355 research outputs found

    Complete Graphical Characterization and Construction of Adjustment Sets in Markov Equivalence Classes of Ancestral Graphs

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    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

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    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

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    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

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    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

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    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

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    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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