Posted on Categories:CS代写, Machine Learning, 机器学习, 计算机代写

# 计算机代写|机器学习代写Machine Learning代考|KIT315 Least Absolute Deviation Regression

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 计算机代写|机器学习代写Machine Learning代考|Least Absolute Deviation Regression

Learning a linear predictor by minimizing the average squared error loss incurred on training data is not robust against the presence of outliers. This sensitivity to outliers is rooted in the properties of the squared error loss $(y-h(\mathbf{x}))^2$. Minimizing the average squared error forces the resulting predictor $\hat{y}$ to not be too far away from any datapoint. However, it might be useful to tolerate a large prediction error $y-h(\mathbf{x})$ for an unusual or exceptional data point that can be considered an outlier.

Replacing the squared loss with a different loss function can make the learning robust against outliers. One important example for such a “robustifying” loss function is the Huber loss [2]
$$L((\mathbf{x}, y), h)= \begin{cases}(1 / 2)(y-h(\mathbf{x}))^2 & \text { for }|y-h(\mathbf{x})| \leq \varepsilon \ \varepsilon(|y-h(\mathbf{x})|-\varepsilon / 2) & \text { else. }\end{cases}$$
Figure $3.3$ depicts the Huber loss as a function of the prediction error $y-h(\mathbf{x})$.
The Huber loss definition (3.9) contains a tuning parameter $\epsilon$. The value of this tuning parameter defines when a data point is considered as an outlier. Figure $3.4$ illustrates the role of this parameter as the width of a band around a hypothesis map. The prediction error of this hypothesis map for data points within this band are measured used squared error loss (2.8). For data points outside this band (outliers) we use instead the absolute value of the prediction error as the resulting loss.

## 计算机代写|机器学习代写Machine Learning代考|The Lasso

We will see in Chap. 6 that linear regression (see Sect. 3.1) typically requires a training set larger than the number of features used to characterized a data point. However, many important application domains generate data points with a number $n$ of features much higher than the number $m$ of available labeled data points in the training set. In this high-dimensional regime, where $m \ll n$, basic linear regression will not be able to learn useful weights $\mathbf{w}$ for a linear hypothesis.

Section $6.4$ shows that for $m \ll n$, linear regression will typically learn a hypothesis that perfectly predicts labels of data points in the training set but delivers poor predictions for data points outside the training set. This phenomenon is referred to as overfitting and poses a main challenge for ML applications in the high-dimensional regime.

Chapter 7 discusses basic regularization techniques that allow to prevent $\mathrm{ML}$ methods from overfitting. We can regularize linear regression by augmenting the squared error loss (2.8) of a hypothesis $h^{(\mathbf{w})}(\mathbf{x})=\mathbf{w}^T \mathbf{x}$ with an additional penalty term. This penalty term depends solely on the weights $\mathbf{w}$ and serves as an estimate for the increase of the average loss on data points outside the training set. Different ML methods are obtained from different choices for this penalty term. The least absolute shrinkage and selection operator (Lasso) is obtained from linear regression by replacing the squared error loss with the regularized loss
$$L\left((\mathbf{x}, y), h^{(\mathbf{w})}\right)=\left(y-\mathbf{w}^T \mathbf{x}\right)^2+\lambda|\mathbf{w}|_1 .$$
Here, the penalty term is given by the scaled norm $\lambda|\mathbf{w}|_1$. The value of $\lambda$ can be chosen based on some probabilistic model that interprets a data point as the realization of a random variable. The label of this random datapoint is related to its features via
$$y=\overline{\mathbf{w}}^T \mathbf{x}+\varepsilon .$$

## 计算机代写|机器学习代写Machine Learning代考|Least Absolute Deviation Regression

$$L((\mathbf{x}, y), h)=\left{(1 / 2)(y-h(\mathbf{x}))^2 \quad \text { for }|y-h(\mathbf{x})| \leq \varepsilon \varepsilon(|y-h(\mathbf{x})|-\varepsilon / 2) \quad\right. \text { else. }$$

Huber 损失定义 (3.9) 包含一个调整参数 $\epsilon$. 此调整参数的值定义了何时将数据点视为异常值。数字 $3.4$ 说明了该参数作为假设图周 围的带宽度的作用。该带内数据点的假设图的预恻误差使用平方淏差损失 (2.8) 进行测量。对于这个范围之外的数据点 (离群 值），我们使用预测误差的绝对值作为结果损失。

## 计算机代写|机器学习代写Machine Learning代考|The Lasso

$$L\left((\mathbf{x}, y), h^{(\mathbf{w})}\right)=\left(y-\mathbf{w}^T \mathbf{x}\right)^2+\lambda|\mathbf{w}|_1 .$$

$$y=\overline{\mathbf{w}}^T \mathbf{x}+\varepsilon$$

## 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。