相关随机时间序列的机器学习方法和极值理论及其在树轮数据中的应用
Machine Learning Approach and Extreme Value Theory to Correlated Stochastic Time Series with Application to Tree Ring Data
摘要：
机器学习（ML）的主要目标是研究和改进数学模型，这些模型可以用环境提供的数据进行训练，以推断未来并做出决策，而不必完全了解所有影响因素。在这项工作中，我们描述了ML如何成为研究气候建模的强大工具。树木年轮生长被用作不同方面的实施，例如，研究建筑物和环境的历史。随着时间的推移，一层新的木材被树的树皮覆盖。经过多年的生长，时间序列可以通过树轮宽度的序列来应用。本文的目的是使用最大似然算法和极值理论，以分析一组树轮宽度数据从九棵树生长在新罕布什尔州。首先，我们通过各种描述性统计方法来探索数据。在这个阶段，转换数据对于找出建模算法中的任何问题都很重要。然后，我们使用算法调整和集成的方法来改善的k-最近邻（KNN）算法。在这项研究中的开发方法和其他方法之间的比较。此外，数据集的极值将得到更多的研究。分析研究的结果表明，随机森林方法中的ML算法将给出准确的结果，从9棵树生长在诺丁汉郡的树轮宽度数据的分析与最低的均方根误差值。此外，我们注意到，随着假设的ARMA模型参数的增加，选择真实模型的概率也增加了。根据极值理论，韦布尔分布将是一个很好的选择，树轮数据建模。
英文摘要：
The main goal of machine learning (ML) is to study and improve mathematical models which can be trained with data provided by the environment to infer the future and to make decisions without necessarily having complete knowledge of all influencing elements. In this work, we describe how ML can be a powerful tool in studying climate modeling. Tree ring growth was used as an implementation in different aspects, for example, studying the history of buildings and environment. By growing and via the time, a new layer of wood to beneath its bark by the tree. After years of growing, time series can be applied via a sequence of tree ring widths. The purpose of this paper is to use ML algorithms and Extreme Value Theory in order to analyse a set of tree ring widths data from nine trees growing in Nottinghamshire. Initially, we start by exploring the data through a variety of descriptive statistical approaches. Transforming data is important at this stage to find out any problem in modelling algorithm. We then use algorithm tuning and ensemble methods to improve the k-nearest neighbors (KNN) algorithm. A comparison between the developed method in this study ad other methods are applied. Also, extreme value of the dataset will be more investigated. The results of the analysis study show that the ML algorithms in the Random Forest method would give accurate results in the analysis of tree ring widths data from nine trees growing in Nottinghamshire with the lowest Root Mean Square Error value. Also, we notice that as the assumed ARMA model parameters increased, the probability of selecting the true model also increased. In terms of the Extreme Value Theory, the Weibull distribution would be a good choice to model tree ring data.
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。
