# Unifying Pairwise Interactions in Complex Dynamics

arXiv: https://arxiv.org/abs/2201.11941 · HTML: https://mlsanity.com/paper/2201.11941/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 159 references that are in the map.
- First posted on arXiv 28 Jan 2022.

## Builds on (most cited first, 21 of 21)

- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [Benchmarking Multivariate Time Series Classification Algorithms](https://mlsanity.com/paper/2007.13156/) (2020)
- [catch22: CAnonical Time-series CHaracteristics](https://mlsanity.com/paper/1901.10200/) (2019)
- [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021)
- [Causal Discovery Toolbox: Uncover causal relationships in Python](https://mlsanity.com/paper/1903.02278/) (2019)
- [Highly comparative time-series analysis: The empirical structure of time series and their methods](https://mlsanity.com/paper/1304.1209/) (2013)
- [Feature-based time-series analysis](https://mlsanity.com/paper/1709.08055/) (2017)
- [Conditional distribution variability measures for causality detection](https://mlsanity.com/paper/1601.06680/) (2016)
- [Network reconstruction and community detection from dynamics](https://mlsanity.com/paper/1903.10833/) (2019)
- [JIDT: An information-theoretic toolkit for studying the dynamics of complex systems](https://mlsanity.com/paper/1408.3270/) (2014)
- [Nonsmooth Analysis and Subgradient Methods for Averaging in Dynamic Time Warping Spaces](https://mlsanity.com/paper/1701.06393/) (2017)
- [hyppo: A Multivariate Hypothesis Testing Python Package](https://mlsanity.com/paper/1907.02088/) (2019)
- [From Distance Correlation to Multiscale Graph Correlation](https://mlsanity.com/paper/1710.09768/) (2017)
- [netrd: A library for network reconstruction and graph distances](https://mlsanity.com/paper/2010.16019/) (2020)
- [Community detection in networks without observing edges](https://mlsanity.com/paper/1808.06079/) (2018)
- [Measuring integrated information from the decoding perspective](https://mlsanity.com/paper/1505.04368/) (2015)
- [A unified framework for information integration based on information geometry](https://mlsanity.com/paper/1510.04455/) (2015)
- [Maturation Trajectories of Cortical Resting-State Networks Depend on the Mediating Frequency Band](https://mlsanity.com/paper/1803.04364/) (2018)
- [Directional and Causal Information Flow in EEG for Assessing Perceived Audio Quality](https://mlsanity.com/paper/1802.06327/) (2018)
- [Experimentally testable whole brain manifolds that recapitulate behavior](https://mlsanity.com/paper/2106.10627/) (2021)

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

- [Geometric Neural Network based on Phase Space for BCI-EEG decoding](https://mlsanity.com/paper/2403.05645/) (2024)
- [Network inference via process motifs for lagged correlation in linear stochastic processes](https://mlsanity.com/paper/2208.08871/) (2022)
- [Beyond Pairwise Connections: Extracting High-Order Functional Brain Network Structures under Global Constraints](https://mlsanity.com/paper/2510.09175/) (2025)
- [Accelerating Benchmarking of Functional Connectivity Modeling via Structure-aware Core-set Selection](https://mlsanity.com/paper/2602.05667/) (2026)
- [Machine learning of network inference enhancement from noisy measurements](https://mlsanity.com/paper/2309.02050/) (2023)
- [Personalized identification, prediction, and stimulation of neural oscillations via data-driven models of epileptic network dynamics](https://mlsanity.com/paper/2310.13480/) (2023)
- [Position: AI for Science Should Treat Measurement-to-Dataset Pipelines as Inference Components](https://mlsanity.com/paper/2605.24558/) (2026)
- [Graph-Based Approaches to Learning Epileptogenic Zone Localization Using Stereo-EEG Recordings](https://mlsanity.com/paper/2608.18887/) (2026)

## Abstract (arXiv)

Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods, from correlation coefficients to causal inference, rely on distinct quantitative theories that remain largely disconnected. Here we introduce a library of 237 statistics of pairwise interactions and assess their behavior on 1053 multivariate time series from a wide range of real-world and model-generated systems. Our analysis highlights new commonalities between different mathematical formulations, providing a unified picture of a rich interdisciplinary literature. Using three real-world case studies, we then show that simultaneously leveraging diverse methods from across science can uncover those most suitable for addressing a given problem, yielding interpretable understanding of the conceptual formulations of pairwise dependence that drive successful performance. Our framework is provided in extendable open software, enabling comprehensive data-driven analysis by integrating decades of methodological advances.