Posted on Categories:图形模型, 计算机代写

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## 计算机代写|图形模型代考Graphical Models代写|Basic Rules

The probability of the disjunction (logical sum) of two propositions is given by the sum rule: $P(A+B \mid C)=P(A \mid C)+P(B \mid C)-P(A, B \mid C)$; if propositions $A$ and $B$ are mutually exclusive given $C$, we can simplify it to: $P(A+B \mid C)=P(A \mid$ $C)+P(B \mid C)$. This can be generalized for $N$ mutually exclusive propositions to:
$$P\left(A_{1}+A_{2}+\cdots A_{N} \mid C\right)=P\left(A_{1} \mid C\right)+P\left(A_{2} \mid C\right)+\cdots+P\left(A_{N} \mid C\right)$$
In the case that there are $N$ mutually exclusive and exhaustive hypothesis, $H_{1}, H_{2}, \ldots, H_{N}$, and if the evidence $B$ does not favor any of them, then according to the principle of indifference: $P\left(H_{i} \mid B\right)=1 / N$.

According to the logical interpretation there are no absolute probabilities, all are conditional on some background information ${ }^{1} . P(H \mid B)$ conditioned only on the background $B$ is called a prior probability; once we incorporate some additional information $D$ we call it a posterior probability, $P(H \mid D, B)$. From the product rule we obtain:
$$P(D, H \mid B)=P(D \mid H, B) P(H \mid B)=P(H \mid D, B) P(D \mid B)$$
From which we obtain:
$$P(H \mid D, B)=\frac{P(H \mid B) P(D \mid H, B)}{P(D \mid B)}$$
This last equation is known as the Bayes rule and the term $P(D \mid H, B)$ as the likelihood, $L(D)$.

## 计算机代写|图形模型代考Graphical Models代写|Random Variables

If we consider a finite set of exhaustive and mutually exclusive propositions ${ }^{2}$, then a discrete variable $X$ can represent this set of propositions, such that each value $x_{i}$ of $X$ corresponds to one proposition. If we assign a numerical value to each proposition $x_{i}$, then $X$ is a discrete random variable. For example, the outcome of the toss of a die is a discrete random variable with 6 possible values $1,2, \ldots, 6$. The probabilities for all possible values of $X, P(X)$ is the probability distribution of $X$. Considering the die example, for a fair die the probability distribution will be:

$$\begin{array}{lcccccc} x & 1 & 2 & 3 & 4 & 5 & 6 \ P(x) & 1 / 6 & 1 / 6 & 1 / 6 & 1 / 6 & 1 / 6 & 1 / 6 \end{array}$$
This is an example of a uniform probability distribution. There are several probability distributions which have been defined. Another common distribution is the binomial distribution. Assume we have an urn with $N$ colored balls, red and black, of which $M$ are red, so the fraction of red balls is $\pi=M / N$. We draw a ball at random, record its color, and return it to the urn, mixing the balls again (so that, in principle, each draw is independent from the previous one). The probability of getting $r$ red balls in $n$ draws is:
$$P(r \mid n, \pi)=\left(\begin{array}{l} n \ r \end{array}\right) \pi^{r}(1-\pi)^{n-r},$$
where $\left(\begin{array}{l}n \ r\end{array}\right)=\frac{n !}{r !(n-r) !}$.
This is an example of a binomial distribution which is applied when there are $n$ independent trials, each with two possible outcomes (success or failure), and the probability of success is constant over all trials. There are many other distributions, we refer the interested reader to the additional reading section at the end of the chapter.

# 图形模型代写

## 计算机代写|图形模型代考Graphical Models代写|Basic Rules

$$P\left(A_{1}+A_{2}+\cdots A_{N} \mid C\right)=P\left(A_{1} \mid C\right)+P\left(A_{2} \mid C\right)+\cdots+P\left(A_{N} \mid C\right)$$

$$P(D, H \mid B)=P(D \mid H, B) P(H \mid B)=P(H \mid D, B) P(D \mid B)$$

$$P(H \mid D, B)=\frac{P(H \mid B) P(D \mid H, B)}{P(D \mid B)}$$

## 计算机代写图形模型代考Graphical Models代写|Random Variables

$$\begin{array}{lllllllllllll} x & 1 & 2 & 3 & 4 & 5 & 6 P(x) & 1 / 6 & 1 / 6 & 1 / 6 & 1 / 6 & 1 / 6 & 1 / 6 \end{array}$$

$$P(r \mid n, \pi)=(n r) \pi^{r}(1-\pi)^{n-r},$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

Posted on Categories:图形模型, 计算机代写

## avatest™帮您通过考试

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## 计算机代写|图形模型代考Graphical Models代写|Representation, Inference and Learning

There are three main aspects for each class of probabilistic graphical model, representation, inference and learning.

The representation is the basic property of each model, and it defines which entities constitute it and how these are related. For instance, all PGMs can be represented as graphs that define the structure of the model and by local functions that describe its parameters. However, the type of graph and the local functions vary for the different types of models.

Inference consists in answering different probabilistic queries based on the model and some evidence. For instance, obtaining the posterior probability distribution of a variable or set of variables given that other variables in the model are known. The challenge is how to do this efficiently.

