## 用琴生(Jensen)不等式证明期望最大值(EM)算法收敛

$$\int\limits_z P(z|x, \theta^{(t)}) \log_{}{\frac{P(z|x, \theta^{(t+1)})}{P(z|x, \theta^{(t)})} } dz \le 0$$

$$a_1f(x_1) + a_2f(x_2) + \dots + a_nf(x_n) \le f(a_1x_1 + a_2x_2 + \dots + a_nx_n) 且 a_1 + a_2 + \dots + a_n = 1$$

$${\frac{P(z|x, \theta^{(t+1)})} {P(z|x, \theta^{(t)})} }$$

$$P(z|x, \theta^{(t)})$$

\begin{aligned} 左边 &\le log_{}{\int\limits_z {\frac{P(z|x, \theta^{(t+1)})} {P(z|x, \theta^{(t)})} } P(z|x, \theta^{(t)})}dz \&=log_{}{}\int \limits_zP(z|x,\theta^{(t+1)})dz=log_{}{1}=0 \end{aligned}

## A very brief Introduction to Neural Network.

I have huge interests in the mysterious Artificial Intelligence. Because of the lack of time to devote into learning AI, I still barely know AI related theories. Tonight I read something about Neural Network, which plays a important role in the AI field.

So, what is A NEURAL NETWORK?
A neural network is a massively parallel distributed processor made up of simple processing units that has a natural propensity for storing experiential knowledge and making it available for use. It resemble the brain in two respects:
knowledge is acquired by the network from its environment through a learning process.
Interneuron connection strengths  known as synaptic weights, are used to store the acquired knowledge.

Let us take the human vision as an example to demonstrate why it is necessary to study neural network. Human vision is a very complex information processing task. It is the function of the visual system to provide a representation of the the environment around us and to supply the information we need to interact with the environment. The brain accomplishes recognition task at the same time. For instance, the brain can recognize a familiar face embedded in an unfamiliar scene in shorter than a blink of eye, actually 100-200ms, whereas tasks of much lesser complexity take a great deal longer on a very powerful computer.

What's the reason makes the biological brains so efficient? How to let our machines think and do reasoning like biological brains do. The course of Neural Network has been trying to answer these questions from the day the course was established.
A typical neural network has many useful properties and capacities. 1. Nonlinearity 2. Input-output Mapping 3. Adaptivity 4. Evidential Response 5. Contextual Information 6. Fault Tolerance 7. VLSI(Very Large Scale Integrated) Implementability. 8. Uniformity of Analysis and Design 9. Neurobiological Analogy.

## 十分钟，教你创建自己的聊天机器人

STEP ONE：在pandorabots的首页，找到Sign-up for an Account，按ctrl+F 搜索一下 Sign，就能马上定位到了。点击这个链接就可以注册一个账号了。

STEP TWO：和大多数注册过程一样，填上一些最基本的信息就注册成功。记得勾选上 By checking this box and clicking on the button labeled “Submit Account Request” you are agreeing to the Term Service 复选框。点击 SUBMIT ACCOUT REQUEST.

STEP THREE：接着网站提示: There are no Pandorabots defined yet. You must first create a new  chat robot。点击 create 单词上的链接。

STEP FOUR:  接着是聊天机器人最基本的设定。

Name:      // 这里填上你要创建的机器人的名字。

– automatically discover spaces between words (suggested for Japanese)   // 建议勾选上，因为中文和日文都没有用空格分词。

Startup AIML – Please select the AIML set you wish to include:     // 让你选择你创建的机器人的知识库。不要选最后一个就好！因为最后一个是没有任何知识库~你需要从头开始创建。但如果你喜欢从头开始。那就选最后一个吧。

– Standard AIML – Sept 2001
– Dr Wallace's A.L.I.C.E – March 2002
– Annotated A.L.I.C.E. AIML – September 2003
– Christian Drossmann's standalone German AIML – January 2002
– Sandro Pons' Italian AIML set – April 2001

– No initial content, the pandorabot starts with no knowledge.

Human: 你是学生吗
Matched:
 * (category defined in star.aiml )
zzz: A deeper algorithm is needed to respond to that correctly.

zzz是我刚创建的机器人的名字，上面提示当前聊天机器人不知道如何回答。因为基本上没有人用中文教过他。其它他已经对英文回答得相当好了。

STEP FIVE: 下面我们可以验证下。

Human: Because you are so stupid                    // 我说因为你好笨呀

zzz: Interesting explanation. Wrong. I am smart.          // 它说：你的解释真有意思，但是错了，我很聪明呢

Human: Are you a robot                                   // 问它你是机器人吗
zzz: How did you know I am a machine?    // 它回答： 你怎么知道我是机器。

Human: what's your name                           // 对英文回答得很好
zzz: My name is zzz.

Human: 你叫什么名字                                        # 不识别其它中文
zzz: I will mention that to my botmaster, .

Human: 你是学生吗                                           # 这是刚才教他的。
zzz: 我是，我在中山大学读书。

## 什么是AIML，人工智能标志语言

AIML是Artificial Intelligence Markup Language的缩写。这种语言基于XML，它易学习易掌握。使用AIML可以很容易的定制一个Alicebot或者从头开始创建一个Alicebot。Alicebot是种聊天机器人，参见http://www.alicebot.org/ 。

AIML语言中最重要的四个标志：

· <aiml>: 这个标签用来标志一个AIML文档的开始和结束。

· <category>: 这个标志表示在Alicebot的知识体系里暂时无法理解的东西。

· <pattern>: 用来描述一个简单的模式表示用户会同Alicebot说什么。

· <template>: 用来描述Alicebot的回复。

<category>
<pattern>WHAT ARE YOU</pattern>
<template>
<think><set name="topic">Me</set></think>
I am the latest result in artificial intelligence,
which can reproduce the capabilities of the human brain
with greater speed and accuracy.
</template>
</category>

<aiml>标签在这里没有显示出来，因为这里只是文档的一个节选。