General Transportability – Synthesizing Observations and Experiments from Heterogeneous Domains

Abstract

The process of transporting and synthesizing experimental findings from heterogeneous data collections to construct causal explanations is arguably one of the most central and challenging problems in modern data science. This problem has been studied in the causal inference literature under the rubric of causal effect identifiability and transportability (Bareinboim and Pearl 2016). In this paper, we investigate a general version of this challenge where the goal is to learn conditional causal effects from an arbitrary combination of datasets collected under different conditions, observational or experimental, and from heterogeneous populations. Specifically, we introduce a unified graphical criterion that characterizes the conditions under which conditional causal effects can be uniquely determined from the disparate data collections. We further develop an efficient, sound, and complete algorithm that outputs an expression for the conditional effect whenever it exists, which synthesizes the available causal knowledge and empirical evidence; if the algorithm is unable to find a formula, then such synthesis is provably impossible, unless further parametric assumptions are made. Finally, we prove that do-calculus (Pearl 1995) is complete for this task, i.e., the inexistence of a do-calculus derivation implies the impossibility of constructing the targeted causal explanation.

Causal Structure Learning: a Combinatorial Perspective

“…, M K . The relation between these structural causal models is encoded using a selection diagram, and the task of using the selection diagram to identify the functional is covered by a rich literature on transportability [9,10,104,37]. Once the target functional is transformed into a functional of the available distributions, it becomes essential to estimate the functional in a sample-efficient way.…”

Multi-Source Causal Inference Using Control Variates

“…And if that has sufficient correlation with the target estimand one is interested in, it could be potentially used to construct control variates. To this end, our work relates to the literature on transportability in causal inference [Bareinboim and Pearl, 2014, Lee et al, 2020, Bareinboim and Pearl, 2016. These works investigate what causal quantities are identifiable, and allow us to construct control variates accordingly.…”

Multivariate Counterfactual Systems And Causal Graphical Models

“…The equations provide recipes for generating a value for each variable in turn, given the previous values that have already been simulated plus an independently simulated error term. 13 See Table 2 for an example.…”

“…For the sole purpose of establishing the SWIG global Markov property it is sufficient to show thatp(V i (a) = v i | V pa i \A (a) = v pa i \A )is not a function of the fixed nodes that are not in pa i , that is a A\pa i . This is established by(13). Under the FFRCISTG, p(V i (a pa i ∩A , v pa i \A )) exists even if p(a pa i ∩A , v pa i \A ) = 0.21 This is because the extended g-formula includes the value a variable takes on just before it is intervened upon and set to a constant a i .…”