Estimating high-dimensional intervention effects from observational data

By Marloes H. Maathuis, Markus Kalisch, Peter Buhlmann. 2008

415 citations recorded by the source corpus.

We assume that we have observational data generated from an unknown underlying directed acyclic graph (DAG) model. A DAG is typically not identifiable from observational data, but it is possible to consistently estimate the equivalence class of a DAG. Moreover, for any given DAG, causal effects can be estimated using intervention calculus. In this paper, we combine these two parts. For each DAG in the estimated equivalence class, we use intervention calculus to estimate the causal effects of the covariates on the response. This yields a collection of estimated causal effects for each covariate. We show that the distinct values in this set can be consistently estimated by an algorithm that uses only local information of the graph. This local approach is computationally fast and feasible in high-dimensional problems. We propose to use summary measures of the set of possible causal effects to determine variable importance. In particular, we use the minimum absolute value of this set, since that is a lower bound on the size of the causal effect. We demonstrate the merits of our methods in a simulation study and on a data set about riboflavin production.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Causal inference by using invariant prediction: identification and confidence intervals (2015, methodology): “As alternative methods we consider IDA [Maathuis et al., 2009] based on the PC algorithm [Spirtes et al., 2000] and a method that ranks the absolute value of marginal correlation ( j 1 → j 2 and j 2 → j 1 obtain the same score and are ranked randomly), both of which make use only of the observationa”
Order-independent constraint-based causal structure learning (2012, methodology): “We then deﬁned the top 10% of the largest eﬀects in absolute value as the target set of eﬀects, and we evaluated how well IDA (Maathuis et al., 2009, 2010) identiﬁed these eﬀects from the observational data.”
Causal Structure Learning (2017, background): “Moreover, the (possible) parents of X j can be used to estimate (bounds on) the total causal eﬀect of X j on any of the other variables (Maathuis et al., 2009, 2010; Stekhoven et al., 2012; Nandy et al., 2017b).”
Structure Learning in Graphical Modeling (2016, background): “These ideas can be combined with the structure learning methods that we discuss in Section 4 to estimate (bounds on) causal eﬀects from observational data (Maathuis et al., 2009, 2010; Perkovi´c et al., 2015; Nandy et al., 2016b).”
The Risks of Invariant Risk Minimization (2020, background): “Under such a condition, results from causal inference (Maathuis et al., 2009; Peters et al., 2017) allow for formal guarantees of the identiﬁcation of the invariant features, or at least a strict subset of them.”
Learning high-dimensional directed acyclic graphs with latent and selection variables (2011, methodology): “for an IDA-like method [10, 11] to obtain bounds on causal effects based on observational data that is faithful to an unknown underlying causal graph with arbitrarily many latent and selection variables.”
Modelling local gene networks increases power to detect trans-acting genetic effects on gene expression (2016, background): “Other more global discovery procedures, such as the PC algorithm [52, 53], could be considered as an alternative.”
High-Dimensional Statistics with a View Toward Applications in Biology (2014, neutral): “However, it is still possible to identify lower bounds for |γj | with the so-called IDA (Inference when Dag is Absent) procedure (Maathuis et al., 2009, 2010).”
High-dimensional consistency in score-based and hybrid structure learning (2015, positive): “Moreover, an advantage of (AR)GES compared to PC is that its output is always a CPDAG, which is important for some applications such as (joint)IDA [Maathuis et al., 2009; Nandy et al., 2017] and the generalized adjustment criterion [Perkovic et al.”
Causal network inference using biochemical kinetics (2014, neutral): “The statistical connection between linear ODEs and network inference using linear models has been discussed in Oates and Mukherjee (2012) and exploited in Bansal et al.”
Repair of Partly Misspecified Causal Diagrams. (2017, background): “12 Thus we do not propose replacing expert opinion with a graphical structure learned entirely from an observed data set, as discussed in references 13, 14.”
Do-calculus when the True Graph Is Unknown (2015, background): “Effectively, this is what is done in the IDA-algorithm which returns (multi-sets of) estimates of the causal effects of variables from an equivalence class of causal structures under the assumption that there are no latent variables (Maathuis et al., 2009).”
D’ya Like DAGs? A Survey on Structure Learning and Causal Discovery (2021, neutral): “PC [223] 1993 constraint yes yes yes no CPDAG CCD [196] 1996 constraint yes yes both no PAG FCI [223] 2000 constraint no yes yes no PAG TPDA [31] 2002 constraint yes yes yes no CPDAG CPC [190] 2006 constraint yes relaxed yes no CPDAG KCL [227] 2007 constraint yes yes yes no CPDAG ION [234] 2008 cons”
Efficient Sampling and Structure Learning of Bayesian Networks (2018, background): “…in describing causal models (Greenland et al., 1999; Pearl, 2000; Hern´an and Robins, 2006; VanderWeele and Robins, 2007) and facilitating causal discovery from observational data (Maathuis et al., 2009; Moﬀa et al., 2017), though caution is warranted in their use and interpretation (Dawid, 2010).”
Estimating the effect of joint interventions from observational data in sparse high-dimensional settings (2014, methodology): “As an easy extension of the method of [20] to multiple interventions, one could try to obtain jointly valid parent sets by taking all combinations of the locally valid parent sets of all intervention nodes.”
Causal Inference Using Graphical Models with the R Package pcalg (2012, methodology): “Recently, we proposed and mathematically justiﬁed a statistical method (IDA - intervention calculus when a directed acyclic graph is absent) to obtain bounds on total causal eﬀects based on observational data under some assumptions (see Maathuis, Kalisch, and B¨uhlmann (2009)).”