Detecting Long-Timescale Pairwise Interactions Between Time Series Using Feature-Based Information Theory

Core Concepts

A feature-based information-theoretic approach can outperform traditional signal-based methods in detecting long-timescale pairwise interactions between time series, especially in scenarios with short time-series lengths, high noise levels, and long interaction timescales.

Abstract

The article introduces a feature-based adaptation of conventional information-theoretic dependence detection methods to address the challenges in detecting long-timescale interactions between time series. The key insights are:

Traditional methods that operate directly on the raw time-series values can fail to capture underlying dependencies when interactions are mediated by statistical properties of the time series over longer timescales. This is due to the curse of dimensionality in estimating high-dimensional probability distributions from limited and noisy data.

The proposed feature-based approach extracts a candidate set of time-series features from sliding windows of the source time series and assesses their role in mediating a relationship to the target process. This reduces the dimensionality of the inference problem and can provide more interpretable insights into the nature of the interactions.

Through simulations of three different generative processes, the feature-based approach is shown to outperform the traditional signal-based approach, especially in challenging scenarios with short time-series lengths, high noise levels, and long interaction timescales.

The feature-based method introduces a new tool for inferring and interpreting feature-mediated interactions from time-series data, contributing to the broader landscape of quantitative analysis in complex systems research, with potential applications in various domains.

Stats

The target process y is a noisy linear function of the driving feature ˜z, as given by Eq. (8).

Quotes

"When one has limited knowledge of a system, this raises the need for a method capable of detecting long-timescale interactions driven by properties of the dynamics while making no strict assumptions on the systems, and ideally offering interpretability that can provide insights into the nature of interactions."
"Notably, recent years have seen an expansion in such general-purpose time-series feature sets [29], including: the comprehensive hctsa set of over 7000 features [30, 31]; a high-performing subset of 22 features catch22 [32]; the Python-based tsfresh [33]; and the R-based feasts [34]. These feature sets offer a promising ground for implementing a data-driven feature-based approach for inferring and understanding pairwise dependencies from time-series data."

Key Insights Distilled From

A feature-based information-theoretic approach for detecting interpretable, long-timescale pairwise interactions from time series

by Aria Nguyen,... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2404.05929.pdf

Deeper Inquiries

How can the feature-based approach be extended to detect higher-order interactions beyond pairwise dependencies

The feature-based approach can be extended to detect higher-order interactions beyond pairwise dependencies by incorporating higher-order statistical properties or interactions into the feature set. This can involve considering combinations of features or creating new features that capture interactions between multiple variables simultaneously. For example, one approach could be to include features that represent interactions between three or more variables at a time, such as higher-order moments, cross-correlations, or nonlinear dependencies. By expanding the feature set to include these higher-order interactions, the feature-based approach can provide insights into more complex relationships within the data.

What are the limitations of the feature-based approach in terms of its ability to capture nonlinear interactions compared to traditional signal-based methods

The limitations of the feature-based approach in capturing nonlinear interactions compared to traditional signal-based methods stem from the nature of the features used. While traditional signal-based methods directly analyze the raw time-series data, capturing complex nonlinear relationships, the feature-based approach relies on summarizing the data into predefined statistical properties. This summarization may not fully capture the intricacies of nonlinear interactions present in the data. Additionally, the choice of features in the feature-based approach may not encompass all possible nonlinear relationships, limiting its ability to detect complex interactions. Furthermore, the feature-based approach may struggle with capturing dynamic changes in nonlinear relationships over time, as the predefined features may not adapt to evolving patterns in the data.

How can the feature-based approach be integrated with causal inference techniques to uncover the underlying mechanisms driving complex system behaviors

Integrating the feature-based approach with causal inference techniques can provide a comprehensive understanding of the underlying mechanisms driving complex system behaviors. By combining feature-based analysis with causal inference methods such as Granger causality or structural equation modeling, researchers can identify not only the statistical dependencies between variables but also the directionality and causal relationships among them. This integration allows for the detection of causal pathways and feedback loops within the system, shedding light on how different variables influence each other over time. By leveraging the interpretability of the features extracted from the time series data, researchers can uncover the causal mechanisms that govern the dynamics of complex systems, leading to a more nuanced understanding of system behavior.