SC3D: Dynamic and Differentiable Causal Discovery for Temporal and Instantaneous Graphs

TL;DR

SC3D introduces a novel two-stage differentiable framework for accurately discovering dynamic and instantaneous causal structures from multivariate time series data, improving stability and recovery accuracy.

Contribution

The paper presents SC3D, a new method that jointly learns lag-specific and instantaneous causal graphs with a two-stage differentiable approach, addressing the complexity of dynamic causal discovery.

Findings

SC3D outperforms existing methods in synthetic and real-world datasets.

It achieves more stable and accurate causal structure recovery.

Demonstrates effectiveness across various complex time series benchmarks.

Abstract

Discovering causal structures from multivariate time series is a key problem because interactions span across multiple lags and possibly involve instantaneous dependencies. Additionally, the search space of the dynamic graphs is combinatorial in nature. In this study, we propose Stable Causal Dynamic Differentiable Discovery (SC3D), a two-stage differentiable framework that jointly learns lag-specific adjacency matrices and, if present, an instantaneous directed acyclic graph (DAG). In Stage 1, SC3D performs edge preselection through node-wise prediction to obtain masks for lagged and instantaneous edges, whereas Stage 2 refines these masks by optimizing a likelihood with sparsity along with enforcing acyclicity on the instantaneous block. Numerical results across synthetic SVAR systems, nonlinear and chaotic benchmarks, nonstationary dynamics and real-world datasets demonstrate that SC3D achieves improved stability and more accurate recovery of both lagged and instantaneous causal structures compared to existing baselines.