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# CS代写|机器学习代写Machine Learning代考|COMP5328 Logistic Regression

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## CS代写|机器学习代写Machine Learning代考|Logistic Regression

The previous section discussed the use of linear models in regression problems, but how can we solve classification problems? The answer lies in the generalized linear model (3.15): we just need to find a monotonic differentiable function $g(\cdot)$ that links the predictions of linear regression to the ground-truth labels of the classification problem.

For binary classification with output label $y \in{0,1}$, the real-valued predictions of the linear regression model $z=$ $\boldsymbol{w}^{\top} \boldsymbol{x}+b$ need to be converted into $0 / 1$. Ideally, the unit-step function is desired:
$$y= \begin{cases}0, & z<0 \\ 0.5, & z=0 \\ 1, & z>0\end{cases}$$
which predicts positive for $z$ greater than 0 , negative for $z$ smaller than 0 , and an arbitrary output when $z$ equals to 0 . The unit-step function is plotted in $\boldsymbol{\bullet}$ Figure $3.2$.

Nevertheless, $-$ Figure $3.2$ shows that the unit-step function is not continuous, and hence it cannot be used as $g^{-1}(\cdot)$ in (3.15). Therefore, we need to find a monotonic differentiable surrogate function to approximate the unit-step function, and a common choice is the logistic function:
$$y=\frac{1}{1+e^{-z}} .$$

## CS代写|机器学习代写Machine Learning代考|Linear Discriminant Analysis

Linear Discriminant Analysis (LDA) is a classic linear method, also known as Fisher’s Linear Discriminant (FLD) since it was initially proposed by Fisher (1936) for binary classification problems.

The idea of LDA is straightforward: projecting the training samples onto a line such that samples of the same class are close to each other, while samples of different classes are far away from each other. When classifying new samples, they are projected onto the same line and their classes are determined by their projected locations. $-$ Figure $3.3$ gives a two-dimensional illustration.

Given a data set $D=\left{\left(\boldsymbol{x}i, y_i\right)\right}{i=1}^m, y_i \in{0,1}$, let $X_i, \boldsymbol{\mu}_i$, and $\boldsymbol{\Sigma}_i$ denote, respectively, the sample set, mean vector, and covariance matrix of the $i$ th class $(i \in{0,1})$. After projecting data onto the line $w$, the centers of those two classes samples are $\boldsymbol{w}^{\top} \boldsymbol{\mu}_0$ and $\boldsymbol{w}^{\top} \boldsymbol{\mu}_1$, respectively. The covariances of the two classes samples are $\boldsymbol{w}^{\top} \boldsymbol{\Sigma}_0 \boldsymbol{w}$ and $\boldsymbol{w}^{\top} \boldsymbol{\Sigma}_1 \boldsymbol{w}$, respectively. Since the line is a one-dimensional space, $\boldsymbol{w}^{\top} \boldsymbol{\mu}_0, \boldsymbol{w}^{\top} \boldsymbol{\mu}_1, \boldsymbol{w}^{\top} \boldsymbol{\Sigma}_0 \boldsymbol{w}$, and $\boldsymbol{w}^{\top} \boldsymbol{\Sigma}_1 \boldsymbol{w}$ are all real numbers.

## CS代写|机器学习代写Machine Learning代考|Logistic Regression

. Logistic回归 . CS代写|机器学习代写Machine Learning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。