Standardizing Structural Causal Models

2024-06-17

arXiv.org

AI Summary

Synthetic data generated by Structural Causal Models (SCMs) often exhibit statistical artifacts—such as monotonic increases in variance and pairwise correlation along the causal order (e.g., Var-/R²-sortability)—leading causal discovery algorithms to overfit benchmark datasets and suffer poor generalization. To address this, we propose internally standardized SCMs (iSCMs), which dynamically standardize each variable during SCM generation—not as a post-hoc step. This mechanism theoretically eliminates Var-sortability and empirically removes R²-sortability, while avoiding the identifiability degradation and deterministic collapse induced by post-hoc normalization. We prove that linear iSCMs retain causal identifiability under standard weight priors, and demonstrate empirically that they do not degenerate into deterministic relationships even in large-scale systems. Overall, iSCMs significantly enhance the realism and generalizability of causal structure learning benchmarks.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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, and as we show experimentally, not $operatorname{R^2}$-sortable either 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.

Problem

• Addresses artifacts in SCM data affecting causal structure learning.
• Proposes iSCMs to standardize variables during generative process.
• Improves generalizability of causal inference beyond benchmarking.

Innovation

• Introduces internally-standardized structural causal models (iSCMs)
• Standardizes variables during generative process
• Reduces identifiability issues in linear iSCMs