aiqbench analysis
This research challenges the standard practice of summarizing causal relationships in nonlinear time series as simple scalar scores, arguing instead for function-valued analysis to capture state-dependent effects. By leveraging Individual Conditional Expectation within Neural Additive Vector Autoregression frameworks, the authors demonstrate how this approach reveals distinct functional behaviors—such as thresholding or saturation—that are otherwise obscured. The study provides a methodological advance for accurately modeling complex causal structures in dynamic systems without conflating regime variations with residual noise.
Function-Valued Causal Influence in Nonlinear Time Series
arXiv:2605.26408v3 Announce Type: replace Abstract: Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true object learned by nonlinear autoregressive models: a state-dependent function whose effect varies across regimes, magnitudes, and contexts. We formalize function-valued causal influence for additive, contribution-decomposable architectures and show that scalar causal scores constitute a severe information bottleneck, conflating between-state variation with within-state residual noise. Using Neural Additive Vector Autoregression as a representative architecture, we introduce a practical framework based on Individual Conditional Expectation for estimating causal response functions directly from trained models. Through controlled synthetic experiments, we demonstrate that edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors, including monotonic, thresholded, saturating, and sign-changing effects. An applied case study on democratic development further shows that function-valued analysis reveals regime-specific and asymmetric causal structure systematically missed by score-centric approaches.
Abstract:Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true object learned by nonlinear autoregressive models: a state-dependent function whose effect varies across regimes, magnitudes, and contexts. We formalize function-valued causal influence for additive, contribution-decomposable architectures and show that scalar causal scores constitute a severe information bottleneck, conflating between-state variation with within-state residual noise. Using Neural Additive Vector Autoregression as a representative architecture, we introduce a practical framework based on Individual Conditional Expectation for estimating causal response functions directly from trained models. Through controlled synthetic experiments, we demonstrate that edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors, including monotonic, thresholded, saturating, and sign-changing effects. An applied case study on democratic development further shows that function-valued analysis reveals regime-specific and asymmetric causal structure systematically missed by score-centric approaches.
Machine Learning (cs.LG); Methodology (stat.ME); Machine Learning (stat.ML)
arXiv:2605.26408 [cs.LG]
(or arXiv:2605.26408v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.26408 Focus to learn more arXiv-issued DOI via DataCite
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