355 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
Learning Adjustment Sets from Observational and Limited Experimental Data
Estimating causal effects from observational data is not always possible due
to confounding. Identifying a set of appropriate covariates (adjustment set)
and adjusting for their influence can remove confounding bias; however, such a
set is typically not identifiable from observational data alone. Experimental
data do not have confounding bias, but are typically limited in sample size and
can therefore yield imprecise estimates. Furthermore, experimental data often
include a limited set of covariates, and therefore provide limited insight into
the causal structure of the underlying system. In this work we introduce a
method that combines large observational and limited experimental data to
identify adjustment sets and improve the estimation of causal effects. The
method identifies an adjustment set (if possible) by calculating the marginal
likelihood for the experimental data given observationally-derived prior
probabilities of potential adjustmen sets. In this way, the method can make
inferences that are not possible using only the conditional dependencies and
independencies in all the observational and experimental data. We show that the
method successfully identifies adjustment sets and improves causal effect
estimation in simulated data, and it can sometimes make additional inferences
when compared to state-of-the-art methods for combining experimental and
observational data.Comment: 10 pages, 5 figure
Interpreting and using CPDAGs with background knowledge
We develop terminology and methods for working with maximally oriented
partially directed acyclic graphs (maximal PDAGs). Maximal PDAGs arise from
imposing restrictions on a Markov equivalence class of directed acyclic graphs,
or equivalently on its graphical representation as a completed partially
directed acyclic graph (CPDAG), for example when adding background knowledge
about certain edge orientations. Although maximal PDAGs often arise in
practice, causal methods have been mostly developed for CPDAGs. In this paper,
we extend such methodology to maximal PDAGs. In particular, we develop
methodology to read off possible ancestral relationships, we introduce a
graphical criterion for covariate adjustment to estimate total causal effects,
and we adapt the IDA and joint-IDA frameworks to estimate multi-sets of
possible causal effects. We also present a simulation study that illustrates
the gain in identifiability of total causal effects as the background knowledge
increases. All methods are implemented in the R package pcalg.Comment: 17 pages, 6 figures, UAI 201
On the Representation of Causal Background Knowledge and its Applications in Causal Inference
Causal background knowledge about the existence or the absence of causal
edges and paths is frequently encountered in observational studies. The shared
directed edges and links of a subclass of Markov equivalent DAGs refined due to
background knowledge can be represented by a causal maximally partially
directed acyclic graph (MPDAG). In this paper, we first provide a sound and
complete graphical characterization of causal MPDAGs and give a minimal
representation of a causal MPDAG. Then, we introduce a novel representation
called direct causal clause (DCC) to represent all types of causal background
knowledge in a unified form. Using DCCs, we study the consistency and
equivalency of causal background knowledge and show that any causal background
knowledge set can be equivalently decomposed into a causal MPDAG plus a minimal
residual set of DCCs. Polynomial-time algorithms are also provided for checking
the consistency, equivalency, and finding the decomposed MPDAG and residual
DCCs. Finally, with causal background knowledge, we prove a sufficient and
necessary condition to identify causal effects and surprisingly find that the
identifiability of causal effects only depends on the decomposed MPDAG. We also
develop a local IDA-type algorithm to estimate the possible values of an
unidentifiable effect. Simulations suggest that causal background knowledge can
significantly improve the identifiability of causal effects
Conditional Adjustment in a Markov Equivalence Class
We consider the problem of identifying a conditional causal effect through
covariate adjustment. We focus on the setting where the causal graph is known
up to one of two types of graphs: a maximally oriented partially directed
acyclic graph (MPDAG) or a partial ancestral graph (PAG). Both MPDAGs and PAGs
represent equivalence classes of possible underlying causal models. After
defining adjustment sets in this setting, we provide a necessary and sufficient
graphical criterion -- the conditional adjustment criterion -- for finding
these sets under conditioning on variables unaffected by treatment. We further
provide explicit sets from the graph that satisfy the conditional adjustment
criterion, and therefore, can be used as adjustment sets for conditional causal
effect identification.Comment: 29 pages, 6 figure
Establishing Markov Equivalence in Cyclic Directed Graphs
We present a new, efficient procedure to establish Markov equivalence between
directed graphs that may or may not contain cycles under the
\textit{d}-separation criterion. It is based on the Cyclic Equivalence Theorem
(CET) in the seminal works on cyclic models by Thomas Richardson in the mid
'90s, but now rephrased from an ancestral perspective. The resulting
characterization leads to a procedure for establishing Markov equivalence
between graphs that no longer requires tests for d-separation, leading to a
significantly reduced algorithmic complexity. The conceptually simplified
characterization may help to reinvigorate theoretical research towards sound
and complete cyclic discovery in the presence of latent confounders. This
version includes a correction to rule (iv) in Theorem 1, and the subsequent
adjustment in part 2 of Algorithm 2.Comment: Correction to original version published at UAI-2023. Includes
additional experimental results and extended proof details in supplemen
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