### 计算机代写|深度学习代写deep learning代考|STAT3007

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|深度学习代写deep learning代考|Subdifferentials

The directional derivative of $f$ at $\boldsymbol{x} \in \operatorname{dom} f$ in the direction of $\boldsymbol{y} \in \mathcal{H}$ is defined by
$$f^{\prime}(x ; y)=\lim _{\alpha \downarrow 0} \frac{f(x+\alpha y)-f(x)}{\alpha}$$ if the limit exists. If the limit exists for all $y \in \mathcal{H}$, then one says that $f$ is Gãteaux differentiable at $\boldsymbol{x}$. Suppose $f^{\prime}(\boldsymbol{x} ; \cdot)$ is linear and continuous on $\mathcal{H}$. Then, there exist a unique gradient vector $\nabla f(\boldsymbol{x}) \in \mathcal{H}$ such that
$$f^{\prime}(\boldsymbol{x} ; \boldsymbol{y})=\langle\boldsymbol{y}, \nabla f(\boldsymbol{x})\rangle, \quad \forall \boldsymbol{y} \in \mathcal{H}$$
If a function is differentiable, the convexity of a function can easily be checked using the first- and second-order differentiability, as stated in the following:

Proposition $1.1$ Let $f: \mathcal{H} \mapsto(-\infty, \infty]$ be proper. Suppose that $\operatorname{dom} f$ is open and convex, and $f$ is Gâteux differentiable on $\operatorname{dom} f$. Then, the followings are equivalent:

1. $f$ is convex.
2. (First-order): $f(\boldsymbol{y}) \geq f(\boldsymbol{x})+\langle\boldsymbol{y}-\boldsymbol{x}, \nabla f(\boldsymbol{x})\rangle, \quad \forall \boldsymbol{x}, \boldsymbol{y} \in \mathcal{H}$.
3. (Monotonicity of gradient): $\langle\boldsymbol{y}-\boldsymbol{x}, \nabla f(\boldsymbol{y})-\nabla f(\boldsymbol{x})\rangle \geq 0, \quad \forall \boldsymbol{x}, \boldsymbol{y} \in \mathcal{H}$.
If the convergence in (1.48) is uniform with respect to $\boldsymbol{y}$ on bounded sets, i.e.
$$\lim _{\boldsymbol{0} \neq \boldsymbol{y} \rightarrow \mathbf{0}} \frac{f(\boldsymbol{x}+\boldsymbol{y})-f(\boldsymbol{x})-\langle\boldsymbol{y}, \nabla f(\boldsymbol{x})\rangle}{|\boldsymbol{y}|}=0$$

## 计算机代写|深度学习代写deep learning代考|Linear and Kernel Classifiers

Classification is one of the most basic tasks in machine learning. In computer vision, an image classifier is designed to classify input images in corresponding categories. Although this task appears trivial to humans, there are considerable challenges with regard to automated classification by computer algorithms.

For example, let us think about recognizing “dog” images. One of the first technical issues here is that a dog image is usually taken in the form of a digital format such as JPEG, PNG, etc. Aside from the compression scheme used in the digital format, the image is basically just a collection of numbers on a twodimensional grid, which takes integer values from 0 to 255 . Therefore, a computer algorithm should read the numbers to decide whether such a collection of numbers corresponds to a high-level concept of “dog”. However, if the viewpoint is changed, the composition of the numbers in the array is totally changed, which poses additional challenges to the computer program. To make matters worse, in a natural setting a dog is rarely found on a white background; rather, the dog plays on the lawn or takes a nap in the living room, hides underneath furniture or chews with her eyes closed, which makes the distribution of the numbers very different depending on the situation. Additional technical challenges in computer-based recognition of a dog come from all kinds of sources such as different illumination conditions, different poses, occlusion, intra-class variation, etc., as shown in Fig. 2.1. Therefore, designing a classifier that is robust to such variations was one of the important topics in computer vision literature for several decades.

In fact, the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) [7] was initiated to evaluate various computer algorithms for image classification at large scale. ImageNet is a large visual database designed for use in visual object recognition software research [8]. Over 14 million images have been hand-annotated in the project to indicate which objects are depicted, and at least one million of the images also have bounding boxes. In particular, ImageNet contains more than 20,000 categories made up of several hundred images. Since 2010, the ImageNet project has organized an annual software competition, the ImageNet Large Scale Visual Recognition Challenge (ILSVRC), in which software programs compete for the correct classification and recognition of objects and scenes. The main motivation is to allow researchers to compare progress in classification across a wider variety of objects. Since the introduction of AlexNet in 2012 [9], which was the first deep learning approach to win the ImageNet Challenge, the state-of-the art image classification methods are all deep learning approaches, and now their performance even surpasses human observers.

## 计算机代写|深度学习代写deep learning代考|Subdifferentials

$$f^{\prime}(x ; y)=\lim _{\alpha \downarrow 0} \frac{f(x+\alpha y)-f(x)}{\alpha}$$

$$f^{\prime}(\boldsymbol{x} ; \boldsymbol{y})=\langle\boldsymbol{y}, \nabla f(\boldsymbol{x})\rangle, \quad \forall \boldsymbol{y} \in \mathcal{H}$$

1. $f$ 是凸的。
2. (第一个订单) : $f(\boldsymbol{y}) \geq f(\boldsymbol{x})+\langle\boldsymbol{y}-\boldsymbol{x}, \nabla f(\boldsymbol{x})\rangle, \quad \forall \boldsymbol{x}, \boldsymbol{y} \in \mathcal{H}$.
3. (梯度的单调性) : $\langle\boldsymbol{y}-\boldsymbol{x}, \nabla f(\boldsymbol{y})-\nabla f(\boldsymbol{x})\rangle \geq 0, \quad \forall \boldsymbol{x}, \boldsymbol{y} \in \mathcal{H}$. 如果 (1.48) 中的收敛是一致的 $\boldsymbol{y}$ 在有界集上，即
$$\lim _{\boldsymbol{0} \neq \boldsymbol{y} \rightarrow 0} \frac{f(\boldsymbol{x}+\boldsymbol{y})-f(\boldsymbol{x})-\langle\boldsymbol{y}, \nabla f(\boldsymbol{x})\rangle}{|\boldsymbol{y}|}=0$$

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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。