# Causal Discovery from Subsampled Time Series Data by Constraint Optimization

arXiv: https://arxiv.org/abs/1602.07970 · HTML: https://mlsanity.com/paper/1602.07970/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2016.

## Built on by (most cited first, 13 of 13)

- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Causal Inference for Time series Analysis: Problems, Methods and Evaluation](https://mlsanity.com/paper/2102.05829/) (2021)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [CUTS: Neural Causal Discovery from Irregular Time-Series Data](https://mlsanity.com/paper/2302.07458/) (2023)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [Identifying Causal Effects using Instrumental Time Series: Nuisance IV and Correcting for the Past](https://mlsanity.com/paper/2203.06056/) (2022)
- [Causal Discovery from Subsampled Time Series with Proxy Variables](https://mlsanity.com/paper/2305.05276/) (2023)
- [Causal discovery in a complex industrial system: A time series benchmark](https://mlsanity.com/paper/2310.18654/) (2023)
- [Causal Discovery for fMRI data: Challenges, Solutions, and a Case Study](https://mlsanity.com/paper/2312.12678/) (2023)
- [DKCD: Domain Knowledge-Enhanced Causal Discovery from Unstructured Data](https://mlsanity.com/paper/2607.09348/) (2026)
- [Did the Grid Erase the Event? EndoClock for Auditing Medical World-Model Pipelines](https://mlsanity.com/paper/2608.09266/) (2026)
- [One Thing Leads to Another: The Essentials of Time Series Causal Discovery](https://mlsanity.com/paper/2610.13430/) (2026)

## Abstract (arXiv)

This paper focuses on causal structure estimation from time series data in which measurements are obtained at a coarser timescale than the causal timescale of the underlying system. Previous work has shown that such subsampling can lead to significant errors about the system's causal structure if not properly taken into account. In this paper, we first consider the search for the system timescale causal structures that correspond to a given measurement timescale structure. We provide a constraint satisfaction procedure whose computational performance is several orders of magnitude better than previous approaches. We then consider finite-sample data as input, and propose the first constraint optimization approach for recovering the system timescale causal structure. This algorithm optimally recovers from possible conflicts due to statistical errors. More generally, these advances allow for a robust and non-parametric estimation of system timescale causal structures from subsampled time series data.