11 research outputs found
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
Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams
We consider the problem of structure learning for bow-free acyclic path
diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG
models that allow for certain hidden variables. We present a first method for
this problem using a greedy score-based search algorithm. We also prove some
necessary and some sufficient conditions for distributional equivalence of BAPs
which are used in an algorithmic ap- proach to compute (nearly) equivalent
model structures. This allows us to infer lower bounds of causal effects. We
also present applications to real and simulated datasets using our publicly
available R-package
Robust causal structure learning with some hidden variables
We introduce a new method to estimate the Markov equivalence class of a
directed acyclic graph (DAG) in the presence of hidden variables, in settings
where the underlying DAG among the observed variables is sparse, and there are
a few hidden variables that have a direct effect on many of the observed ones.
Building on the so-called low rank plus sparse framework, we suggest a
two-stage approach which first removes the effect of the hidden variables, and
then estimates the Markov equivalence class of the underlying DAG under the
assumption that there are no remaining hidden variables. This approach is
consistent in certain high-dimensional regimes and performs favourably when
compared to the state of the art, both in terms of graphical structure recovery
and total causal effect estimation
Local search for efficient causal effect estimation
Causal effect estimation from observational data is an important but
challenging problem. Causal effect estimation with unobserved variables in data
is even more difficult. The challenges lie in (1) whether the causal effect can
be estimated from observational data (identifiability); (2) accuracy of
estimation (unbiasedness), and (3) fast data-driven algorithm for the
estimation (efficiency). Each of the above problems by its own, is challenging.
There does not exist many data-driven methods for causal effect estimation so
far, and they solve one or two of the above problems, but not all. In this
paper, we present an algorithm that is fast, unbiased and is able to confirm if
a causal effect is identifiable or not under a very practical and commonly seen
problem setting. To achieve high efficiency, we approach the causal effect
estimation problem as a local search for the minimal adjustment variable sets
in data. We have shown that identifiability and unbiased estimation can be both
resolved using data in our problem setting, and we have developed theorems to
support the local search for searching for adjustment variable sets to achieve
unbiased causal effect estimation. We make use of frequent pattern mining
strategy to further speed up the search process. Experiments performed on an
extensive collection of synthetic and real-world datasets demonstrate that the
proposed algorithm outperforms the state-of-the-art causal effect estimation
methods in both accuracy and time-efficiency.Comment: 30 page
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