Invariant Causal Prediction for Nonlinear Models

Abstract

An important problem in many domains is to predict how a system will respond to interventions. This task is inherently linked to estimating the system's underlying causal structure. To this end, Invariant Causal Prediction (ICP) (Peters et al., 2016) has been proposed which learns a causal model exploiting the invariance of causal relations using data from different environments. When considering linear models, the implementation of ICP is relatively straightforward. However, the nonlinear case is more challenging due to the difficulty of performing nonparametric tests for conditional independence.In this work, we present and evaluate an array of methods for nonlinear and nonparametric versions of ICP for learning the causal parents of given target variables. We find that an approach which first fits a nonlinear model with data pooled over all environments and then tests for differences between the residual distributions across environments is quite robust across a large variety of simulation settings. We call this procedure "invariant residual distribution test". In general, we observe that the performance of all approaches is critically dependent on the true (unknown) causal structure and it becomes challenging to achieve high power if the parental set includes more than two variables.As a real-world example, we consider fertility rate modeling which is central to world population projections. We explore predicting the effect of hypothetical interventions using the accepted models from nonlinear ICP. The results reaffirm the previously observed central causal role of child mortality rates. arXiv:1706.08576v2 [stat.ME] 19 Sep 2018 Structural causal modelsAssume an underlying structural causal model (also called structural equation model) (e.g. Pearl, 2009)

Should air pollution health effects assumptions be tested? Fine particulate matter and COVID-19 mortality as an example

“…, even if other variables have different values, or are set to different values). Formalizing this intuition leads to statistical tests for the property of Invariant Causal Prediction (ICP): that the dependence of an effect on its direct causes (e.g., its conditional probability distribution, given the values of its direct causes) is the same in different environments and under different interventions [ 23 ]. Information flows from causes to their direct effects over time.…”

Toward Causal Representation Learning

“…The study [220] empirically corroborated these predictions, thus establishing an intriguing bridge between the structure of learning problems and certain physical properties (cause-effect direction) of real-world data generating processes. It also led to a range of follow-up work [32], [78], [97], [114], [115], [152], [153], [156], [167], [195], [204], [243], [263], [267], [277], [278], [281], complementing the studies of Bareinboim and Pearl [14], [185], and it inspired a thread of work in the statistics community exploiting invariance for causal discovery and other tasks [105], [106], [114], [187], [191].…”

Veridical data science

“…Another example of model perturbation is sensitivity analysis in Bayesian modeling (38,39). Many of the model conditions used in causal inference are in fact stability concepts that assume away confounding factors by asserting that different conditional distributions are the same (40,41).…”