### 计算机代写|机器学习代写machine learning代考|COMP4702

statistics-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|Consistency regularization

Consistency regularizalion leverages the simple idea that perturbing a given dalapoint (or the model itself) should not cause the model’s output to change dramatically. Since measuring consistency in this way only makes use of the model’s outputs (and not ground-truth labels), it is readily applicable to unlabeled data and therefore can be used to create appropriate loss functions for semi-supervised learning. This idea was first proposed under the framework of “learning with pseudo-ensembles” [BAP14], with similar variants following soon thereafter [LA16; SJT16].

In its most general form, both the model $p_\theta(y \mid x)$ and the transformations applied to the input can be stochastic. For example, in computer vision problems we may transform the input by using data augmentation like randomly rotating or adding noise the input image, and the network may include stochastic components like dropout (Section 13.5.4) or weight noise [Gra11]. A common and simple form of consistency regularization first samples $\boldsymbol{x}^{\prime} \sim q\left(\boldsymbol{x}^{\prime} \mid \boldsymbol{x}\right)$ (where $q\left(\boldsymbol{x}^{\prime} \mid x\right)$ is the distribution induced by the stochastic input transformations) and then minimizes the loss $\left|p_\theta(y \mid x)-p_\theta\left(y \mid x^{\prime}\right)\right|^2$. In practice, the first term $p_\theta(y \mid x)$ is typically treated as fixed (i.e. gradients are not propagated through it). In the semi-supervised setting, the combined loss function over a batch of labeled data $\left(\boldsymbol{x}1, y_1\right),\left(\boldsymbol{x}_2, y_2\right), \ldots,\left(\boldsymbol{x}_M, y_M\right)$ and unlabeled data $\boldsymbol{x}_1, \boldsymbol{x}_2, \ldots, \boldsymbol{x}_N$ is $$\mathcal{L}(\boldsymbol{\theta})=-\sum{i=1}^M \log p_\theta\left(y=y_i \mid \boldsymbol{x}i\right)+\lambda \sum{j=1}^N\left|p_\theta\left(y \mid \boldsymbol{x}j\right)-p\theta\left(y \mid \boldsymbol{x}_j^{\prime}\right)\right|^2$$
where $\lambda$ is a scalar hyperparameter that balances the importance of the loss on unlabeled data and, for simplicity, we write $\boldsymbol{x}_j^{\prime}$ to denote a sample drawn from $q\left(\boldsymbol{x}^{\prime} \mid \boldsymbol{x}_j\right)$.

The basic form of consistency regularization in Equation (19.27) reveals many design choices that impact the success of this semi-supervised learning approach. First, the value chosen for the $\lambda$ hyperparameter is important. If it is too large, then the model may not give enough weight to learning the supervised task and will instead start to reinforce its own bad predictions (as with confirmation bias in self-training). Since the model is often poor at the start of training before it has been trained on much labeled data, it is common in practice to initialize set $\lambda$ to zero and increase its value over the course of training.

## 计算机代写|机器学习代写machine learning代考|Variational autoencoders

In Section 20.3.5, we describe the variational autoencoder (VAE), which defines a probabilistic model of the joint distribution of data $\boldsymbol{x}$ and latent variables $\boldsymbol{z}$. Data is assumed to be generated by first sampling $\boldsymbol{z} \sim p(\boldsymbol{z})$ and then sampling $\boldsymbol{x} \sim p(\boldsymbol{x} \mid \boldsymbol{z})$. For learning, the VAE uses an encoder $\boldsymbol{q}{\boldsymbol{\lambda}}(\boldsymbol{z} \mid \boldsymbol{x})$ to approximate the posterior and a decoder $p\theta(\boldsymbol{x} \mid \boldsymbol{z})$ to approximate the likelihood. The encoder and decoder are typically deep neural networks. The parameters of the encoder and decoder can be jointly trained by maximizing the evidence lower bound (ELBO) of data.

