6,862 research outputs found
Searching for the Causal Structure of a Vector Autoregression
Vector autoregressions (VARs) are economically interpretable only when identified by being transformed into a structural form (the SVAR) in which the contemporaneous variables stand in a well-defined causal order. These identifying transformations are not unique. It is widely believed that practitioners must choose among them using a priori theory or other criteria not rooted in the data under analysis. We show how to apply graph-theoretic methods of searching for causal structure based on relations of conditional independence to select among the possible causal orders – or at least to reduce the admissible causal orders to a narrow equivalence class. The graph-theoretic approaches were developed by computer scientists and philosophers (Pearl, Glymour, Spirtes among others) and applied to cross-sectional data. We provide an accessible introduction to this work. Then building on the work of Swanson and Granger (1997), we show how to apply it to searching for the causal order of an SVAR. We present simulation results to show how the efficacy of the search method algorithm varies with signal strength for realistic sample lengths. Our findings suggest that graph-theoretic methods may prove to be a useful tool in the analysis of SVARs.search, causality, structural vector autoregression, graph theory, common cause, causal Markov condition, Wold causal order, identification; PC algorithm
Structural Agnostic Modeling: Adversarial Learning of Causal Graphs
A new causal discovery method, Structural Agnostic Modeling (SAM), is
presented in this paper. Leveraging both conditional independencies and
distributional asymmetries in the data, SAM aims at recovering full causal
models from continuous observational data along a multivariate non-parametric
setting. The approach is based on a game between players estimating each
variable distribution conditionally to the others as a neural net, and an
adversary aimed at discriminating the overall joint conditional distribution,
and that of the original data. An original learning criterion combining
distribution estimation, sparsity and acyclicity constraints is used to enforce
the end-to-end optimization of the graph structure and parameters through
stochastic gradient descent. Besides the theoretical analysis of the approach
in the large sample limit, SAM is extensively experimentally validated on
synthetic and real data
Causal Reasoning with Ancestral Graphs
Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate post-intervention probabilities to pre-intervention probabilities that are estimable from observational data. However, such causal diagrams are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on data-mining can only output an equivalence class of causal diagrams (rather than a single one). This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a (partial) ancestral graph. We present two main results. The first result extends Pearl (1995)'s celebrated do-calculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl's calculus---the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (1993)
Unifying Gaussian LWF and AMP Chain Graphs to Model Interference
An intervention may have an effect on units other than those to which it was
administered. This phenomenon is called interference and it usually goes
unmodeled. In this paper, we propose to combine Lauritzen-Wermuth-Frydenberg
and Andersson-Madigan-Perlman chain graphs to create a new class of causal
models that can represent both interference and non-interference relationships
for Gaussian distributions. Specifically, we define the new class of models,
introduce global and local and pairwise Markov properties for them, and prove
their equivalence. We also propose an algorithm for maximum likelihood
parameter estimation for the new models, and report experimental results.
Finally, we show how to compute the effects of interventions in the new models.Comment: v2: Section 6 has been added. v3: Sections 7 and 8 have been added.
v4: Major reorganization. v5: Major reorganization. v6-v7: Minor changes. v8:
Addition of Appendix B. v9: Section 7 has been rewritte
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
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