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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我们提供的机器学习machine learning及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (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|The basic idea and history of machine learning

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.

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


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


机器学习实际上是关于构建机器,通常在软件中,可以学习执行特定任务。机器学习的常见任务示例是从数字图片中识别物体,或者从各种传感器测量中预测机器人或自动驾驶汽车的位置。这些技术在很大程度上促成了通常与人工智能 (AI) 相关的新一波技术。本书致力于介绍该学科的基础知识。


我们经常简单地说我们从数据中学习,但意识到数据可能意味着几件事是很有用的。在其最基本的形式中,数据通常包括测量值,例如数码相机中的光强度、脑电图 (EEG) 中的电位测量值或股票市场数据的记录。但是,我们学习需要的是一位老师,他可以为我们提供有关这些数据应该预测什么的信息。这样的信息可以采取许多不同的形式。例如,我们可能有一种称为标签的数据形式,例如数码照片中对象的身份。这正是我们学习光学物体识别所需要的信息。教师提供学生(学习者)应该学习预测新输入的期望答案的示例。

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

目前与机器学习成功最相关的大部分是监督学习,有时也称为预测学习。监督学习的基本任务是收集输入数据X,例如图像的像素值、测量的医疗数据或机器人传感器数据,以及预测输出值是例如图像中对象的名称、患者的健康状况或障碍物的位置。通常每个输入都有许多分量,例如图像中的数百万像素值,将这些值收集到数学结构中很有用,例如向量(一维)、矩阵(二维) ,或将这种结构推广到更高维度的张量。我们经常将机器学习问题称为高维问题,在这种情况下,它指的是输入结构中的大量组件,而不是输入张量的维度。






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


这是一个低维示例,只有一个特征,值X,和一个标量标签,值 y。我们大多数人在高中时就学会了使用均方回归。在这种方法中,我们选择偏移参数的值在0和斜率参数在1最小化回归点和数据点之间的平方和差的值。如图 1.4A 所示。我们稍后将更详细地解释此过程。这是一个示例,其中数据用于确定参数化模型的参数,然后可以使用具有拟合参数的模型来预测是新的价值观X价值观。这本质上是监督学习。现代机器学习超越这种建模的原因是我们现在通常描述高维(许多特征)的数据并使用非线性函数。这似乎是直截了当的,但在实践中沿着这条路线走会有几个问题。例如,图 1.4B 显示了一个非线性函数,它似乎比图 1.4A 中的线性模型更好地描述了数据的模式。然而,图 1.4C 所示的非线性模型也是一种解决方案。它甚至通过了所有的训练点。这是一个特别困难的问题。如果允许我们任意增加模型复杂度,那么我们总能找到一个遍历所有数据点的模型。但是,数据点可能具有简单的关系,例如图 1.4A 的线性关系,并且变化仅代表噪声。因此,如图 1.4C 所示,用这种噪声拟合数据点确实意味着我们过度拟合了数据。

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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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。