2021/10/13 by Guillaume Martinet, Martinet, Guillaume, Alexander Strzalkowski +3 · 1 citation
Computer Science · Mathematics · #Artificial intelligence #Bayesian Modeling and Causal Inference #Benchmark (surveying) #Causal inference #Computer science #Domain Adaptation and Few-Shot Learning #Econometrics #Equivalence (formal languages) #FOS: Computer and information sciences #Inference #Invariant (physics) #Machine Learning (cs.LG) #Machine learning #Mathematical economics #Mathematics #Methodology (stat.ME) #Nonparametric statistics #Outcome (game theory) #Property (philosophy) #Statistical Methods and Inference #cs.LG #stat.ME
paper · pdf · doi:10.48550/arxiv.2110.07064
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2021/10/13 · arxiv created 2022/02/28 · arxiv updated 2022/03/01 · openalex created_date 2022/07/25 · openalex updated_date 2026/08/05
Selecting powerful predictors for an outcome is a cornerstone task for machine learning. However, some types of questions can only be answered by identifying the predictors that causally affect the outcome. A recent approach to this causal inference problem leverages the invariance property of a causal mechanism across differing experimental environments (Peters et al., 2016; Heinze-Deml et al., 2018). This method, invariant causal prediction (ICP), has a substantial computational defect -- the runtime scales exponentially with the number of possible causal variables. In this work, we show that the approach taken in ICP may be reformulated as a series of nonparametric tests that scales linearly in the number of predictors. Each of these tests relies on the minimization of a novel loss function -- the Wasserstein variance -- that is derived from tools in optimal transport theory and is used to quantify distributional variability across environments. We prove under mild assumptions that our method is able to recover the set of identifiable direct causes, and we demonstrate in our experiments that it is competitive with other benchmark causal discovery algorithms.