arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1907.01552stat.MLcs.LG
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利用次优嵌入预测高维动态

Forecasting high-dimensional dynamics exploiting suboptimal embeddings

Institute of Industrial Science, The University of Tokyo(东京大学工业科学研究所);Kozo Keikaku Engineering Inc.(构计工程株式会社);International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo(东京大学国际神经智能研究中心(WPI-IRCN));Mathematics and Informatics Center, The University of Tokyo(东京大学数学与信息学中心)

Shunya Okuno, Kazuyuki Aihara, Yoshito Hirata

摘要:

延迟嵌入是一种利用延迟坐标重构动力系统的方法,作为一种无模型方法,被广泛应用于非线性时间序列的预测。当观察到多变量时间序列时,可以应用几个现有的框架来产生组合从各种嵌入导出的多个预测的单个预测。然而,这些框架的性能并不总是令人满意的,因为它们随机选择嵌入或使用蛮力,并且不考虑要组合的嵌入的多样性。在这里,我们开发了一个预测框架,克服了这些现有的问题。该框架利用各种“次优嵌入”通过组合优化最小化样本误差获得。该框架在现有的样本玩具数据集和真实世界的洪水数据集框架中取得了最好的结果。我们表明,该框架适用于广泛的数据长度和尺寸。因此,该框架可以应用于神经科学、生态学、金融、流体动力学、天气和防灾等各个领域。

英文摘要:

Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be applied to yield a single forecast combining multiple forecasts derived from various embeddings. However, the performance of these frameworks is not always satisfactory because they randomly select embeddings or use brute force and do not consider the diversity of the embeddings to combine. Herein, we develop a forecasting framework that overcomes these existing problems. The framework exploits various "suboptimal embeddings" obtained by minimizing the in-sample error via combinatorial optimization. The framework achieves the best results among existing frameworks for sample toy datasets and a real-world flood dataset. We show that the framework is applicable to a wide range of data lengths and dimensions. Therefore, the framework can be applied to various fields such as neuroscience, ecology, finance, fluid dynamics, weather, and disaster prevention.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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