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

Huanfei Man Soochow University Siyang Leng Fudan University Kazuyuki Aihara Tokyo University Wei Lin Fudan University Luonan Chen Shanghai Institute of Biochemistry and Cell Biology, Chinese Academy of Sciences

Data Analysis, Bio-Statistics, Bio-Mathematics mathscidoc:1904.42006

Best Paper Award in 2019

Proceedings of the National Academy of Sciences of the United States of America, 115, (43), E9994-E10002, 2018.10
Future state prediction for nonlinear dynamical systems is a challenging task, particularly when only a few time series samples for high-dimensional variables are available from real-world systems. In this work, we propose a model-free framework, named randomly distributed embedding (RDE), to achieve accurate future state prediction based on short-term high-dimensional data. Specifically, from the observed data of high-dimensional variables, the RDE framework randomly generates a sufficient number of low-dimensional “nondelay embeddings” and maps each of them to a “delay embedding,” which is constructed from the data of a to be predicted target variable. Any of these mappings can perform as a low-dimensional weak predictor for future state prediction, and all of such mappings generate a distribution of predicted future states. This distribution actually patches all pieces of association information from various embeddings unbiasedly or biasedly into the whole dynamics of the target variable, which after operated by appropriate estimation strategies, creates a stronger predictor for achieving prediction in a more reliable and robust form. Through applying the RDE framework to data from both representative models and real-world systems, we reveal that a high-dimension feature is no longer an obstacle but a source of information crucial to the accurate prediction for short-term data, even under noise deterioration.
prediction; nonlinear dynamics; time series; high-dimensional data; short-term data
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@inproceedings{huanfei2018randomly,
  title={Randomly distributed embedding making short-term high-dimensional data predictable},
  author={Huanfei Man, Siyang Leng, Kazuyuki Aihara, Wei Lin, and Luonan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190428193456550227288},
  booktitle={Proceedings of the National Academy of Sciences of the United States of America},
  volume={115},
  number={43},
  pages={E9994-E10002},
  year={2018},
}
Huanfei Man, Siyang Leng, Kazuyuki Aihara, Wei Lin, and Luonan Chen. Randomly distributed embedding making short-term high-dimensional data predictable. 2018. Vol. 115. In Proceedings of the National Academy of Sciences of the United States of America. pp.E9994-E10002. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190428193456550227288.
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