### 统计代写|机器学习作业代写Machine Learning代考| Supervised 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

## 统计代写|机器学习作业代写Machine Learning代考|Classification

In classification, we try to assign a label to a test instance, e.g., we try to predict if the animal in a picture is a “cat” or a “dog”. In other words, we assign a new observation to a specific category. The learning algorithm that assigns the instance to a category is called classifier. Classification answers questions such as: “is that bank client going to repay the loan?”, “will the user who clicked on an ad buy?”, “who is the person in the Facebook picture?”. Classification predicts a discrete target label $y$. If there are two labels such as “spam” / “not spam”, we have a binary classification problem, if there are more labels, we have a multiclass classification problem, e.g., assigning blood samples to the blood types “A”, “B”, “AB” and “O”.

A classifier learns a function $f$ that maps an input $x$ to an output $y$, as shown in equation 4.1. Sometimes, the function $f$ is referred to as classifier instead of the algorithm that implements the classifier.
$$y=f(x)+\varepsilon$$
where
$f=$ Function that maps $x$ to $y$, learned from labeled training data
$x=$ Input, independent variable

$\varepsilon$ is the irreducible error that stems from noise and randomness in the training data and that, as the name suggests, cannot be reduced during training. It can be reduced in some cases through more data preprocessing steps, however, $\varepsilon$ is a theoretical limit of the performance of the learning algorithm.

Typical classifiers include Bayesian models, decision trees, support vector machines and artificial neural networks.

## 统计代写|机器学习作业代写Machine Learning代考|Artificial neural networks

Artificial neural networks are inspired by the human nervous system. They encompass a large number of different models and learning methods. Here, we cover some of the widely-used models inorder to show their principal functioning.

A typical neuron, as found in the human body, looks as depicted in Figure 4.1. It consists of dendrites that receive electrochemical stimulation from upstream neurons through synapses located in different places on the dendrites. Presynaptic cells release neurotransmitters into the synaptic cleft in response to spikes of electrical activity known as action potentials. The neurotransmitter stimulates the receiving neuron which, in turn, creates an action potential. The action potential is transmitted along the cell membrane down the axon to the axon terminals where it triggers the release of neurotransmitters. The neuron is said to “fire”.

The dendrites can receive signals from more than one upstream neuron. Each neuron is typically connected to thousands of other neurons. It is estimated that there are about 100 trillion $\left(10^{14}\right)$ synapses within the human brain [25]. Also, synaptic connections are not static. They can strengthen and weaken over time as a result of increasing or decreasing activity, a process called synaptic plasticity. Neurologists have discovered that the human brain learns by changing the strength of the synaptic connection between neurons upon repeated stimulation by the same impulse [37]. When two neurons frequently interact, they form a bond that allows them to transmit the signal more easily and accurately (Hebb’s rule). Strong input to a postsynaptic cell causes it to traffic more receptors for neurotransmitters to its surface, amplifying the signal it receives from the presynaptic cell. This phenomenon, known as long-term potentiation (LTP), occurs following persistent, high-frequency stimulation of the synapse. For instance, when we learn a foreign language, we repeat new words until we do not have to concentrate on the translation anymore. We subconsciously use the correct foreign language words. The repeating of the words results in the strengthening of the synaptic connections and formation of a bond between the neurons involved in language speaking. The strengthening and weakening of synaptic connections is imitated in artificial neural networks by linearly combining the input signals with weights. The weights are usually represented in a weight matrix $W$. Learning in an artificial neural network consists of modifying the weight matrix until the generative model represents the training data well [25].

## 统计代写|机器学习作业代写Machine Learning代考|Bayesian models

Bayesian models are based on Bayes theorem. Generally speaking, the Bayes classifier minimizes the probability of misclassification. It is a model that draws its inferences from the posterior distribution. Bayesian models utilize a prior distribution and a likelihood, which are related by Bayes’ theorem. Bayes rule decomposes the computation of a posterior probability into the computation of a likelihood and a prior probability [30]. It calculates the posterior probability $P(c \mid x)$ from $P(c), P(x)$ and $P(x \mid c)$, as shown in equation 4.7.
$$P(c \mid x)=\frac{P(x \mid c) P(c)}{P(x)}$$
where $P(c \mid x)=$ Posterior probability of class $c$ (target) given predictor $P(x \mid c)=$ Likelihood which is the probability of predictor given class $c$

$$\begin{array}{ll} P(c) & =\text { Prior probability of class } c \ P(x) & =\text { Prior probability of predictor } x \end{array}$$
The probability in Bayesian models is expressed as a degree of belief in an event that can change in the evidence of new information. The Bayes rule tells us how to do inference about hypotheses from data where uncertainty in inferences is expressed using a probability. Learning and prediction can be seen as forms of inference. Calculating $P(x \mid c)$ is not easy when $x=v_{1}, v_{2}, \ldots v_{n}$ is large and requires a lot of computing power. However, Bayesian methods have become popular in recent years due to the advent of more powerful computers.

## 统计代写|机器学习作业代写Machine Learning代考|Classification

F=映射的函数X到是，从标记的训练数据中学习
X=输入，自变量

e是源于训练数据中的噪声和随机性的不可约误差，顾名思义，在训练期间无法减少。在某些情况下，可以通过更多的数据预处理步骤来减少它，但是，e是学习算法性能的理论极限。

## 广义线性模型代考

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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。