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# 计算机代写|机器学习代写Machine Learning代考|COMP5318 Classification by LS Regression

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## 计算机代写|机器学习代写Machine Learning代考|Classification by LS Regression

One tempting way to perform classification is with least-squares rgression. That is, we could treat the class labels $y \in{-1,1}$ as real numbers, and estimate the weights by minimizing
$$E(\mathbf{w})=\sum_i\left(y_i-\mathbf{x}_i^T \mathbf{w}\right)^2$$
for labeled training data $\left{\mathbf{x}_i, y_i\right}$. Given the optimal regression weights, one could then perform regression on subsequent test inputs and use the sign of the output to determine the output class.
In simple cases this can perform well, but in general it will perform poorly. This is because the objective function in linear regression measures the distance from the modeled class labels (which can be any real number) to the true class labels, which may not provide an accurate measure of how well the model has classified the data. For example, a linear regression model will tend to produce predicted labels that lie outside the range of the class labels for “extreme” members of a given class (e.g. 5 when the class label is 1 ), causing the error to be measured as high even when the classification (given, say, by the sign of the predicted label) is correct. In such a case the decision boundary may be shifted towards such an extreme case, potentially reducing the number of correct classifications made by the model. Figure 13 demonstrates this with a simple example.

The problem arises from the fact that the constraint that $y \in(-1,1)$ is not built-in to the model (the regression algorithm knows nothing about it), and so wastes considerable representational power trying to reproduce this effect. It is much better to build this constraint into the model.

## 计算机代写|机器学习代写Machine Learning代考|Na¨ıve Bayes

One problem with class conditional models, as described above, concerns the large number of parameters required to learn the likelihood model, i.e., the distribution over the inputs conditioned on the class. In Gaussian Class Conditional models, with $d$-dimensional input vectors, we need to estimate the class mean and class covariance matrix for each class. The mean will be a $d$ dimensional vector, but the number of unknowns in the covariance matrix grows quadratically with $d$. That is, the covariance is a $d \times d$ matrix (although because it is symmetric we do not need to estimate all $d^2$ elements).

Naïve Bayes aims to simplify the estimation problem by assuming that the different input features (e.g., the different elements of the input vector), are conditionally independent. That is, they are assumed to be independent when conditioned on the class. Mathematically, for inputs $\mathbf{x} \in \mathbb{R}^d$, we express this as
$$p(\mathbf{x} \mid C)=\prod_{i=1}^d p\left(x_i \mid C\right) .$$
With this assumption, rather than estimating one $d$-dimensional density, we instead estimate $d 1$ dimensional densities. This is important because each 1D Gaussian only has two parameters, its mean and variance, both of which are scalars. So the model has $2 d$ unknowns. In the Gaussian case, the Naïve Bayes model effectively replaces the general $d \times d$ covariance matrix by a diagonal matrix. There are $d$ entries along the diagonal of the covariance matrix; the $i^{\text {th }}$ entry is the variance of $x_i \mid C$. This model is not as expressive but it is much easier to estimate.

## 计算机代写|机器学习代写Machine Learning代考|Classification by LS Regression

$$E(\mathbf{w})=\sum_i\left(y_i-\mathbf{x}i^T \mathbf{w}\right)^2$$ 对于标记的训练数据 $\backslash$ left 缺少或无法识别的分隔符 给定最佳回归权重，然后可以对后续郧试输入执行回归， 并使用输出的符号来确定输出类别。 在简单的情况下，这可以表现良好，但通常表现不佳。这是因为线性回归中的目标函数衡量的是建模类标签 (可以是任何实数) 与 真实类标签之间的距离，这可能无法准确衡量模型对数据的分类情况。例如，线性回归模型将倾向于为給定类的”极端”成员生成位 于类标签范围之外的预测标签 (例如，当类标签为 1 时为 5)，导致措资被测量为高即使分类 (例如，由预则标签的符号给出) 是 正确的。在这种情况下，决策边界可能会转向这种极端情况，从而可能减少模型做出正确分类的数量。 问题源于这样一个事实，即 $y \in(-1,1)$ 不是内置于模型中（回归算法对此一无所知），因此在试图重现这种效果时浪费了相当大 的代表性能力。将此约束构建到模型中要好得客。

## 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。