Latent Causal Recovery from Long-Lag Dependencies

Inferring causal structure from observational time series is challenging in the best of conditions, and even more so when relevant variables are unobserved. Marginalizing latent variables typically induces complex long-lag dependencies among observed variables, where a lag denotes the number of time steps separating cause and effect, making the inverse problem of recovering latent structure ill-posed. To recover latent structure under such confounding, we introduce Causal Hidden Recovery of N-lagged Observed Structures (CHRONOS), a constraint-optimization method built on answer set programming. Given a lagged observed graph, CHRONOS searches for causal graphs with minimal latent complexity that are consistent with the observations. The method explicitly allows for multiple optimal solutions, yielding equivalence classes of latent structures rather than a single reconstruction. Through extensive simulations on synthetic causal graphs with varying graph density and numbers of latent variables, we evaluate when latent structure recovery is completed within the time budget, how many latent variables are required, and the limits of identifiability in the resulting reconstructions. We additionally apply CHRONOS to real traffic-sensor data (METR-LA). Our results characterize the regimes in which latent causal recovery from apparent long-range dependencies is tractable, and the identifiability limits that latent confounding imposes regardless of method.