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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写机器学习 machine 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。我们的专家在代写机器学习 machine learning代写方面经验极为丰富，各种代写机器学习 machine 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

## 计算机代写|机器学习代写machine learning代考|No-Free-Lunch Theorem

In the context of machine learning, the no-free-lunch theorem $[253,57,220]$ states that no learning method is universally superior to other methods for all possible learning problems. Given any two machine learning algorithms, if we use them to learn all possible learning problems we can imagine, the average performance of these two algorithms must be the same. Or even worse, their average performance is no better than random guessing.

We can use the earlier curve-fitting problem as an example to explain why the no-free-lunch theorem makes sense. Given the training samples in Figure 1.3, our goal is to create a model to predict function values for other $x$ points. No matter what learning method we use, we eventually end up with an estimated model, such as the red curve in Figure 1.12. Because we have no knowledge of the ground-truth function $y=f(x)$ other than the training samples, theoretically speaking, the ground-truth function $y=f(x)$ could take any arbitrary value for a new point, which is not in the training set. When we use the estimated model to predict function values at some new points, say, $x_1$ and $x_2$, it is easy to see that the estimated model yields a good prediction if the ground-truth function $y=f(x)$ happens to yield “good” values (as indicated by green dots in Figure 1.12). However, we can always imagine another scenario where the groundtruth function yields “bad” values (as indicated by red squares in Figure 1.12), for which the estimated model will give a very poor prediction. This is true no matter what learning algorithm we use to estimate the model. If we average the prediction performance of any estimated model over all possible scenarios for the ground-truth function, the average performance is close to a random guess because for each good-prediction case, we can also come up with any number of bad-prediction cases.

The no-free-lunch theorem simply says that no machine learning algorithm can learn anything useful merely from the training data. If a machine learning method works well for some problems, the method must have explicitly or implicitly used other knowledge of the underlying problems beyond the training data.

## 计算机代写|机器学习代写machine learning代考|Law of the Smooth World

Despite the aforementioned no-free-lunch theorem, a fundamental reason why many machine learning methods thrive in practice is that our physical world is always smooth. Because of the hard constraints that exist in reality, such as energy and power, any physical process in the macro world is smooth in nature (e.g., audios, images, videos). Furthermore, our intuition and perception are all built on top of the law of the smooth world. Therefore, if we use machine learning to tackle any problems arising from the real world, the law of the smooth world is always applicable, dramatically simplifying many of our learning problems at hand.

For example, as shown in Figure 1.13, assume that a training set contains some measurements of a physical process at three points in the space, that is, $\mathbf{x}, \mathbf{y}$, and $\mathbf{z}$, where $\mathbf{x}$ and $\mathbf{y}$ are located far apart, whereas $\mathbf{x}$ and $\mathbf{z}$ are close by. If we need to learn a model to predict the process in the yellow region between $\mathbf{x}$ and $\mathbf{y}$, it is a hard problem because the training data do not provide any information for this, and many unpredictable things could happen within such a wide range. On the other hand, if we need to predict this process in the blue region between two nearby points, it should be relatively simple because the law of the smooth world significantly restricts the behavior of the process within such a narrow region given the two observations at $\mathbf{x}$ and $\mathbf{z}$. In fact, some machine learning models can be built to give fairly accurate predictions in the blue region by simply interpolating these two observations at $\mathbf{x}$ and $\mathbf{z}$. The exact prediction accuracy actually depends on the smoothness of the underlying process. In machine learning, such smoothness is often mathematically quantified using the concept of Lipschitz continuity (see margin note) or a more recent notion of bandlimitedness [115].

Moreover, let us go back to the no-free-lunch example in Figure 1.12. If we have enough training samples to ensure that the gaps between all samples are small enough, then many “bad” values as assumed by the no-free-lunch theorem will not actually occur in practice because they violate the law of the smooth world. As a result, when we only average all plausible scenarios in practice, suitable machine learning methods achieve much better prediction accuracy than random guessing.

# 机器学习代考

## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师