# Entropy-based Discovery of Summary Causal Graphs in Time Series

arXiv: https://arxiv.org/abs/2105.10381 · HTML: https://mlsanity.com/paper/2105.10381/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 39 references that are in the map.
- First posted on arXiv 21 May 2021.

## Builds on (most cited first, 4 of 4)

- [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)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)

## Built on by (most cited first, 9 of 9)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [A Survey on Causal Discovery Methods for I.I.D. and Time Series Data](https://mlsanity.com/paper/2303.15027/) (2023)
- [Root Cause Identification for Collective Anomalies in Time Series given an Acyclic Summary Causal Graph with Loops](https://mlsanity.com/paper/2303.04038/) (2023)
- [Identifiability of total effects from abstractions of time series causal graphs](https://mlsanity.com/paper/2310.14691/) (2023)
- [Causal Discovery from Time Series with Hybrids of Constraint-Based and Noise-Based Algorithms](https://mlsanity.com/paper/2306.08765/) (2023)
- [Causal Discovery for Irregularly Time Series with Consistency Guarantees](https://mlsanity.com/paper/2507.03310/) (2025)
- [Transforming Causality: Transformer-Based Temporal Causal Discovery with Prior Knowledge Integration](https://mlsanity.com/paper/2508.15928/) (2025)
- [Orientability of Causal Relations in Time Series using Summary Causal Graphs and Faithful Distributions](https://mlsanity.com/paper/2508.21742/) (2025)
- [Causal Local States: Scalable Simultaneous Causal Network Inference and Forecasting for Dynamical Systems](https://mlsanity.com/paper/2608.17452/) (2026)

## Abstract (arXiv)

This study addresses the problem of learning a summary causal graph on time series with potentially different sampling rates. To do so, we first propose a new causal temporal mutual information measure for time series. We then show how this measure relates to an entropy reduction principle that can be seen as a special case of the probability raising principle. We finally combine these two ingredients in PC-like and FCI-like algorithms to construct the summary causal graph. There algorithm are evaluated on several datasets, which shows both their efficacy and efficiency.