Optimal state space reconstruction via Monte Carlo decision tree search
Optimal state space reconstruction via Monte Carlo decision tree search
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DOI：
10.1007/s11071-022-07280-2
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发表时间：
2022-03-02
影响因子：
5.6
通讯作者：
Marwan, Norbert
中科院分区：
文献类型：
--
作者：
Kraemer, K. Hauke;Gelbrecht, Maximilian;Marwan, Norbert
提出了一种从单、多元时间序列中重构最优时滞状态空间的新思路。整个嵌入过程被视为一个博弈，其中每一步都对应一个嵌入周期，并通过目标函数进行评估。这样，嵌入过程可以建模为树，其中每个叶子都包含目标函数的特定值。该算法通过蒙特卡罗方差分析，通过计算不同的可能嵌入路径来填充具有多个叶子的树，并选择最终嵌入路径作为特定路径，该路径以目标函数实现值最低的叶子结束。该方法旨在防止陷入目标函数的局部最小值，并且可以以模块化的方式使用，使从业者能够选择每个嵌入周期中可能出现的延迟的统计量以及合适的目标函数。该方法保证了所选目标函数在延迟嵌入的参数空间上的最优性，只要对树进行了充分的采样。作为概念的证明，我们通过各种应用实例证明了所提出的方法优于经典的时延嵌入方法。我们比较了从Lorenz-96系统重建推断出的基于递归图的统计数据，并强调了对类似地图的模式数据以及古气候同位素时间序列的预测精度的提高。最后，我们利用状态空间重构来检测燃气轮机型热声燃烧室观测值之间的因果关系及其强度。
A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in which each move corresponds to an embedding cycle and is subject to an evaluation through an objective function. This way the embedding procedure can be modeled as a tree, in which each leaf holds a specific value of the objective function. By using a Monte Carlo ansatz, the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path, which ends at the leaf with the lowest achieved value of the objective function. The method aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way, enabling practitioners to choose a statistic for possible delays in each embedding cycle as well as a suitable objective function themselves. The proposed method guarantees the optimization of the chosen objective function over the parameter space of the delay embedding as long as the tree is sampled sufficiently. As a proof of concept, we demonstrate the superiority of the proposed method over the classical time delay embedding methods using a variety of application examples. We compare recurrence plot-based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for palaeoclimate isotope time series. Finally, we utilize state space reconstruction for the detection of causality and its strength between observables of a gas turbine type thermoacoustic combustor.