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Interventional Time Series Priors for Causal Foundation Models

Dennis Thumm, Ying Chen

Abstract

Prior-data fitted networks (PFNs) have emerged as powerful foundation models for tabular causal inference, yet their extension to time series remains limited by the absence of synthetic data generators that provide interventional targets. Existing time series benchmarks generate observational data with ground-truth causal graphs but lack the interventional data required for training causal foundation models. To address this, we propose \textbf{CausalTimePrior}, a principled framework for generating synthetic temporal structural causal models (TSCMs) with paired observational and interventional time series. Our prior supports configurable causal graph structures, nonlinear autoregressive mechanisms, regime-switching dynamics, and multiple intervention types (hard, soft, time-varying). We demonstrate that PFNs trained on CausalTimePrior can perform in-context causal effect estimation on held-out TSCMs, establishing a pathway toward foundation models for time series causal inference.

Interventional Time Series Priors for Causal Foundation Models

Abstract

Prior-data fitted networks (PFNs) have emerged as powerful foundation models for tabular causal inference, yet their extension to time series remains limited by the absence of synthetic data generators that provide interventional targets. Existing time series benchmarks generate observational data with ground-truth causal graphs but lack the interventional data required for training causal foundation models. To address this, we propose \textbf{CausalTimePrior}, a principled framework for generating synthetic temporal structural causal models (TSCMs) with paired observational and interventional time series. Our prior supports configurable causal graph structures, nonlinear autoregressive mechanisms, regime-switching dynamics, and multiple intervention types (hard, soft, time-varying). We demonstrate that PFNs trained on CausalTimePrior can perform in-context causal effect estimation on held-out TSCMs, establishing a pathway toward foundation models for time series causal inference.
Paper Structure (39 sections, 4 equations, 3 figures, 5 tables, 1 algorithm)

This paper contains 39 sections, 4 equations, 3 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Time series causal discovery benchmarks.
  4. Generators with interventional support.
  5. Causal PFNs for tabular data.
  6. Time series foundation models.
  7. Regime-switching dynamics.
  8. CausalTimePrior
  9. Temporal Structural Causal Models
  10. Prior Distribution over TSCMs
  11. Graph prior $\Pi_\mathcal{G}$.
  12. Mechanism prior $\Pi_\mathbf{F}$.
  13. Noise prior $\Pi_\epsilon$.
  14. Intervention Types
  15. Hard interventions.
  16. ...and 24 more sections

Figures (3)

  • Figure 1: Paired observational and interventional time series for the intervention target variable. The yellow shaded region indicates the intervention period. The divergence between blue (observational) and red (interventional) trajectories demonstrates the causal effect of the intervention.
  • Figure 2: All variables in a sampled 6-variable TSCM with a hard intervention on Variable 4. The intervention target is highlighted with a yellow background. Causal effects propagate through the graph structure, affecting downstream variables while leaving non-causally connected variables unchanged.
  • Figure 3: Distributions of prior properties across 100K sampled TSCMs from CausalTimePrior. The prior produces diverse graph structures, intervention types, and effect magnitudes.