## 计算机代写|机器学习代写machine learning代考|COMP5318

2022年12月27日

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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
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## 计算机代写|机器学习代写machine learning代考|Performance Analysis: Spectral Properties and Functionals

In a classification context, where, conventionally, $\mathbf{x}_i \in \mathbb{R}^p$ belongs to one of the $k$ classes $\mathcal{C}_1, \ldots, \mathcal{C}_k$ with $k \ll n$ (the number of data samples), and thus $k \ll p$ whenever $p \sim n$, the approximation matrices $\tilde{\mathbf{K}}$ and $\tilde{\Phi}$ will often be shown to take a spiked random matrix form. That is, for instance,
$$\tilde{\mathbf{K}}=\mathbf{Z}+\mathbf{P},$$
where $\mathbf{Z} \in \mathbb{R}^{n \times n}$ is a random symmetric matrix, in general, having entries of zero mean and rather “uniform” variances, while $\mathbf{P} \in \mathbb{R}^{n \times n}$ is a low-rank matrix (the rank of which is often related to $k$ ), comprising the statistical information about the data-class associations and the statistical properties of the classes.

These spiked random matrix models have been extensively studied, and it is possible to extract much information about them. In particular, the dominant eigenvectors of $\tilde{\mathbf{K}}$ are known to relate to the eigenvectors of $\mathbf{P}$ (which carry the sought-for data-class information) whenever a phase transition threshold is exceeded.

In a regression setting where the $\mathbf{x}_i$ s are assumed independently and identically distributed, the regression vector $\beta$ of interest is a certain functional of $\mathbf{K}$ or $\Phi$. For instance, a random feature regression from the observations $\mathbf{X} \in \mathbb{R}^{p \times n}$ to the desired outputs $\mathbf{y} \in \mathbb{R}^n$ entails the regression vector:
$$\boldsymbol{\beta}=\sigma(\mathbf{W} \mathbf{X})\left(\boldsymbol{\Phi}+\gamma \mathbf{I}_n\right)^{-1} \mathbf{y},$$ which is thus an (indirect) function of the resolvent $\mathbf{Q}_{\Phi}(-\gamma)=\left(\Phi+\gamma \mathbf{I}_n\right)^{-1}$ of $\Phi$ for a certain $\gamma>0$. Random matrix theory possesses tools to analyze the statistical properties of such vectors $\beta$ as well.

## 计算机代写|机器学习代写machine learning代考|Directions of Improvement and New Ideas

Due to the complete change of paradigm when comparing data from a small-versus a large-dimensional perspective, the overall behavior and the ensuing performance of the studied algorithms are often tainted, when large-dimensional data are handled.
We shall notably see, in the course of the hook, that the conventional heat (or Gaussian) kernel used in varions classification contexis is largely subuplimal. We shall also see that most graph-inspired semi-supervised learning algorithms in the literature fail to properly accomplish their requested task for $n, p$ large and comparable; yet, we will show that the so-called PageRank approach [Avrachenkov et al., 2012] happens not to fail, although the fundamental reasons behind its nondegrading performance are at odds with the initial inspiration for the method; but most importantly, this popular approach will also be shown to perform quite far from optimal and, in particular, not to be capable of benefiting from a large addition of unlabeled data. This observation entails the very unpleasant property that purely unsupervised methods tend to outperform semi-supervised ones when the number of unlabeled data is large.

For all these applications, the book will list a set of recommendations and improved methods, which are tailored to large (as well as practically not so large)-dimensional data learning. Among others, optimal, but quite counterintuitive, kernel functions will be introduced, new regularization procedures for supervised and semi-supervised learning will be discussed that particularly defeat the “curse of dimensionality” in semi-supervised learning (by fully exploiting the additional information from unlabeled data), and some further light on the design of neural networks will be cast.

# 机器学习代考

## 有限元方法代写

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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。