# Compositionality in Time Series: A Proof of Concept using Symbolic Dynamics and Compositional Data Augmentation

## TL;DR

This paper explores the idea that clinical time series can be generated by systematic sequences of latent states, using symbolic dynamics and data augmentation to improve forecasting and understanding in low-resource settings.

## Contribution

It introduces a novel approach to interpret clinical time series as generated by compositional latent states and demonstrates the effectiveness of synthetic data created through this method.

## Key findings

- Synthetic data training yields comparable performance to original data.
- Evaluation on synthetic data aligns well with real data results.
- Significant improvement in SOFA score prediction using synthetic data.

## Abstract

This work investigates whether time series of natural phenomena can be understood as being generated by sequences of latent states which are ordered in systematic and regular ways. We focus on clinical time series and ask whether clinical measurements can be interpreted as being generated by meaningful physiological states whose succession follows systematic principles. Uncovering the underlying compositional structure will allow us to create synthetic data to alleviate the notorious problem of sparse and low-resource data settings in clinical time series forecasting, and deepen our understanding of clinical data. We start by conceptualizing compositionality for time series as a property of the data generation process, and then study data-driven procedures that can reconstruct the elementary states and composition rules of this process. We evaluate the success of this methods using two empirical tests originating from a domain adaptation perspective. Both tests infer the similarity of the original time series distribution and the synthetic time series distribution from the similarity of expected risk of time series forecasting models trained and tested on original and synthesized data in specific ways. Our experimental results show that the test set performance achieved by training on compositionally synthesized data is comparable to training on original clinical time series data, and that evaluation of models on compositionally synthesized test data shows similar results to evaluating on original test data, outperforming randomization-based data augmentation. An additional downstream evaluation of the prediction task of sequential organ failure assessment (SOFA) scores shows significant performance gains when model training is entirely based on compositionally synthesized data compared to training on original data.