The marginal distribution of latent variables $p(\boldsymbol{z})$ is often chosen to be a simple distribution like a diagonal-covariance Gaussian. In practice, this can make the latent variables $\boldsymbol{z}$ more amenable to downstream classification thanks to the facts that $\boldsymbol{z}$ is typically lower-dimensional than $\boldsymbol{x}$, that $\boldsymbol{z}$ is constructed via cascaded nonlinear transformations, and that the dimensions of the latent variables are designed to be independent. In other words, the latent variables can provide a (learned) representation where data may be more easily separable. In [Kin $+14]$, this approach is called M1 and it is indeed shown that the latent variables can be used to train stronger models when labels are scarce. (The general idea of unsupervised learning of representations to help with downstream classification tasks is described further in Section 19.2.4.)

An alternative approach to leveraging VAEs, also proposed in [Kin $+14]$ and called M2, has the form
$$p_{\boldsymbol{\theta}}(\boldsymbol{x}, y)=p_{\boldsymbol{\theta}}(y) p_{\boldsymbol{\theta}}(\boldsymbol{x} \mid y)=p_{\boldsymbol{\theta}}(y) \int p_{\boldsymbol{\theta}}(\boldsymbol{x} \mid y, \boldsymbol{z}) p_{\boldsymbol{\theta}}(\boldsymbol{z}) d \boldsymbol{z}$$
where $\boldsymbol{z}$ is a latent variable, $p_{\boldsymbol{\theta}}(\boldsymbol{z})=\mathcal{N}(\boldsymbol{z} \mid \mathbf{0}, \mathbf{I})$ is the latent prior, $p_{\boldsymbol{\theta}}(y)=\operatorname{Cat}(y \mid \boldsymbol{\pi})$ the label prior, and $p_{\boldsymbol{\theta}}(\boldsymbol{x} \mid y, \boldsymbol{z})=p\left(\boldsymbol{x} \mid f_{\boldsymbol{\theta}}(y, \boldsymbol{z})\right)$ is the likelihood, such as a Gaussian, with parameters computed by $f$ (a deep neural network). The main innovation of this approach is to assume that data is generated according to both a latent class variable $y$ as well as the continuous latent variable $\boldsymbol{z}$. The class variable $y$ is observed for labeled data and unobserved for unlabled data.

# 机器学习代考

## 计算机代写|机器学习代写machine learning代考|Consistency regularization

$\left|p_\theta(y \mid x)-p_\theta\left(y \mid x^{\prime}\right)\right|^2$. 在实践中，第一个词 $p_\theta(y \mid x)$ 通常被视为固定的（即梯度不通过它传播）。在半 监督设置中，一批标记数据的组合损失函数 $\left(\boldsymbol{x} 1, y_1\right),\left(\boldsymbol{x}2, y_2\right), \ldots,\left(\boldsymbol{x}_M, y_M\right)$ 和末标记的数据 $\boldsymbol{x}_1, \boldsymbol{x}_2, \ldots, \boldsymbol{x}_N$ 是 $$\mathcal{L}(\boldsymbol{\theta})=-\sum i=1^M \log p\theta\left(y=y_i \mid \boldsymbol{x} i\right)+\lambda \sum j=1^N\left|p_\theta(y \mid \boldsymbol{x} j)-p \theta\left(y \mid \boldsymbol{x}_j^{\prime}\right)\right|^2$$

## 计算机代写|机器学习代写machine learning代考|Variational autoencoders

[Kin] 中也提出了一种利用 VAE 的替代方法 $+14]$ 并称为 M2，具有以下形式
$$p_\theta(\boldsymbol{x}, y)=p_\theta(y) p_{\boldsymbol{\theta}}(\boldsymbol{x} \mid y)=p_{\boldsymbol{\theta}}(y) \int p_{\boldsymbol{\theta}}(\boldsymbol{x} \mid y, \boldsymbol{z}) p_{\boldsymbol{\theta}}(\boldsymbol{z}) d \boldsymbol{z}$$

## 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。