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Eliciting Causal Effects from Observational and Experimental Data

Elicitation of a causal effect from observations and experiments is central to scientific discovery, or more generally, rational approaches to understanding and interacting with the world around us. Judea Pearl introduced causal diagrams provide a formal representation for combining data with causal information and do-calculus to provide a sound and complete inferential machinery for causal inference.

The practical need to transfer causal effects elicited in one domain (setting, environment, population) e.g., a controlled laboratory setting, to a different setting presents us with the problem of transporting causal information from a source environment to a possibly different target environment. For example, one might want to know if causal relation between teaching strategies and student learning obtained by through a randomized trial in a public school in Chicago can be transported to a public school in Minneapolis that has an admittedly different population of students.

Our recent work has examined m-transportability, a generalization of transportability, which offers a license to use causal information elicited from experiments and observations in m (where m is greater than or equal to 1) source environments to estimate a causal effect in a given target environment. We have provided a novel characterization of m-transportability that directly exploits the completeness of do-calculus to obtain the necessary and sufficient conditions for m-transportability. We have designed an algorithm for deciding m-transportability that determines whether a causal relation is m-transportable; and if it is, produces a transport formula, that is, a recipe for estimating the desired causal effect by combining experimental information from m source environments with observational information from the target environment.

We have introduced z-transportability, the problem of estimating the causal effect of a set of variables X on another set of variables Y in a target domain from experiments on any subset of controllable variables Z where Z is an arbitrary subset of observable variables V in a source domain. Z-Transportability generalizes z-identifiability, the problem of estimating in a given domain the causal effect of X on Y from surrogate experiments on a set of variables Z such that Z is disjoint from X. z-Transportability also generalizes transportability which requires that the causal effect of X
on Y in the target domain be estimable from experiments on any subset of all observable variables in the source domain. We have generalized z-identifiability to allow cases where Z is not necessarily disjoint from X. We have established a necessary and sufficient condition for z-transportability in terms of generalized z-identifiability and transportability. We have provided a sound and complete algorithm that determines whether a causal effect is z-transportable; and if it is, produces a transport formula, that is, a recipe for estimating the causal effect of X on Y in the target domain using information elicited from the results of experimental manipulations of Z in the source domain and observational data from the target domain. Our results also show that do-calculus is complete for z-transportability.

We have recently introduced mz-transportability, the problem of inferring a causal effect of treatment variables on observables in a target domain (environment, experimental setting) by combining data from experiments on simultaneously controllable subsets of variables (together with observations) from multiple domains (including the target domain). We have provided an efficient and complete algorithm that determines if a causal effect is mz-transportable, and if so, outputs a transport formula for estimating the causal effect. These results set the stage for considering more general forms of meta-identifiability by allowing a fully arbitrary information set and for proving the completeness of do-calculus in such settings. Most work on causal inference from observational data has assumed that the observations are independent and identically distributed. However, in many practical applications, the data exhibit relational dependencies. Relational causal models (RCM) allow us to model causal relationships in relational data. Our recent work has led to: (a) A characterization of the properties of abstract ground graphs (AGG), which play a key role in the proofs of completeness of the only previous algorithm for learning relational causal models from data, We showed that AGG representation is not complete for relational d-separation, that is, there can exist conditional independence relations in an RCM that are not entailed by AGG (Lee et al., 2015). (b) An investigation of Relational Causal Models (RCM) under relational counterparts of adjacencyfaithfulness and orientation-faithfulness, yielding a simple approach to identifying a subset of relational d-separation queries needed for determining the structure of an RCM using dseparation against an unrolled DAG representation of the RCM. We provided theoretical underpinnings of a basis of a sound and efficient algorithm for learning the structure of an RCM from relational data. We introduced RCD-Light, a sound and efficient constraint-based algorithm that is guaranteed to yield a correct partially-directed RCM structure with at least as many edges oriented as in that produced by RCD, the only other existing algorithm for learning RCM. We showed that unlike RCD, which requires exponential time and space, RCD- Light requires only polynomial time and space to orient the dependencies of a sparse RCM (Lee et al., 2016). (c) A novel and elegant characterization of the Markov equivalence of RCMs under path semantics, an alternative to bridge-burning semantics used by RCD. We introduced a novel representation that allows us to efficiently determine whether an RCM is Markov equivalent to an-other. Under path semantics, we provide a sound and complete algorithm for recovering the structure of an RCM from conditional independence queries. Our analysis also suggests ways to improve the orientation recall of algorithms for learning the structure of RCM under bridge burning semantics as well (Lee et al., 2016). We have examined the following problem in causal inference: Given a causal graph G, determine MIC(G), that suffices for identifying every causal effect that is identifiable in a causal model characterized by G. We have established the completeness of do-calculus for computing MIC(G) . MIC(G) effectively offers an efficient compilation of all of the information obtainable from all possible interventions in a causal model characterized by G. Minimum intervention cover finds applications in a variety of contexts including counterfactual inference, and generalizing causal effects across experimental settings. We analyze the computational complexity of minimum intervention cover and identify some special cases of practical interest in which MIC(G) can be computed in time that is polynomial in the size of G. Work in progress is aimed at (i) bridging the gap between theory and practice of causal inference to address the needs of real-world applications, e.g., by developing algorithms and software for eliciting causal effects from temporal and temporal-relational data.