SCDM: Scalable Causal Discovery in Nonlinear Temporal Systems with Meta-Learning

Abstract

Causal discovery from nonlinear multivariate time series is challenging in high-dimensional systems, where the number of candidate directed relations grows quadratically with the number of variables. Existing methods are often limited by target-wise model fitting, repeated conditional testing, or expensive graph-search procedures. We propose SCDM, a shared-parameter meta-learning framework for scalable temporal causal discovery. SCDM treats each target variable as a task while learning a shared temporal predictor and a shared causal-strength matrix across tasks. Each meta-episode updates only a subset of target-variable tasks, allowing the model to accumulate structural evidence across the full system without exhaustive target-wise optimization. After training, a post-training graph readout converts the learned predictor into continuous directed causal scores for threshold-independent evaluation. We also provide a finite-error recovery principle showing that, under fully observed delayed-system assumptions and a positive risk-gap condition, thresholding SCDM scores recovers the graph when statistical, meta-optimization, and readout errors are below the population margin. Experiments on controlled synthetic, neuroimaging-inspired, high-dimensional, and real-world temporal benchmarks demonstrate competitive causal recovery and improved scalability in large temporal systems.