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Randomly distributed embedding making short-term high-dimensional data predictable.

Huanfei Ma¹, Siyang Leng^2,3,4, Kazuyuki Aihara^5,6

¹School of Mathematical Sciences, Soochow University, Suzhou 215006, China.

Proceedings of the National Academy of Sciences of the United States of America

|October 10, 2018

Summary

This summary is machine-generated.

We introduce a model-free framework for predicting future states in complex systems using limited high-dimensional data. This approach leverages randomly distributed embeddings to enhance prediction accuracy and robustness, even with noisy data.

Keywords:

high-dimensional data nonlinear dynamics prediction short-term data time series

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Area of Science:

Dynamical Systems and Nonlinear Science
Data Science and Machine Learning
Complex Systems Analysis

Background:

Predicting future states of nonlinear dynamical systems is difficult, especially with limited high-dimensional time series data.
Real-world systems often present challenges due to data scarcity and high dimensionality.

Purpose of the Study:

To propose a novel model-free framework for accurate future state prediction using short-term, high-dimensional data.
To demonstrate that high-dimensional features can be a valuable information source for prediction.

Main Methods:

Developed a randomly distributed embedding (RDE) framework.
RDE randomly generates low-dimensional nondelay embeddings from high-dimensional data.
Mapped nondelay embeddings to delay embeddings of the target variable to create weak predictors.

Main Results:

The RDE framework enables accurate future state prediction from short-term, high-dimensional data.
High-dimensional features, often seen as obstacles, become crucial information sources.
The method shows robustness and reliability, even under noisy conditions and with limited data.

Conclusions:

The RDE framework offers a powerful, model-free solution for future state prediction in complex systems.
It effectively utilizes high-dimensional data, transforming a challenge into an advantage for predictive modeling.
This approach enhances prediction reliability and robustness for real-world applications.