# Bootstrap aggregation and confidence measures to improve time series causal discovery

arXiv: https://arxiv.org/abs/2306.08946 · HTML: https://mlsanity.com/paper/2306.08946/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 37 references that are in the map.
- First posted on arXiv 15 Jun 2023.

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

- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Data Analysis with Bayesian Networks: A Bootstrap Approach](https://mlsanity.com/paper/1301.6695/) (2013)
- [Estimating and Controlling the False Discovery Rate for the PC Algorithm Using Edge-Specific P-Values](https://mlsanity.com/paper/1607.03975/) (2016)
- [Learning directed acyclic graphs via bootstrap aggregating](https://mlsanity.com/paper/1406.2098/) (2014)

## Built on by (most cited first, 8 of 8)

- [Causal-discovery-based root-cause analysis and its application in time-series prediction error diagnosis](https://mlsanity.com/paper/2411.06990/) (2024)
- [Towards Automated Causal Discovery: a case study on 5G telecommunication data](https://mlsanity.com/paper/2402.14481/) (2024)
- [Unified Causality Analysis Based on the Degrees of Freedom](https://mlsanity.com/paper/2410.19469/) (2024)
- [An extensive simulation study evaluating the interaction of resampling techniques across multiple causal discovery contexts](https://mlsanity.com/paper/2503.15436/) (2025)
- [Causal-Audit: A Framework for Risk Assessment of Assumption Violations in Time-Series Causal Discovery](https://mlsanity.com/paper/2604.02488/) (2026)
- [Stable Causal Discovery via Directed Acyclic Graph Aggregation](https://mlsanity.com/paper/2605.18633/) (2026)
- [AutoCause: A Python framework that automates expert decisions in environmental time-series causal discovery](https://mlsanity.com/paper/2608.00198/) (2026)
- [Dynamic Structural Causal Modeling for Sleep](https://mlsanity.com/paper/2608.20285/) (2026)

## Abstract (arXiv)

Learning causal graphs from multivariate time series is a ubiquitous challenge in all application domains dealing with time-dependent systems, such as in Earth sciences, biology, or engineering, to name a few. Recent developments for this causal discovery learning task have shown considerable skill, notably the specific time-series adaptations of the popular conditional independence-based learning framework. However, uncertainty estimation is challenging for conditional independence-based methods. Here, we introduce a novel bootstrap approach designed for time series causal discovery that preserves the temporal dependencies and lag structure. It can be combined with a range of time series causal discovery methods and provides a measure of confidence for the links of the time series graphs. Furthermore, next to confidence estimation, an aggregation, also called bagging, of the bootstrapped graphs by majority voting results in bagged causal discovery methods. In this work, we combine this approach with the state-of-the-art conditional-independence-based algorithm PCMCI+. With extensive numerical experiments we empirically demonstrate that, in addition to providing confidence measures for links, Bagged-PCMCI+ improves in precision and recall as compared to its base algorithm PCMCI+, at the cost of higher computational demands. These statistical performance improvements are especially pronounced in the more challenging settings (short time sample size, large number of variables, high autocorrelation). Our bootstrap approach can also be combined with other time series causal discovery algorithms and can be of considerable use in many real-world applications.