Standardizing Structural Causal Models

Weronika Ormaniec, Scott Sussex, Lars Lorch, Bernhard Schölkopf, Andreas Krause

Keywords: Causality, Causal Discovery, Structural Causal Model, Standardized Structural Causal Model, Variance Artifact, Covariance Artifact, Simulation, Benchmark

TL;DR: Model for benchmarking causal structure learning methods that does not induce variance and covariance artifacts in datasets.

Abstract:

Synthetic datasets generated by structural causal models (SCMs) are commonly used for benchmarking causal structure learning algorithms. However, the variances and pairwise correlations in SCM data tend to increase along the causal ordering. Several popular algorithms exploit these artifacts, possibly leading to conclusions that do not generalize to real-world settings. Existing metrics like $\operatorname{Var}$-sortability and $\operatorname{R^2}$-sortability quantify these patterns, but they do not provide tools to remedy them. To address this, we propose internally-standardized structural causal models (iSCMs), a modification of SCMs that introduces a standardization operation at each variable during the generative process. By construction, iSCMs are not $\operatorname{Var}$-sortable. We also find empirical evidence that they are mostly not $\operatorname{R^2}$-sortable for commonly-used graph families. Moreover, contrary to the post-hoc standardization of data generated by standard SCMs, we prove that linear iSCMs are less identifiable from prior knowledge on the weights and do not collapse to deterministic relationships in large systems, which may make iSCMs a useful model in causal inference beyond the benchmarking problem studied here. Our code is publicly available at: https://github.com/werkaaa/iscm.

Primary Area: causal reasoning

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Submission Number: 6477