Scalable Time-Series Causal Discovery with Approximate Causal Ordering

TL;DR

This paper presents a scalable heuristic approximation of the VarLiNGAM causal discovery algorithm for time-series data, significantly reducing computation time while maintaining reliability, enabling large-scale analysis on standard hardware.

Contribution

Introduces a heuristic modification of VarLiNGAM that reduces computational complexity and enables scalable causal discovery in large time-series datasets.

Findings

Achieves 7-13x speedup on large financial datasets.

Maintains empirical reliability comparable to standard VarLiNGAM.

Demonstrates robustness across diverse real-world applications.

Abstract

Causal discovery in time-series data presents a significant computational challenge. Standard algorithms are often prohibitively expensive for datasets with many variables or samples. This study introduces and validates a heuristic approximation of the VarLiNGAM algorithm to address this scalability problem. The standard VarLiNGAM method relies on an iterative search, recalculating statistical dependencies after each step. Our heuristic modifies this procedure by omitting the iterative refinement. This change permits a one-time precomputation of all necessary statistical values. The algorithmic modification reduces the time complexity from $O(m^3n)$ to $O(m^2n + m^3)$ while keeping the space complexity at $O(m^2)$, where $m$ is the number of variables and $n$ is the number of samples. While an approximation, our approach retains VarLiNGAM's essential structure and empirical reliability. On large-scale financial data with up to 400 variables, our algorithm achieves a 7--13x speedup over the standard implementation and a 4.5x speedup over a GPU-accelerated version. Evaluations across medical imaging, web server monitoring, and finance demonstrate the heuristic's robustness and practical scalability. This work offers a validated balance between computational efficiency and discovery quality, making large-scale causal analysis feasible on personal computers.