1,354 research outputs found
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
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
Model selection and local geometry
We consider problems in model selection caused by the geometry of models
close to their points of intersection. In some cases---including common classes
of causal or graphical models, as well as time series models---distinct models
may nevertheless have identical tangent spaces. This has two immediate
consequences: first, in order to obtain constant power to reject one model in
favour of another we need local alternative hypotheses that decrease to the
null at a slower rate than the usual parametric (typically we will
require or slower); in other words, to distinguish between the
models we need large effect sizes or very large sample sizes. Second, we show
that under even weaker conditions on their tangent cones, models in these
classes cannot be made simultaneously convex by a reparameterization.
This shows that Bayesian network models, amongst others, cannot be learned
directly with a convex method similar to the graphical lasso. However, we are
able to use our results to suggest methods for model selection that learn the
tangent space directly, rather than the model itself. In particular, we give a
generic algorithm for learning Bayesian network models
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
Learning high-dimensional directed acyclic graphs with latent and selection variables
We consider the problem of learning causal information between random
variables in directed acyclic graphs (DAGs) when allowing arbitrarily many
latent and selection variables. The FCI (Fast Causal Inference) algorithm has
been explicitly designed to infer conditional independence and causal
information in such settings. However, FCI is computationally infeasible for
large graphs. We therefore propose the new RFCI algorithm, which is much faster
than FCI. In some situations the output of RFCI is slightly less informative,
in particular with respect to conditional independence information. However, we
prove that any causal information in the output of RFCI is correct in the
asymptotic limit. We also define a class of graphs on which the outputs of FCI
and RFCI are identical. We prove consistency of FCI and RFCI in sparse
high-dimensional settings, and demonstrate in simulations that the estimation
performances of the algorithms are very similar. All software is implemented in
the R-package pcalg.Comment: Published in at http://dx.doi.org/10.1214/11-AOS940 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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
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