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# 数学代写|统计机器学习作业代写Statistical Machine Learning代考|Bootstrap Cross-validation

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## 数学代写|统计机器学习作业代写Statistical Machine Learning代考|bootstrapping method

First, we will define the bootstrapping method to understand how it is used in the CV approach, which should then be straightforward. Bootstrapping is a type of resampling method where, for example, $B=10$ samples of the same size are repeatedly drawn, with replacement, from a single original sample. Afterward, each of these $B$ samples is used to estimate statistics (for example, the mean, variance, median, minimum, etc.) of a population, and the average of all the $B$ sample estimates of the target statistic is reported as the final estimate. In the context of statistical machine learning, these samples are used to evaluate the prediction performance of the algorithm under study for unseen data. One important difference between this CV approach and all the procedures explained above is that now the training set has the same size (number of observations) as the original sample because the bootstrap method replaced some individuals more than once. According to Kuhn and Johnson (2013), as a result, some observations will be represented multiple times in the bootstrap sample, while others will not be selected at all; those observations not selected are referred to as the testing set, however, this CV strategy is quite different than the previously explained. Efron (1983) pointed out that the prediction performance of the bootstrap samples tends to have less uncertainty than the $k$-fold cross-validation since on average, $63.2 \%$ of the data points are represented (for training) at least once in any sample size. For this reason,this CV approach has a bias similar to implementing a $k=$ two fold cross-validation, and as the training set becomes smaller, the bias becomes more problematic.

## 数学代写|统计机器学习作业代写STATISTICAL MACHINE LEARNING代考|bootstrap sample

To understand this CV method, we provide a simple example of how the training and testing samples are constructed. If we have a sample with 12 individuals denoted as $\mathrm{I} 1, \mathrm{I} 2, \ldots, \mathrm{I} 12$, we will select $B=5$ bootstrap samples. Each bootstrap sample is obtained with replacement and the individuals that appear in each one correspond to the training sample; those that are not present will correspond to the testing set. Figure $4.6$ provides the five bootstrap samples; each training sample has the same size as the original, however, only some individuals appear in each bootstrap sample, while those individuals that do not appear are included in the testing set. For example, in the first fold, the training bootstrap sample contains seven different individuals (I2, I3, I4, I6, I7, I8, and I9), while the testing set contains five individuals (I1, I5, I10, I11, and I12). It is important to point out that since the training sample has the same size as the original sample, some individuals in the training sample are repeated at least twice; in the first fold, the individual I4 are repeated three times, whereas I6, I7, and I8 are repeated twice. Finally, similar to other methods, the statistical machine learning model is trained with each training set; likewise, the prediction performance of the model is evaluated in each testing set. The average of these sample predictions is reported as the estimated testing error.

## 广义线性模型代考

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。