# Scalable Time-Series Causal Discovery with Approximate Causal Ordering

arXiv: https://arxiv.org/abs/2409.05500 · HTML: https://mlsanity.com/paper/2409.05500/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 55 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 14 of 14)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [Causal Recurrent Variational Autoencoder for Medical Time Series Generation](https://mlsanity.com/paper/2301.06574/) (2023)
- [CausalFormer: An Interpretable Transformer for Temporal Causal Discovery](https://mlsanity.com/paper/2406.16708/) (2024)
- [Structural Intervention Distance (SID) for Evaluating Causal Graphs](https://mlsanity.com/paper/1306.1043/) (2013)
- [Case Studies of Causal Discovery from IT Monitoring Time Series](https://mlsanity.com/paper/2307.15678/) (2023)
- [cuPC: CUDA-based Parallel PC Algorithm for Causal Structure Learning on GPU](https://mlsanity.com/paper/1812.08491/) (2018)
- [Score-based Causal Learning in Additive Noise Models](https://mlsanity.com/paper/1311.6359/) (2013)
- [Interactive Causal Structure Discovery in Earth System Sciences](https://mlsanity.com/paper/2107.01126/) (2021)
- [Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes](https://mlsanity.com/paper/2209.04480/) (2022)
- [AcceleratedLiNGAM: Learning Causal DAGs at the speed of GPUs](https://mlsanity.com/paper/2403.03772/) (2024)
- [ParaLiNGAM: Parallel Causal Structure Learning for Linear non-Gaussian Acyclic Models](https://mlsanity.com/paper/2109.13993/) (2021)

## Abstract (arXiv)

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(m3n) to O(m2n + m3) while keeping the space complexity at O(m2), 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.