for four different classes of causal graphical models: directed
acyclic graphs (DAGs), maximum ancestral graphs (MAGs), completed partially
directed acyclic graphs (CPDAGs), and partial ancestral graphs (PAGs). Our
criterion unifies covariate adjustment for a large set of graph classes.
Moreover, we define an explicit set that satisfies our criterion, if there is
any set that satisfies our criterion. We also give efficient algorithms for
constructing all sets that fulfill our criterion, implemented in the R package
dagitty. Finally, we discuss the relationship between our criterion and other
criteria for adjustment, and we provide new soundness and completeness proofs
for the adjustment criterion for DAGs.Comment: 58 pages, 12 figures, to appear in JML
A Complete Generalized Adjustment Criterion
Covariate adjustment is a widely used approach to estimate total causal
effects from observational data. Several graphical criteria have been developed
in recent years to identify valid covariates for adjustment from graphical
causal models. These criteria can handle multiple causes, latent confounding,
or partial knowledge of the causal structure; however, their diversity is
confusing and some of them are only sufficient, but not necessary. In this
paper, we present a criterion that is necessary and sufficient for four
different classes of graphical causal models: directed acyclic graphs (DAGs),
maximum ancestral graphs (MAGs), completed partially directed acyclic graphs
(CPDAGs), and partial ancestral graphs (PAGs). Our criterion subsumes the
existing ones and in this way unifies adjustment set construction for a large
set of graph classes.Comment: 10 pages, 6 figures, To appear in Proceedings of the 31st Conference
on Uncertainty in Artificial Intelligence (UAI2015
pgmpy: A Python Toolkit for Bayesian Networks
Bayesian Networks (BNs) are used in various fields for modeling, prediction,
and decision making. pgmpy is a python package that provides a collection of
algorithms and tools to work with BNs and related models. It implements
algorithms for structure learning, parameter estimation, approximate and exact
inference, causal inference, and simulations. These implementations focus on
modularity and easy extensibility to allow users to quickly modify/add to
existing algorithms, or to implement new algorithms for different use cases.
pgmpy is released under the MIT License; the source code is available at:
https://github.com/pgmpy/pgmpy, and the documentation at: https://pgmpy.org
A Simple Unified Approach to Testing High-Dimensional Conditional Independences for Categorical and Ordinal Data
Conditional independence (CI) tests underlie many approaches to model testing
and structure learning in causal inference. Most existing CI tests for
categorical and ordinal data stratify the sample by the conditioning variables,
perform simple independence tests in each stratum, and combine the results.
Unfortunately, the statistical power of this approach degrades rapidly as the
number of conditioning variables increases. Here we propose a simple unified CI
test for ordinal and categorical data that maintains reasonable calibration and
power in high dimensions. We show that our test outperforms existing baselines
in model testing and structure learning for dense directed graphical models
while being comparable for sparse models. Our approach could be attractive for
causal model testing because it is easy to implement, can be used with
non-parametric or parametric probability models, has the symmetry property, and
has reasonable computational requirements
Reply to Comment on "Inverse Square L\'evy Walks are not Optimal Search Strategies for d \geq 2 "
We refute here the concernes raised in the Comment of our letter. This reply
states clearly the validity range of our results and shows that the optimality
of inverse-square Levy walks at the basis of the Levy flight foraging
hypothesis is generically unfounded. We also give the precise set of conditions
for which inverse-levy square Levy walks turn to be optimal, conditions which
are unlikely to be verified biologically
Inverse square L\'evy walks are not optimal search strategies for
The L\'evy hypothesis states that inverse square L\'evy walks are optimal
search strategies because they maximise the encounter rate with sparse,
randomly distributed, replenishable targets. It has served as a theoretical
basis to interpret a wealth of experimental data at various scales, from
molecular motors to animals looking for resources, putting forward the
conclusion that many living organisms perform L\'evy walks to explore space
because of their optimal efficiency. Here we provide analytically the
dependence on target density of the encounter rate of L\'evy walks for any
space dimension ; in particular, this scaling is shown to be {\it
independent} of the L\'evy exponent for the biologically relevant case
, which proves that the founding result of the L\'evy hypothesis is
incorrect. As a consequence, we show that optimizing the encounter rate with
respect to is {\it irrelevant} : it does not change the scaling with
density and can lead virtually to {\it any} optimal value of depending
on system dependent modeling choices. The conclusion that observed inverse
square L\'evy patterns are the result of a common selection process based
purely on the kinetics of the search behaviour is therefore unfounded.Comment: Accepted in Phys. Rev. Let
Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Framework
Principled reasoning about the identifiability of causal effects from
non-experimental data is an important application of graphical causal models.
This paper focuses on effects that are identifiable by covariate adjustment, a
commonly used estimation approach. We present an algorithmic framework for
efficiently testing, constructing, and enumerating -separators in ancestral
graphs (AGs), a class of graphical causal models that can represent uncertainty
about the presence of latent confounders. Furthermore, we prove a reduction
from causal effect identification by covariate adjustment to -separation in
a subgraph for directed acyclic graphs (DAGs) and maximal ancestral graphs
(MAGs). Jointly, these results yield constructive criteria that characterize
all adjustment sets as well as all minimal and minimum adjustment sets for
identification of a desired causal effect with multivariate exposures and
outcomes in the presence of latent confounding. Our results extend several
existing solutions for special cases of these problems. Our efficient
algorithms allowed us to empirically quantify the identifiability gap between
covariate adjustment and the do-calculus in random DAGs and MAGs, covering a
wide range of scenarios. Implementations of our algorithms are provided in the
R package dagitty.Comment: 52 pages, 20 figures, 12 table
Robust causal inference using directed acyclic graphs: the R package ‘dagitty’
Directed acyclic graphs (DAGs), which offer systematic representations of causal relationships, have become an established framework for the analysis of causal inference in epidemiology, often being used to determine covariate adjustment sets for minimizing confounding bias. DAGitty is a popular web application for drawing and analysing DAGs. Here we introduce the R package ‘dagitty’, which provides access to all of the capabilities of the DAGitty web application within the R platform for statistical computing, and also offers several new functions. We describe how the R package ‘dagitty’ can be used to: evaluate whether a DAG is consistent with the dataset it is intended to represent; enumerate ‘statistically equivalent’ but causally different DAGs; and identify exposure outcome adjustment sets that are valid for causally different but statistically equivalent DAGs. This functionality enables epidemiologists to detect causal misspecifications in DAGs and make robust inferences that remain valid for a range of different DAGs. The R package ‘dagitty’ is available through the comprehensive R archive network (CRAN) at
[https://cran.r-project.org/web/packages/dagitty/]. The source code is available on github at [https://github.com/jtextor/dagitty]. The web application ‘DAGitty’ is free software, licensed under the GNU general public licence (GPL) version 2 and is available at [http://
dagitty.net/]
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