### cs代写|机器学习代写machine learning代考|The basic idea and history of machine learning

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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

## cs代写|机器学习代写machine learning代考|Introduction

This chapter provides a high-level overview of machine learning, in particular of how it is related to building models from data. We start with a basic idea in the historical context and phrase the learning problem in a simple mathematical term as function approximation as well as in a probabilistic context. In contrast to more traditional models we can characterize machine learning as nonlinear regression in high-dimensional spaces. This chapter seeks to point out how diverse sub-areas such as deep learning and Bayesian networks fit into the scheme of things and aims to motivate the further study with some examples of recent progress.

Machine learning is literally about building machines, often in software, that can learn to perform specific tasks. Examples of common tasks for machine learning is recognizing objects from digital pictures or predicting the location of a robot or a selfdriving car from a variety of sensor measurements. These techniques have contributed largely to a new wave of technologies that are commonly associated with artificial intelligence (AI). This books is dedicated to introducing the fundamentals of this discipline.

The recent importance of machine learning and its rapid development with new industrial applications has been breath taking, and it is beyond the scope of this book to anticipate the multitude of developments that will occur. However, the knowledge of basic ideas behind machine learning, many of which have been around for some time, and their formalization for building probabilistic models to describe data are now important basic skills. Machine learning is about modeling data. Describing data and uncertainty has been the traditional domain of Bayesian statistics and probability theory. In contrast, it seems that many exciting recent techniques come from an area now called deep learning. The specific contribution of this book is its attempt to highlight the relationship between these areas.

We often simply say that we learn from data, but it is useful to realize that data can mean several things. In its most fundamental form, data usual consist of measurements such as intensity of light in a digital camera, the measurement of electric potentials in Electroencephalography (EEG), or the recording of stock-market data. However, what we need for learning is a teacher who provides us with information about what these data should predict. Such information can take many different forms. For example, we might have a form of data that we call labels, such as the identity of objects in a digital photograph. This is exactly the kind of information we need to learn optical object recognition. The teacher provides examples of the desired answers that the student (learner) should learn to predict for novel inputs.

## cs代写|机器学习代写machine learning代考|Mathematical formulation of the basic learning problem

Much of what is currently most associated with the success of machine learning is supervised learning, sometimes also called predictive learning. The basic task of supervised learning is that of taking a collection of input data $x$, such as the pixel values of an image, measured medical data, or robotic sensor data, and predicting an output value $y$ such as the name of an object in an image, the state of a patient’s health, or the location of obstacles. It is common that each input has many components, such as many millions of pixel values in an image, and it is useful to collect these values in a mathematical structure such as a vectors (1-dimensional), a matrix (2-dimensional), or a tensor that is the generalization of such structures to higher dimensions. We often refer to machine learning problems as high-dimensional which refers, in this context, to the large number of components in the input structure and not to the dimension of the input tensor.

We use the mathematical terms vector, matrix, and tensor mainly to signify a data structure. In a programming context these are more commonly described as $1-$ dimensional, 2-dimensional, or higher-dimensional arrays. The difference between arrays and tensors (a vector and matrix are special forms of a tensor) is, however, that the mathematical definitions also include rules on how to calculate with these data structures. This book is not a course on mathematics; we are only users of mathematical notations and methods, and mathematical notation help us to keep the text short while being precise. We follow here a common notation of denoting a vector, matrix, or tensor with bold-faced letters, whereas we use regular fonts for scalars. We usually call the input vector a feature vector as the components of this are typically a set feature values of an object. The output could also be a multi-dimensional object such as a vector or tensor itself. Mathematically, we can denote the relations between the input and the output as a function
$$y=f(\mathbf{x}) .$$
We consider the function above as a description of the true underlying world, and our task in science or engineering is to find this relation. In the above formula we considered a single output value and several input values for illustration purposes, although we see later that we can extend this readily to multiple output values.

Before proceeding, it is useful to clarify our use of the term “feature.” Features represent components that describe the inputs to our learning systems. Feature values are often measured data in machine learning. Sometime the word “attributes” is used instead. In the most part, we use these terms interchangeably. However, sometimes researchers make a small distinction betwen the terms, using attributes to denote unique content while using feature as a derived value, such as the square of an attribute. This strict distinction is usually not crucial for the understanding of the context so our use of the term feature includes attributes.

Returning to the world model in equation $1.1$, the challenge for machine learning is to find this function, or at least to approximate it sufficiently. Machine learning offers several approaches to deal with this. One approach that we will predominantly follow is to define a general parameterized function
$$\hat{y}=\hat{f}(\mathbf{x} ; \mathbf{w})$$

## cs代写|机器学习代写machine learning代考|Non-linear regression in high-dimensions

The simplest example of supervised machine learning is linear regression. In linear regression we assume a linear model such as the function,
$$y=w_{0}+w_{1} x$$
This is a low-dimensional example with only a single feature, value $x$, and a scalar label, value y. Most of us learned in high school to use mean square regression. In this method we choose as values for the offset parameter $w_{0}$ and the slope parameter $w_{1}$ the values that minimize the summed squared difference between the regressed and the data points. This is illustrated in Fig. 1.4A. We will later explain this procedure in more detail. This is an example where data are used to determine the parameters of a parameterized model, and this model with the fitted parameters can then be used to predict $y$ values for new $x$ values. This is in essence supervised learning.What makes modern machine learning go beyond this type of modeling is that we are now usually describing data in high dimensions (many features) and to use non-linear functions. This seems straight forward, but there are several problems in practice going down this route. For example, Fig. 1.4B shows a non-linear function that seems somewhat to describe the pattern of the data much better than the linear model in Fig. 1.4A. However, the non-linear model shown in Fig. 1.4C is also a solution. It even goes through all the training points. This is a particularly difficult problem. If we are allowed to increase the model complexity arbitrarily, then we can always find a model which goes through all the data points. However, the data points might have a simple relation, such as the linear one of Fig. 1.4A, and the variation only represents noise. Fitting the data point with this noise as in Fig. 1.4C does therefore mean that we are overfitting the data.

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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。