# Shylock: Causal Discovery in Multivariate Time Series based on Hybrid Constraints

arXiv: https://arxiv.org/abs/2510.21181 · HTML: https://mlsanity.com/paper/2510.21181/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [A Graph Autoencoder Approach to Causal Structure Learning](https://mlsanity.com/paper/1911.07420/) (2019)
- [The Bayesian Structural EM Algorithm](https://mlsanity.com/paper/1301.7373/) (2013)
- [Learning the Structure of Dynamic Probabilistic Networks](https://mlsanity.com/paper/1301.7374/) (2013)

## Abstract (arXiv)

Causal relationship discovery has been drawing increasing attention due to its prevalent application. Existing methods rely on human experience, statistical methods, or graphical criteria methods which are error-prone, stuck at the idealized assumption, and rely on a huge amount of data. And there is also a serious data gap in accessing Multivariate time series(MTS) in many areas, adding difficulty in finding their causal relationship. Existing methods are easy to be over-fitting on them. To fill the gap we mentioned above, in this paper, we propose Shylock, a novel method that can work well in both few-shot and normal MTS to find the causal relationship. Shylock can reduce the number of parameters exponentially by using group dilated convolution and a sharing kernel, but still learn a better representation of variables with time delay. By combing the global constraint and the local constraint, Shylock achieves information sharing among networks to help improve the accuracy. To evaluate the performance of Shylock, we also design a data generation method to generate MTS with time delay. We evaluate it on commonly used benchmarks and generated datasets. Extensive experiments show that Shylock outperforms two existing state-of-art methods on both few-shot and normal MTS. We also developed Tcausal, a library for easy use and deployed it on the EarthDataMiner platform