### 统计代写|机器学习作业代写machine learning代考|Performance Considerations

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|机器学习作业代写machine learning代考|Performance Considerations

The $k-\mathrm{NN}$ technique is easy to implement in a computer program, and its behavior is easy to understand. But is there a reason to believe that its classification performance is good enough?
1-NN Versus Ideal Bayes The ultimate yardstick by which to assess any classifier’s success is the Bayesian formula. If the probabilities and $p d f$ ‘s employed in the Bayesian classifier are known with absolute accuracy, then this classifier-let us call it Ideal Bayes-exhibits the lowest error rate theoretically achievable on the given (noisy) data. It would be reassuring to realize that the $k$-NN paradigm does not trail too far behind.

The question was subjected to rigorous mathematical analysis, and here are the results. Figure $3.4$ shows the comparison under such idealized circumstances as infinitely large training sets filling the instance space with infinite density. The solid curve represents the two-class case where each example is either positive or negative. We can see that if the error rate of Ideal Bayes is $5 \%$, the error rate of the 1-NN classifier (vertical axis) is $10 \%$. With the growing amount of noise, the difference between the two classifiers decreases, only to disappear when Ideal Bayes reaches $50 \%$ error rate – in which event, of course, the labels of the training examples are virtually random, and any attempt at automated classification is futile.

## 统计代写|机器学习作业代写machine learning代考|Weighted Nearest Neighbors

So far, the voting mechanism has been democratic in the sense that each nearest neighbor has the same vote. But while this seems appropriate, classification performance often improves if democracy is reduced.

Here is why. In Fig. 3.6, the task is to determine the class of object 1. Since three of the nearest neighbors are squares and only two circles, the 5 -NN classifier decides the object is square. However, a closer look reveals that the three square neighbors are quite distant from 1 , so much so that they perhaps should not have the same impact as the two circles in the object’s immediate vicinity. After all, we want to adhere to the requirement that $k$-NN should classify based on similarity-and more distant neighbors are less similar than closer ones.

Weighted Nearest Neighbors Domains of this kind motivate the introduction of weighted voting in which the weight of each neighbor depends on its distance from the object: the closer the neighbor, the greater its impact.

Let us denote the weights as $w_{1}, \ldots, w_{k}$. The weighted $k$ – $N N$ classifier sums up the weights of those neighbors that recommend the positive class (let the result be denoted by $\Sigma^{+}$) and then sums up the weights of those neighbors that support the negative class $\left(\Sigma^{-}\right)$. The final verdict depends on which is higher: if $\Sigma^{+}>\Sigma^{-}$, then the object is deemed positive; otherwise, it is labeled as negative. Generalization to domains with $n>2$ classes is straightforward.

For illustration, suppose the positive label is found in neighbors with weights $0.6$ and $0.7$, respectively, and the negative label is found in neighbors with weights $0.1,0.2$, and $0.3$. Weighted $k-\mathrm{NN}$ will choose the positive class because the combined weight of the positive neighbors, $\Sigma^{+}=0.6+0.7=1.3$, is greater than that of the negative neighbors, $\Sigma^{-}=0.1+0.2+0.3=0.6$. Just as in Fig. 3.6, the more frequent negative neighbors are outvoted by the less frequent positive neighbors because the latter are closer (and thus more similar) to the object we want to classify.

## 统计代写|机器学习作业代写machine learning代考|Removing Dangerous Examples

The value of each training example can be different. Some are typical of the classes they represent, others less so, and yet others may be downright misleading. This is why it is often a good thing to pre-process the training set: to remove examples suspected of not being useful.

The method of pre-processing is guided by the two observations illustrated in Fig. 3.7. First, an example labeled with one class but surrounded by examples of another class may indicate class-label noise. Second, examples from the borderline region separating two classes are unreliable: even small amount of noise in their attribute values can shift their locations in the wrong directions, thus affecting classification. Pre-processing seeks to remove these two types of examples from the training set.

## 统计代写|机器学习作业代写machine learning代考|Performance Considerations

1-NN 与理想贝叶斯 评估任何分类器成功与否的最终标准是贝叶斯公式。如果概率和pdF在贝叶斯分类器中使用的 ‘ 以绝对准确度为人所知，那么这个分类器——让我们称之为理想贝叶斯——表现出理论上在给定（嘈杂）数据上可实现的最低错误率。意识到ķ-NN 范式并没有落后太多。

## 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。