assignmentutor-lab™ 为您的留学生涯保驾护航 在代写贝叶斯分析Bayesian Analysis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。我们的专家在代写贝叶斯分析Bayesian Analysis代写方面经验极为丰富，各种代写贝叶斯分析Bayesian Analysis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
assignmentutor™您的专属作业导师

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|FIRST EXAMPLE: THE LATENT DIRICHLET

We begin the technical discussion with an example model for topic modeling: the latent Dirichlet allocation (LDA) model. It demonstrates several technical points that are useful to know when approaching a problem in NLP with Bayesian analysis in mind. The original LDA paper by Blei et al. (2003) also greatly popularized variational inference techniques in Machine Learning and Bayesian NLP, to which Chapter 6 is devoted.

LDA elegantly extends the simplest computational representation for documents-the bag-of-words representation. With the bag-of-words representation, we treat a document as a multiset of words (or potentially as a set as well). This means that we dispose of the order of the words in the document and focus on just their isolated appearance in the text. The words are assumed to originate in a fixed vocabulary that includes all words in all documents (see Zhai and Boyd-Graber (2013) on how to avoid this assumption).

The bag-of-words representation is related to the “unigram language model,” which also models sentences by ignoring the order of the words in these sentences.

As mentioned above, with the bag-of-words model, documents can be mathematically represented as multisets. For example, assume there is a set $V$ of words (the vocabulary) with a special symbol $\diamond$, and a text such ss $^{3}$ :
Goldman Sachs said Thursday it has adopted all 39 initiatives it proposed to strengthen its business practices in the wake of the 2008 financial crisis, a step designed to help both employees and clients move past one of most challenging chapters in the company’s history. $\diamond$
The symbol $\diamond$ terminates the text. All other words in the document must be members of $V \backslash{\diamond}$. The mathematical object that describes this document, $d$, is the multiset ${w: c}$, where the notation $w: c$ is used to denote that the word $w$ appears in the document $c$ times. For example, for the above document, business: 1 belongs to its corresponding multiset, and so does both: 1. A bag of words can have even more extreme representation, in which counts are ignored, and $c=1$ is used for all words. From a practical perspective, the documents are often preprocessed, so that, for example, function words or extremely common words are removed.
To define a probabilistic model over these multisets, we first assume a probability distribution over $V, p(W \mid \beta)$. This means that $\beta$ is a set of parameters for a multinomial distribution such that $p(w \mid \beta)=\beta_{w}$. This vocabulary distribution induces a distribution over documents, denoted by the random variable $D$ (a random multiset), as follows:
$$p(D=d \mid \beta)=\prod_{(w: c) \in d} p(w \mid \beta)^{c}=\prod_{(w: c) \in d}\left(\beta_{w}\right)^{c}$$

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|THE DIRICHLET DISTRIBUTION

The Dirichlet distribution is a multivariate distribution over the probability simplex of a fixed dimension. This means it defines a distribution over $K$ continuous random variables, $0 \leq \theta_{k} \leq 1$ for $k \in{1, \ldots, K}$ such that:
$$\sum_{k=1}^{K} \theta_{k}=1$$
Its probability density depends on $K$ positive real values, $\alpha_{1}, \ldots, \alpha_{K}$. The PDF appears in Equation $2.2$ where $C(\alpha)$ is a normalization constant defined as:
$$C(\alpha)=\frac{\Gamma\left(\sum_{k=1}^{K} \alpha_{k}\right)}{\Gamma\left(\alpha_{1}\right) \ldots \Gamma\left(\alpha_{K}\right)}$$
with $\Gamma(x)$ being the Gamma function for $x \geq 0$ (see also Appendix B)-a generalization of the factorial function such that whenever $x$ is natural number it holds that $\Gamma(x)=(x-1)$ !.

Vectors in the “probability simplex,” as the name implies, can be treated as probability distributions over a finite set of size $K$. This happens above, with LDA, where $\theta$ is treated as a probability distribution over the $K$ topics (each topic is associated with one of the $K$ dimensions of the probability simplex), and used to draw topics for each word in the document.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|INFERENCE

As was briefly mentioned earlier, in topic modeling the topics are considered to be latent. While datasets exist in which documents are associated with various human-annotated topics, the vast majority of document collections do not have such an annotation-certainly not in the style of the LDA model, where each word has some degree of association with each topic. In fact, asking an annotator to annotate topics the way they are defined in an LDA-style topic model is probably an ill-defined task because these topics are often not crisp or fully interpretable in their word association (see Chang et al. (2009) for a study on human interpretation of topic models; also see Mimno et al. (2011) and Newman et al. (2010) for automatic topic coherence evaluation). For LDA, this means that the distribution over topics, $\theta$, and the topic identity for each word are latent variables – they are never observed in the data, which are just pure text.
This is typical in Bayesian NLP as well. Usually, there is a random variable $X$ (a document or a sentence, for example) which is associated with a predicted structure, denoted by a random variable $Z$. The generation of $X$ and $Z$ is governed by some distribution parametrized by $\theta$. The parameters $\theta$ themselves are a random variable that is governed, for example, by the Dirichlet distribution, or more generally by a distribution $p(\theta)$. This distribution is also called the prior distribution. Generative story $2.2$ describes this process.

There is a striking similarity to the LDA generative process, where the topic distribution plays the role of the set of parameters, the topic assignments play the role of the latent structure, and the words in the document play the role of the observed data.

The generative process above dictates the following joint probability distribution $p(X, Z, \theta):$
$$p(x, z, \theta)=p(\theta) p(z \mid \theta) p(x \mid \theta, z) .$$

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|FIRST EXAMPLE: THE LATENT DIRICHLET

LDA 优雅地扩展了文档最简单的计算表示一一词袋表示。使用词袋表示，我们将文档视为一个多词集（或者也可能是一个词集）。这意 味着我们处理文档中单词的顺序，只关注它们在文本中的孤立外观。假设这些词来源于一个固定的词汇表，包括所有文档中的所有词（参 见 Zhai 和 Boyd-Graber (2013) 关于如何避免这种假设）。

$$p(D=d \mid \beta)=\prod_{(w: c) \in d} p(w \mid \beta)^{c}=\prod_{(w: c) \in d}\left(\beta_{w}\right)^{c}$$

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|THE DIRICHLET DISTRIBUTION

Dirichlet 分布是在固定维度的概率单纯形上的多元分布。这意味着它定义了一个分布 $K$ 连续随机变量， $0 \leq \theta_{k} \leq 1$ 为了 $k \in 1, \ldots, K$ 这 样:
$$\sum_{k=1}^{K} \theta_{k}=1$$

$$C(\alpha)=\frac{\Gamma\left(\sum_{k=1}^{K} \alpha_{k}\right)}{\Gamma\left(\alpha_{1}\right) \ldots \Gamma\left(\alpha_{K}\right)}$$

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|INFERENCE

$$p(x, z, \theta)=p(\theta) p(z \mid \theta) p(x \mid \theta, z)$$

## 有限元方法代写

assignmentutor™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。