Unmixing Causal Dynamics: Learning Latent Mechanisms from Aggregate Time Series

Observed time series are often superpositions of multiple causal mechanisms that evolve concurrently over the same variables, so the causal relations of individual mechanisms are entangled in the aggregate signal. At each time step, each latent mechanism produces its own state vector, but we observe only the elementwise sum across mechanisms, together with sparse measurements that occasionally reveal mechanism states. We introduce UCD ($\text{U}$nmixing $\text{C}$ausal $\text{D}$ynamics) to recover mechanism-specific causal structure from such aggregated observations. UCD models each mechanism with a temporal structural equation model (SEM) with independent additive noise and performs particle-based inference over the unobserved mechanism trajectories. It maintains a set of particles, each representing a plausible joint history of all mechanisms. Between measurements, particles propose and reweight next-step mechanism states that are consistent with the observed aggregate; when sparse state measurements arrive, particles are corrected to match the revealed states and reweighted by their plausibility. We then learn each mechanism's causal graph and noise scales by maximizing the likelihood of the residuals between predicted and revealed mechanism states under the assumed noise model. Experiments show that UCD reliably recovers mechanism-specific causal structure from aggregated time series given sparse state measurements.