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

2026-02-02

AI Summary

This work addresses the challenge of combinatorial explosion in jointly discovering lagged and instantaneous causal relationships from multivariate time series. The authors propose SC3D, a two-stage differentiable framework that jointly learns a lagged adjacency matrix and an instantaneous directed acyclic graph (DAG). In the first stage, node-wise prediction is employed to preselect candidate edges and generate a mask that effectively reduces the search space. The second stage integrates sparsity-inducing regularization with DAG acyclicity constraints within a likelihood-based optimization to ensure structural identifiability and interpretability. By uniquely combining edge preselection with differentiable causal discovery, SC3D significantly improves accuracy, stability, and scalability. Experimental results demonstrate that SC3D consistently outperforms existing methods on both synthetic datasets and standard dynamical systems.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Interdisciplinary science discovery with web data mining

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 \textit{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 and benchmark dynamical systems demonstrate that SC3D achieves improved stability and more accurate recovery of both lagged and instantaneous causal structures compared to existing temporal baselines.

Problem

• causal discovery
• temporal graphs
• instantaneous dependencies
• multivariate time series
• combinatorial search space

Innovation

• causal discovery
• differentiable framework
• temporal graphs
• instantaneous DAG
• acyclicity constraint