Causal State-Space Models for Time Series
Motivation
Standard time-series forecasting models learn correlations, not causes. This matters when interventions change the data-generating process — a model trained on observational data will fail precisely when you need it, i.e., when you act. The goal here is to integrate structural causal models (SCMs) with modern state-space architectures.
Approach
I augment SSM architectures (S4, Mamba) with a causal graph layer that encodes the structural equations governing the latent state transitions. The causal graph is estimated from data using PC algorithm / NOTEARS, then used to constrain the transition matrix of the SSM.
Formally, given a structural equation:
$$X_t = f(PA(X_t), \epsilon_t)$$
the intervention distribution under $do(X_j = x)$ is estimated by graph surgery in the latent space before decoding to the observed series.
Baselines
- Granger causality VAR models
- Standard Mamba without causal constraints
- PCMCI+ for causal discovery
- CausalImpact (Google) for intervention estimation
Datasets
Evaluating on: M4 financial series (observational), MIMIC-III vitals (clinical interventions), ERA5 climate reanalysis (physical causal structure known). Counterfactual evaluation via synthetic interventions with known ground truth.
Status
Ongoing. Causal discovery pipeline complete. SSM integration in progress.