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# 计算机代写|机器学习代写Machine Learning代考|ENGG3300 Parameter estimation

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## 计算机代写|机器学习代写Machine Learning代考|Parameter estimation

Quite often, we are interested in finding a single estimate of the value of an unknown parameter, even if this means discarding all uncertainty. This is called estimation: determining the values of some unknown variables from observed data. In this chapter, we outline the problem, and describe some of the main ways to do this, including Maximum A Posteriori (MAP), and Maximum Likelihood (ML). Estimation is the most common form of learning – given some data from the world, we wish to “learn” how the world behaves, which we will describe in terms of a set of unknown variables.

Strictly speaking, parameter estimation is not justified by Bayesian probability theory, and can lead to a number of problems, such as overfitting and nonsensical results in extreme cases. Nonetheless, it is widely used in many problems.

## 计算机代写|机器学习代写Machine Learning代考|MAP, ML, and Bayes’ Estimates

We can now define the MAP learning rule: choose the parameter value $\theta$ that maximizes the posterior, i.e.,
\begin{aligned} \hat{\theta} & =\arg \max \theta p(\theta \mid \mathcal{D}) \ & =\arg \max \theta P(\mathcal{D} \mid \theta) p(\theta) \end{aligned}
Note that we don’t need to be able to evaluate the evidence term $p(\mathcal{D})$ for MAP learning, since there are no $\theta$ terms in it.

Very often, we will assume that we have no prior assumptions about the value of $\theta$, which we express as a uniform prior: $p(\theta)$ is a uniform distribution over some suitably large range. In this case, the $p(\theta)$ term can also be ignored from MAP learning, and we are left with only maximizing the likelihood. Hence, the Maximum Likelihood (ML) learning principle (i.e., estimator) is
$$\hat{\theta}{M L}=\arg \max \theta P(\mathcal{D} \mid \theta)$$
It often turns out that it is more convenient to minimize the negative-log of the objective function. Because “- $\ln$ ” is a monotonic decreasing function, we can pose MAP estimation as:
\begin{aligned} \hat{\theta}{\text {MAP }} & =\arg \max \theta P(\mathcal{D} \mid \theta) p(\theta) \ & =\arg \min \theta-\ln (P(\mathcal{D} \mid \theta) p(\theta)) \ & =\arg \min \theta-\ln P(\mathcal{D} \mid \theta)-\ln p(\theta) \end{aligned}

## 计算机代写|机器学习代写Machine Learning代考|MAP, ML, and Bayes’ Estimates

$$\hat{\theta}=\arg \max \theta p(\theta \mid \mathcal{D}) \quad=\arg \max \theta P(\mathcal{D} \mid \theta) p(\theta)$$

$$\hat{\theta} M L=\arg \max \theta P(\mathcal{D} \mid \theta)$$

$$\hat{\theta} \mathrm{MAP}=\arg \max \theta P(\mathcal{D} \mid \theta) p(\theta) \quad=\arg \min \theta-\ln (P(\mathcal{D} \mid \theta) p(\theta))=\arg \min \theta-\ln P(\mathcal{D} \mid \theta)-\ln p(\theta)$$

## 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。