# Parallelizing Convergent Cross Mapping Using Apache Spark

## TL;DR

This paper presents a method to accelerate convergent cross mapping (CCM) using Apache Spark, enabling faster causal analysis in complex systems with large time series data.

## Contribution

It introduces parallelized solutions for CCM on Spark, achieving significant speedups and scalability for causal inference in complex systems.

## Key findings

- Achieved over tenfold performance improvement with parallelized CCM.
- Demonstrated high scalability of the Spark-based CCM implementation.
- Enabled faster causal analysis in large, complex datasets.

## Abstract

Identifying the causal relationships between subjects or variables remains an important problem across various scientific fields. This is particularly important but challenging in complex systems, such as those involving human behavior, sociotechnical contexts, and natural ecosystems. By exploiting state space reconstruction via lagged embedding of time series, convergent cross mapping (CCM) serves as an important method for addressing this problem. While powerful, CCM is computationally costly; moreover, CCM results are highly sensitive to several parameter values. While best practice entails exploring a range of parameter settings when assessing casual relationships, the resulting computational burden can raise barriers to practical use, especially for long time series exhibiting weak causal linkages. We demonstrate here several means of accelerating CCM by harnessing the distributed Apache Spark platform. We characterize and report on results of several experiments with parallelized solutions that demonstrate high scalability and a capacity for over an order of magnitude performance improvement for the baseline configuration. Such economies in computation time can speed learning and robust identification of causal drivers in complex systems.