To construct these models there are basically two alternatives: to build it “by hand” with the aid of domain experts or to induce the model from data. The emphasis in recent years has been to induce the models based on machine learning techniques, because it is difficult and costly to do it with the aid of experts. In particular obtaining the parameters for the models is usually done based on data, as humans tend to be bad estimators of probabilities.

An important property of these techniques from an application point of view is that they tend to separate the inference and learning techniques from the model. That is, as in other artificial intelligence representations such as logic and production rules, the reasoning mechanisms are general and can be applied to different models. As a result, the techniques developed for probabilistic inference and learning in each class of PGM, can be applied directly for different models in a variety of applications.

## 计算机代写|图形模型代考Graphical Models代写|Applications

Most real-world problems imply dealing with uncertainty and usually involve a large number of factors or variables to be considered when solving them. Probabilistic graphical models constitute an ideal framework to solve complex problems with uncertainty, so they are applied in a wide range of domains such as:

Medical diagnosis and decision making.

Mobile robot localization, navigation and planning.

Diagnosis for complex industrial equipment such as turbines and power plants.

User modeling for adaptive interfaces and intelligent tutors.

Speech recognition and natural language processing.

Pollution modeling and prediction.

Reliability analysis of complex processes.

Modeling the evolution of viruses.

Object recognition in computer vision.Error correction in communications.

Information retrieval.

Gesture and activity recognition.

Energy markets.

Agricultural planning.

Different types of PGMs are more appropriate for different applications, as will be shown in the following chapters when we present application examples for each class of PGM.

# 图形模型代写

## 计算机代写|图形模型代考Graphical Models代写|Applications

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

Posted on Categories:图形模型, 计算机代写

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

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## 计算机代写|图形模型代考Graphical Models代写|A Brief History

From an artificial intelligence perspective, we can consider the following stages in the development of uncertainty management techniques:

Beginnings (1950s and 60s)—artificial intelligence (AI) researchers focused on solving problems such as theorem proving, games like chess, and the “blocks world” planning domain, which do not involve uncertainty, making it unnecessary to develop techniques for managing uncertainty. The symbolic paradigm dominated $\mathrm{AI}$ in the beginnings.

Ad hoc techniques (1970s) – the development of expert systems for realistic applications such as medicine and mining, required the development of uncertainty management approaches. Novel ad hoc techniques were developed for specific expert systems, such as MYCIN’s certainty factors [16] and Prospector’s pseudo-probabilities [4]. It was later shown that these techniques had a set of implicit assumptions which limited their applicability [6]. Also in this period, alternative theories were pro- posed to manage uncertainty in expert systems, including fuzzy logic [18] and the Dempster-Shafer theory [15].

Resurgence of probability (1980s)—probability theory was used in some initial expert systems, however it was later discarded because its application in naive ways implies a high computational complexity (see Sect. 1.3). New developments, in particular Bayesian networks [10], make it possible to build complex probabilistic systems in an efficient manner, starting a new era for uncertainty management in AI.
Diverse formalisms (1990s)_Bayesian networks continued and were consolidated with the development of efficient inference and learning algorithms. Meanwhile, other techniques such as fuzzy and non-monotonic logics were considered as alternatives for reasoning under uncertainty.

Probabilistic graphical models (2000s) —several techniques based on probability and graphical representations were consolidated as powerful methods for representing, reasoning and making decisions under uncertainty, including Bayesian networks, Markov networks, influence diagrams and Markov decision processes, among others.

## 计算机代写|图形模型代考Graphical Models代写|Basic Probabilistic Models

Probability theory provides a well established foundation for managing uncertainty, therefore it is natural to use it for reasoning under uncertainty. However, if we apply probability in a naive way to complex problems, we are soon deterred by computational complexity

In this section we will show how we can model a problem using a naive probabilistic approach based on a flat representation; and then how we can use this representation to answer some probabilistic queries. This will help to understand the limitations of the basic approach, motivating the development of probabilistic graphical models. ${ }^{1}$

Many problems can be formulated as a set of variables, $X_{1}, X_{2}, \ldots X_{n}$ such that we know the values for some of these variables and the others are unknown. For instance, in medical diagnosis, the variables might represent certain symptoms and the associated diseases; usually we know the symptoms and we want to find the most probable disease(s). Another example could be a financial institution developing a system to help decide the amount of credit given to a certain customer. In this case the relevant variables are the attributes of the customer, i.e. age, income, previous credits, etc.; and a variable that represents the amount of credit to be given. Based on the customer attributes we want to determine, for instance, the maximum amount of credit that is safe to give to the customer. In general there are several types of problems that can be modeled in this way, such as diagnosis, classification, and perception problems; among others.

# 图形模型代写

## 计算机代写|图形模型代考Graphical Models代写|A Brief History

Ad hoc 技术（1970 年代）——为医学和采矿等实际应用开发专家系统，需要开发不确定性管理方法。为特定的专家系统开发了新的 ad hoc 技术，例如 MYCIN 的确定性因素 [16] 和 Prospector 的伪概率 [4]。后来表明，这些技术有一组隐含的假设，限制了它们的适用性[6]。同样在这一时期，提出了替代理论来管理专家系统中的不确定性，包括模糊逻辑 [18] 和 Dempster-Shafer 理论 [15]。

## 计算机代写|图形模型代考Graphical Models代写|Basic Probabilistic Models

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。