# 数学代写|凸优化作业代写Convex Optimization代考|CPD131

#### Doug I. Jones

Lorem ipsum dolor sit amet, cons the all tetur adiscing elit

couryes-lab™ 为您的留学生涯保驾护航 在代写凸优化Convex Optimization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。我们的专家在代写凸优化Convex Optimization代写方面经验极为丰富，各种代写凸优化Convex Optimization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
couryes™为您提供可以保分的包课服务

## 数学代写|凸优化作业代写Convex Optimization代考|Detection probability matrix

For the randomized detector defined by the matrix $T$, we define the detection probability matrix as $D=T P$. We have
$$D_{i j}=(T P){i j}=\operatorname{prob}(\hat{\theta}=i \mid \theta=j)$$ so $D{i j}$ is the probability of guessing $\hat{\theta}=i$, when in fact $\theta=j$. The $m \times m$ detection probability matrix $D$ characterizes the performance of the randomized detector defined by $T$. The diagonal entry $D_{i i}$ is the probability of guessing $\hat{\theta}=i$ when $\theta=i$, i.e., the probability of correctly detecting that $\theta=i$. The off-diagonal entry $D_{i j}$ (with $i \neq j$ ) is the probability of mistaking $\theta=i$ for $\theta=j$, i.e., the probability that our guess is $\hat{\theta}=i$, when in fact $\theta=j$. If $D=I$, the detector is perfect: no matter what the parameter $\theta$ is, we correctly guess $\hat{\theta}=\theta$.

The diagonal entries of $D$, arranged in a vector, are called the detection probabilities, and denoted $P^{\mathrm{d}}$ :
$$P_i^{\mathrm{d}}=D_{i i}=\operatorname{prob}(\hat{\theta}=i \mid \theta=i)$$
The error probabilities are the complements, and are denoted $P^{\mathrm{e}}$ :
$$P_i^e=1-D_{i i}=\operatorname{prob}(\hat{\theta} \neq i \mid \theta=i)$$
Since the columns of the detection probability matrix $D$ add up to one, we can express the error probabilities as
$$P_i^{\mathrm{e}}=\sum_{j \neq i} D_{j i}$$

## 数学代写|凸优化作业代写Convex Optimization代考|Bias, mean-square error, and other quantities

In this section we assume that the ordering of the values of $\theta$ have some significance, i.e., that the value $\theta=i$ can be interpreted as a larger value of the parameter than $\theta=j$, when $i>j$. This might be the case, for example, when $\theta=i$ corresponds to the hypothesis that $i$ events have occurred. Here we may be interested in quantities such as
$$\operatorname{prob}(\hat{\theta}>\theta \mid \theta=i)$$
which is the probability that we overestimate $\theta$ when $\theta=i$. This is an affine function of $D$ :
$$\operatorname{prob}(\hat{\theta}>\theta \mid \theta=i)=\sum_{j>i} D_{j i}$$ so a maximum allowable value for this probability can be expressed as a linear inequality on $D$ (hence, $T$ ). As another example, the probability of misclassifying $\theta$ by more than one, when $\theta=i$,
$$\operatorname{prob}(|\hat{\theta}-\theta|>1 \mid \theta=i)=\sum_{|j-i|>1} D_{j i}$$
is also a linear function of $D$.
We now suppose that the parameters have values $\left{\theta_1, \ldots, \theta_m\right} \subseteq \mathbf{R}$. The estimation or detection (parameter) error is then given by $\hat{\theta}-\theta$, and a number of quantities of interest are given by linear functions of $D$. Examples include:

• Bias. The bias of the detector, when $\theta=\theta_i$, is given by the linear function
$$\underset{i}{\mathbf{E}}(\hat{\theta}-\theta)=\sum_{j=1}^m\left(\theta_j-\theta_i\right) D_{j i}$$
where the subscript on $\mathbf{E}$ means the expectation is with respect to the distribution of the hypothesis $\theta=\theta_i$.
• Mean square error. The mean square error of the detector, when $\theta=\theta_i$, is given by the linear function
• Average absolute error. The average absolute error of the detector, when $\theta=\theta_i$, is given by the linear function
$$\underset{i}{\mathbf{E}}|\hat{\theta}-\theta|=\sum_{j=1}^m\left|\theta_j-\theta_i\right| D_{j i}$$

## 数学代写|凸优化作业代写Convex Optimization代考|Separating a point and a convex set

$$\left(P C\left(x_0\right)-x_0\right)\left(x-(12)\left(x_0+P\left(x_0\right)\right)\right)=0$$
(严格) 分开 $x_0$ 从C，如图 8.1 所示。然而，在其他规范中，投影问题和分离超 平面问题之间最明显的联系是通过拉格朗日对偶性。 我们先表达 (8.2)作为
$$\text { minimize }|y| \text { subject to } \quad f(x) \leq 0, \quad i=1, \ldots, m \quad A x=b \quad x_0-x$$

$$L(x, y, \lambda, \mu, \nu)=|y|+\sum_{=1}^m \lambda f(x)+\nu(A x-b)+\mu^{\top}\left(x_0-x-y\right)$$

$$(\lambda, \mu, \nu)=\left{\text { in } x\left(\sum i=1^m \lambda f(x)+\nu(A x-b)+\mu^T\left(x_0-x\right)\right) \quad|\mu|* \leq\right]$$ 所以我们得到对偶问题 $$\text { maximize } \left.\quad \mu^T x_0+\text { in } x \sum i=1^m \lambda f(x)+\nu(A x-b)-\mu^T x\right) \text { subject }$$ 有变量 $\lambda, \mu, \nu$. 我们可以如下解释对偶问题。认为 $\lambda, \mu, \nu$ 是双重可行的，具有积极 的双重目标价值，即 $\lambda \succeq 0,|\mu|* \leq 1$ ，和
$$\mu^T x_0-\mu^T x+\sum_{=1}^m \lambda f(x)+\nu^{\top}(A x-b)>0$$

## 数学代写|凸优化作业代写Convex Optimization代考|Projection and separation via indicator and support functions

$$S(x)=\sup {y \in C} x^{\top} y, \quad I_C(x)= \begin{cases}0 & x \in C+\infty \quad x \notin C .\end{cases}$$ 投影的问题 $x_0$ 在闭凸集上 可以简洁地表示为 $$\text { minimize }\left|x-x_0\right| \text { subject to } \quad I_C(x) \leq 0$$ 或者，等价地，作为 $$\text { minimize }|y| \text { subject to } \quad I_C(x) \leq 0 \quad x_0-x=y$$ 变量在哪里 $x$ 和 $y$. 这个问题的对偶函数是 所以我们得到对偶问题 $$\text { maximize } \quad z^{\top} x_0-S(z) \text { subject to } \quad|z|* \leq 1$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

Days
Hours
Minutes
Seconds

# 15% OFF

## On All Tickets

Don’t hesitate and buy tickets today – All tickets are at a special price until 15.08.2021. Hope to see you there :)