本栏目来源于对Coursera 在线课程 NLP（by Michael Collins）的理解。课程链接为：https://class.coursera.org/nlangp-001
1. Tagging Problems
1.1 POS Tagging
问题描述
Input：Profits soared at Boeing Co., easily topping forecasts on Wall Street, as their CEO Alan Mulally announced first quarter results.
Output：Profits/N soared/V at/P Boeing/N Co./N ,/, easily/ADV topping/V forecasts/N on/P Wall/N Street/N ,/, as/P their/POSS CEO/N Alan/N Mulally/N announced/V first/ADJ quarter/N results/N ./.
PS:N = Noun;V = Verb;P = Preposition;Adv = Adverb;Adj = Adjective;...
给定训练集，(x(i),y(i)),其中x(i)为句子x1(i)...nix(i),y(i)为tag序列,ni为第i个样本的长度。因此xj(i)为句子x(i)中第j个词，yj(i)为xj(i)的tag。例如Penn WSJ 的treebank 标注语料。而POS的难点包括（1）一词多义（即不同语境下一词可以被标注为多种tag）；（2）不常见单词的处理（即训练语料中未出现的单词）；另外，在POS过程中要考虑词的统计特性，如常见的词性和语法常识（比如“quarter”一般作为名词出现而非动词，D N V比D V N结构在句中更为常见）。
1.2 Named-Entity Recognition
问题描述
Input：Profits soared at Boeing Co., easily topping forecasts on Wall Street, as their CEO Alan Mulally announced first quarter results.
Output1：Profits soared at [Company Boeing Co.], easily topping forecasts on [LocationWall Street], as their CEO [Person Alan Mulally] announced first quarter results.
输出结果为命名实体识别的结果，如 PERSON, LOCATION, COMPANY...;与POS不同，每个单词或者被标注为NA(不包括命名实体)或者标注为命名实体的一部分(如SC为公司名开始，CC为公司名中间部分...)即输出如下结果：
Output2: Profits/NA soared/NA at/NA Boeing/SC Co./CC ,/NA easily/NA topping/NA forecasts/NA on/NA Wall/SL Street/CL ,/NA as/NA their/NA CEO/NA Alan/SP Mulally/CP announced/NA first/NA quarter/NA results/NA ./NA
PS：NA = No entity;SC = Start Company;CC = Continue Company;SL = Start Location;CL = Continue Location;...
2 Generative Models
2.1. hidden Markov models
training example:(x(1),y(1))...(x(m),y(m)),我们希望通过训练样本得到函数f:X→Y
方法一：conditional model
给定测试样本x，模型输出为：
方法二：generative model
应用联合概率分布p(x,y),且p(x,y)=p(y)p(x|y)
其中p(y)是先验概率，p(x|y)是给定标签y的条件概率。
因此我们可以使用贝叶斯规则来得到条件概率p(y|x):
其中
故：
2.2 Generative Tagging Models
V：单词集合，如：V ={the, dog, saw, cat, laughs,...}
K: 标注集合
S：sequence/tag-sequence pairs <x1,...xn,y1,...yn>
给定Generative Tagging Model，x1...xn的tag结果y1...yn为：
2.3 Trigram Hidden Markov Models (Trigram HMMs)
q(s|u,v)：bigram标记为(u,v)后标记为s的概率，对trigram(u,v,s)，s属于{K,STOP},u,v属于{K,*}；
e(x|s)：在s状态下观察结果为x的概率，x属于V，s属于K；
S：所有的sequence/tag-sequence对<x1...xn,y1...yn+1>,yn+1=STOP
PS：y0=y-1=*
例如：若n=3，x1x2x3= the dog laughs,y1y2y3y4=D N V STOP,那么：
该模型为noisy-channel model，
为二阶马尔科夫过程，标注为D N V STOP的先验概率，
是条件概率p(the dog laughs|D N V STOP)。