### 机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Support Vector Machines

statistics-lab™ 为您的留学生涯保驾护航 在代写监督学习Supervised and Unsupervised learning方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写监督学习Supervised and Unsupervised learning代写方面经验极为丰富，各种代写监督学习Supervised and Unsupervised learning相关的作业也就用不着说。

• 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

## 机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Regression – An Introduction

This is an introductory chapter on the supervised (machine) learning from empirical data (i.e., examples, samples, measurements, records, patterns or observations) by applying support support vector machines (SVMs) a.k.a. kernel machines $^{1}$. The parts on the semi-supervised and unsupervised learning are given later and being entirely different tasks they use entirely different math and approaches. This will be shown shortly. Thus, the book introduces the problems gradually in an order of loosing the information about the desired output label. After the supervised algorithms, the semi-supervised ones will be presented followed by the unsupervised learning methods in Chap. 6 . The basic aim of this chapter is to give, as far as possible, a condensed (but systematic) presentation of a novel learning paradigm embodied in SVMs. Our focus will be on the constructive part of the SVMs’ learning algorithms for both the classification (pattern recognition) and regression (function approximation) problems. Consequently, we will not go into all the subtleties and details of the statistical learning theory (SLT) and structural risk minimization (SRM) which are theoretical foundations for the learning algorithms presented below. The approach here seems more appropriate for the application oriented readers. The theoretically minded and interested reader may find an extensive presentation of both the SLT and SRM in $[146,144,143,32,42,81,123]$. Instead of diving into a theory, a quadratic programming based learning, leading to parsimonious SVMs, will be presented in a gentle way – starting with linear separable problems, through the classification tasks having overlapped classes but still a linear separation boundary, beyond the linearity assumptions to the nonlinear separation boundary, and finally to the linear and nonlinear regression problems. Here, the adjective ‘parsimonious’ denotes a SVM with a small number of support vectors (‘hidden layer neurons’). The scarcity of the model results from a sophisticated, QP based, learning that matches the

model capacity to data complexity ensuring a good generalization, i.e., a good performance of SVM on the future, previously, during the training unseen, data.

Same as the neural networks (or similarly to them), SVMs possess the wellknown ability of being universal approximators of any multivariate function to any desired degree of accuracy. Consequently, they are of particular interest for modeling the unknown, or partially known, highly nonlinear, complex systems, plants or processes. Also, at the very beginning, and just to be sure what the whole chapter is about, we should state clearly when there is no need for an application of SVMs’ model-building techniques. In short, whenever there exists an analytical closed-form model (or it is possible to devise one) there is no need to resort to learning from empirical data by SVMs (or by any other type of a learning machine)

## 机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Basics of Learning from Data

SVMs have been developed in the reverse order to the development of neural networks (NNs). SVMs evolved from the sound theory to the implementation and experiments, while the NNs followed more heuristic path, from applications and extensive experimentation to the theory. It is interesting to note that the very strong theoretical background of SVMs did not make them widely appreciated at the beginning. The publication of the first papers by Vapnik and Chervonenkis [145] went largely unnoticed till 1992 . This was due to a widespread belief in the statistical and/or machine learning community that, despite being theoretically appealing, SVMs are neither suitable nor relevant for practical applications. They were taken seriously only when excellent results on practical learning benchmarks were achieved (in numeral recognition, computer vision and text categorization). Today, SVMs show better results than (or comparable outcomes to) NNs and other statistical models, on the most popular benchmark problems.

