统计代写|机器学习作业代写Machine Learning代考| k-means clustering

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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|k-means clustering

k-means clustering is one of the most popular cluster and machine learning algorithm. k-means clustering falls into the category of centroid-based algorithms. A centroid is the geometric center of a geometric plane figure. The centroid is also called barycenter. In centroidbased clustering, $n$ observations are grouped into $k$ clusters in such a way that each observation belongs to the cluster with the nearest centroid. Here, the criterion for clustering is distance. The centroid itself does not need to be an observation point. Figure $2.7$ shows k-means clustering with 3 clusters.

In k-means clustering, the number of clusters $k$ needs to be defined beforehand, which is sometimes a problem since the number of clusters might not be known beforehand. For instance, in biology, if we want to classify plants given their features, we might not know how many different types of plants there are in a given data set. Other clustering methods, such as hierarchical clustering, do not need an assumption on the number of clusters. Also, there is no absolute criterion; it has to be defined by the user in such a way that the result of the clustering will suite the aim of the analytics task at hand. Cluster analysis is often just the starting point for other purposes, for instance a pre-processing step for other algorithms.Humans and animals learn mostly from experience, not from labeled data. Humans discover the world by observing it, not by being told the label of every object. So, human learning is largely unsupervised. That is why some authors argue that unsupervised learning will become fare more important than supervised learning in the future [18].

统计代写|机器学习作业代写Machine Learning代考|Semi-supervised learning

Semi-supervised learning uses a combination of labeled and unlabeled data. It is typically used when a small amount of labeled data and a large amount of unlabeled data is present. Since semi-supervised learning still requires labeled data, it can be considered a subset of supervised learning. However, other forms of partial supervision other than classification are possible.

Data is often labeled by a data scientist, which is a laborious task and bares the risk of introducing a human bias. Bias stems from human prejudice that, in the case of labeling data, might result in the underor overrepresentation of some features in the data set. Machine learning heavily depends on the quality of the data. If the data set is biased, the result of the machine learning task will be biased. However, human bias cannot only negatively influence machine learning through data

but also through algorithms and interaction. Human bias does not need to be conscious. It can originate from ignorance, for instance, an underrepresentation of minorities in a sample population or from a lack of data that includes minorities. Generally speaking, training data should equally represent all our world.

There are many different semi-supervised training methods. Probably the earliest idea about using unlabeled data in classification is self-learning, which is also known as self-training, self-labeling, or decision-directed learning [4]. The basic idea of self-learning is to use the labeled data set to train a learning algorithm, then use the trained learner iteratively to label chunks of the unlabeled data until all data is labeled using pseudo labels. Then the trained learner is retrained using its own predictions. Self-learning bears the risk that the pseudolabeled data will have no effect on the learner or that self-labeling happens without knowing on which assumptions the self-learning is based on. The central question for using semi-supervised learning is, under which conditions does taking into consideration unlabeled data contribute to the prediction accuracy? In the worst case, the unlabeled data will deteriorate the prediction accuracy.

统计代写|机器学习作业代写Machine Learning代考| Function approximation

Function approximation (FA) is sometimes used interchangeably with regression. Regression is a way to approximate a given data set. Function approximation can be considered a more general concept since there are many different methods to approximate data or functions. The goal of function approximation is to find a function $f$ that maps an input to an output vector. The function is selected among a defined class, e.g., quadratic functions or polynomials. For instance, equation $4.14$ is a first degree polynomial equation. Contrary to function fitting, where a curve is fitted to a set of data points, function approximation aims to find a function $f$ that approximates a target function. Given one set of samples $(x, y)$, we try to find a function $f$ :
$$f: X \rightarrow Y$$

where
$X=$ Input space
$Y \quad=$ Output space, number of predictions
where the input space can be multidimensional $\mathbf{X} \subseteq \mathbb{R}^{2}$, in this case $n$-dimensional. The function:
$$f(x)=y$$
maps $x \in X$ to $y \in Y$, where the distribution of $x$ and the function $f$ are unknown. $f$ can have some unknown properties for a space where no data points are available.

Figure $2.8$ shows an unknown function $f(x)$ and some random data points.

Function approximation is similar to regression and techniques such as interpolation, extrapolation or regression analysis can be used. Regression does essentially the same thing, create a model from a given data set. However, regression focuses more on statistical concepts, such as variance and expectation. Function approximation tries to explain the underlying data by finding a model $h(x)$ for all samples $(x, y)$, such that $h(x) \approx y$. Ideally, the model equals the underlying function $f(x)$ such

that $h(x)=f(x)$. However, there might be sub-spaces where no data points are available. To find a model, we need to measure the quality of the model. To do so, function approximation tries to minimize the prediction error. This is similar to evaluating a trained machine learning model, such as a Bayesian or a logistic regression model. An intuitive measure for the error is the mean absolute error (MAE). Given $n$ instances $(x, y)$, the model $h(x)$ can be evaluated by calculating the mean absolute error as:
$$M A E=\frac{1}{n} \sum_{i=1}^{n}\left|y_{i}-h\left(x_{i}\right)\right|$$

统计代写|机器学习作业代写Machine Learning代考|k-means clustering

k-means 聚类是最流行的聚类和机器学习算法之一。k-means 聚类属于基于质心的算法。质心是几何平面图形的几何中心。质心也称为重心。在基于质心的聚类中，n观察被分组为到以这样一种方式进行聚类，即每个观测值都属于具有最近质心的聚类。这里，聚类的标准是距离。质心本身不需要是观察点。数字2.7显示了具有 3 个聚类的 k 均值聚类。

F:X→是

X=输入空间

F(X)=是

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。