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From Causal Discovery to Dynamic Causal Inference in Neural Time Series

Valentina Kuskova, Dmitry Zaytsev, Michael Coppedge

Abstract

Time-varying causal models provide a powerful framework for studying dynamic scientific systems, yet most existing approaches assume that the underlying causal network is known a priori - an assumption rarely satisfied in real-world domains where causal structure is uncertain, evolving, or only indirectly observable. This limits the applicability of dynamic causal inference in many scientific settings. We propose Dynamic Causal Network Autoregression (DCNAR), a two-stage neural causal modeling framework that integrates data-driven causal discovery with time-varying causal inference. In the first stage, a neural autoregressive causal discovery model learns a sparse directed causal network from multivariate time series. In the second stage, this learned structure is used as a structural prior for a time-varying neural network autoregression, enabling dynamic estimation of causal influence without requiring pre-specified network structure. We evaluate the scientific validity of DCNAR using behavioral diagnostics that assess causal necessity, temporal stability, and sensitivity to structural change, rather than predictive accuracy alone. Experiments on multi-country panel time-series data demonstrate that learned causal networks yield more stable and behaviorally meaningful dynamic causal inferences than coefficient-based or structure-free alternatives, even when forecasting performance is comparable. These results position DCNAR as a general framework for using AI as a scientific instrument for dynamic causal reasoning under structural uncertainty.

From Causal Discovery to Dynamic Causal Inference in Neural Time Series

Abstract

Time-varying causal models provide a powerful framework for studying dynamic scientific systems, yet most existing approaches assume that the underlying causal network is known a priori - an assumption rarely satisfied in real-world domains where causal structure is uncertain, evolving, or only indirectly observable. This limits the applicability of dynamic causal inference in many scientific settings. We propose Dynamic Causal Network Autoregression (DCNAR), a two-stage neural causal modeling framework that integrates data-driven causal discovery with time-varying causal inference. In the first stage, a neural autoregressive causal discovery model learns a sparse directed causal network from multivariate time series. In the second stage, this learned structure is used as a structural prior for a time-varying neural network autoregression, enabling dynamic estimation of causal influence without requiring pre-specified network structure. We evaluate the scientific validity of DCNAR using behavioral diagnostics that assess causal necessity, temporal stability, and sensitivity to structural change, rather than predictive accuracy alone. Experiments on multi-country panel time-series data demonstrate that learned causal networks yield more stable and behaviorally meaningful dynamic causal inferences than coefficient-based or structure-free alternatives, even when forecasting performance is comparable. These results position DCNAR as a general framework for using AI as a scientific instrument for dynamic causal reasoning under structural uncertainty.
Paper Structure (89 sections, 46 equations, 4 figures)

This paper contains 89 sections, 46 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Scientific Challenge: Dynamic Causality Without Known Structure
  3. Scientific Evidence in Dynamic Causal Models
  4. Limits of prediction-centric evaluation
  5. Impulse responses and counterfactual behavior
  6. Stability as causal evidence
  7. Implications for model evaluation
  8. DCNAR: Learned Networks as Structural Priors for Dynamic Causal Modeling
  9. Dynamic causality with unknown structure
  10. Overview of the DCNAR framework
  11. Stage I: Neural autoregressive causal network discovery
  12. Alternative Ways to Provide Structure for Dynamic Causal Modeling
  13. Coefficient-Based Structure from Linear VAR Models
  14. Implicit Structure in Black-Box Predictive Models
  15. Static Assumed Networks
  16. ...and 74 more sections

Figures (4)

  • Figure 1: Comparison of DCNAR with Ridge VAR, TV-VAR, and LSTM (MC Dropout) across predictive (panel A, CRPS), distributional (panel B, local distributional accuracy - mean one-step-ahead CRPS), and causal diagnostics (panel C, nominal 90% prediction intervals across horizons) on the short-panel democracy dataset. Panel D shows representative counterfactual impulse response following a positive shock to freedom of expression (Albania).
  • Figure 2: System-level counterfactual trajectories under DCNAR, summarized by the $L^2$ normalization across all democracy components, for Albania, the United States, and Mexico. Solid lines denote trajectories under a localized positive shock to freedom of expression at horizon $h=1$; dashed lines denote corresponding baseline trajectories without intervention.
  • Figure 3: Comparison of DCNAR on 89-countries, 75-year panel, with Ridge VAR, TV-VAR, and LSTM (MC Dropout) across predictive (panel A, CRPS), distributional (panel B, local distributional accuracy - mean one-step-ahead CRPS), and causal diagnostics (panel C, nominal 90% prediction intervals across horizons) on the short-panel democracy dataset. Panel D shows representative counterfactual impulse response following a positive shock to freedom of expression (Albania).
  • Figure 4: System-level counterfactual trajectories under DCNAR on 89-coutries, 75-year panel, summarized by the $L^2$ normalization across all democracy components, for Albania, the United States, and Mexico. Solid lines denote trajectories under a localized positive shock to freedom of expression at horizon $h=1$; dashed lines denote corresponding baseline trajectories without intervention.