The learning problem setting for SVMs is as follows: there is some unknown and nonlinear dependency (mapping, function) $y=f(\mathbf{x})$ between some high-dimensional input vector $\mathbf{x}$ and the scalar output $y$ (or the vector output $\mathbf{y}$ as in the case of multiclass SVMs). There is no information about the underlying joint probability functions here. Thus, one must perform a distribution-free learning. The only information available is a training data set $\left{\mathcal{X}=[\mathbf{x}(i), y(i)] \in \mathfrak{R}^{m} \times \mathfrak{R}, i=1, \ldots, n\right}$, where $n$ stands for the number of the training data pairs and is therefore equal to the size of the training data set $\mathcal{X}$. Often, $y_{i}$ is denoted as $d_{i}$ (i.e., $t_{i}$ ), where $d(t)$ stands for a desired (target) value. Hence, SVMs belong to the supervised learning techniques.
Note that this problem is similar to the classic statistical inference. However, there are several very important differences between the approaches and assumptions in training SVMs and the ones in classic statistics and/or NNs

modeling. Classic statistical inference is based on the following three fundamental assumptions:

1. Data can be modeled by a set of linear in parameter functions; this is a foundation of a parametric paradigm in learning from experimental data.
2. In the most of real-life problems, a stochastic component of data is the normal probability distribution law, that is, the underlying joint probability distribution is a Gaussian distribution.
3. Because of the second assumption, the induction paradigm for parameter estimation is the maximum likelihood method, which is reduced to the minimization of the sum-of-errors-squares cost function in most engineering applications.

All three assumptions on which the classic statistical paradigm relied turned out to be inappropriate for many contemporary real-life problems [143] because of the following facts:

1. Modern problems are high-dimensional, and if the underlying mapping is not very smooth the linear paradigm needs an exponentially increasing number of terms with an increasing dimensionality of the input space (an increasing number of independent variables). This is known as ‘the curse of dimensionality’.
2. The underlying real-life data generation laws may typically be very far from the normal distribution and a model-builder must consider this difference in order to construct an effective learning algorithm.
3. From the first two points it follows that the maximum likelihood estimator (and consequently the sum-of-error-squares cost function) should be replaced by a new induction paradigm that is uniformly better, in order to model non-Gaussian distributions.

## 机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Support Vector Machines in Classification

Below, we focus on the algorithm for implementing the SRM induction principle on the given set of functions. It implements the strategy mentioned previously – it keeps the training error fixed and minimizes the confidence interval. We first consider a ‘simple’ example of linear decision rules (i.e., the separating functions will be hyperplanes) for binary classification (dichotomization) of linearly separable data. In such a problem, we are able to perfectly classify data pairs, meaning that an empirical risk can be set to zero. It is the easiest classification problem and yet an excellent introduction of all relevant and important ideas underlying the SLT, SRM and SVM.

Our presentation will gradually increase in complexity. It will begin with a Linear Maximal Margin Classifier for Linearly Separable Data where there is no sample overlapping. Afterwards, we will allow some degree of overlapping of training data pairs. However, we will still try to separate classes by using linear hyperplanes. This will lead to the Linear Soft Margin Classifier for Overlapping Classes. In problems when linear decision hyperplanes are no longer feasible, the mapping of an input space into the so-called feature space (that ‘corresponds’ to the HL in NN models) will take place resulting in the Nonlinear Classifier. Finally, in the subsection on Regression by SV Machines we introduce same approaches and techniques for solving regression (i.e., function approximation) problems.

## 机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Basics of Learning from Data

1. 数据可以通过一组线性参数函数来建模；这是从实验数据中学习的参数范式的基础。
2. 在现实生活中的大多数问题中，数据的随机分量是正态概率分布规律，即潜在的联合概率分布是高斯分布。
3. 由于第二个假设，参数估计的归纳范式是最大似然法，在大多数工程应用中，它被简化为误差平方和成本函数的最小化。

1. 现代问题是高维的，如果底层映射不是很平滑，则线性范式需要随着输入空间维数的增加（自变量数量的增加）呈指数增加的项数。这被称为“维度的诅咒”。
2. 现实生活中的基本数据生成规律通常可能与正态分布相差甚远，模型构建者必须考虑这种差异才能构建有效的学习算法。
3. 从前两点可以看出，为了模拟非高斯分布，最大似然估计量（以及因此误差平方和成本函数）应该被一种更好的新归纳范式代替。

## 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。