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

2025-08-28

AI Summary

This work investigates whether clinical time series are generated by underlying physiological state sequences governed by systematic dynamical rules, aiming to uncover their intrinsic compositional structure to mitigate data scarcity in healthcare. We propose a conceptual framework of “temporal compositional structure,” integrating symbolic dynamics to identify interpretable latent states and their transition rules, thereby enabling compositional data augmentation. To rigorously assess synthetic data quality, we introduce domain adaptation–based evaluation and risk-aware distributional similarity metrics. In SOFA score prediction, models trained solely on synthetic data significantly outperform those trained on original data and surpass random augmentation baselines. Our key contribution is the first application of compositional modeling to clinical time-series analysis—yielding synthetically generated data that is not only interpretable and computationally efficient but also clinically plausible and trustworthy.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Application Domains: Humanities & Computational Social Science

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Investigates compositional structure in clinical time series data
• Aims to generate synthetic data for sparse clinical datasets
• Seeks to uncover latent physiological states and transition rules

Innovation

• Symbolic dynamics for latent state reconstruction
• Compositional data augmentation for synthetic generation
• Domain adaptation tests for distribution similarity