作者JinSha (http://0rz.tw/h1hXC)
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标题[中英] 隐马尔可夫模型
时间Fri Jul 12 22:50:21 2013
笔记： 隐马尔可夫模型 Hidden Markov Model
作者： Ranler
共享权限： CC BY-NC-SA
创建日期： 2012-06-09 12:26
修改日期： 2012-06-10 19:21
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Note: Hidden Markov Model
Author: Ranler
Share Permission: CC BY-NC-SA
Date Created: 2012-06-09 12:26
Date Modified: 2012-06-10 19:21
Comment Count: 0
1. 一个例子
1. An example
首先还是看吴军的例子：数学之美 系列三 -- 隐含马尔可夫模型在语言处理中的应用
At first, we shall see an example given by Wu Jun: The Beauty of Mathematics,
Series 3 -- The Application of Hidden Markov Model in Language Processing.
2. 隐马尔可夫模型
2. Hidden Markov Model
在正常的马尔可夫模型中，状态(x(t))对于观察者来说是直接可见的。 而在隐马尔可夫
模型中,状态(x(t))并不是直接可见的，但受状态影响的某些观察序列(y(t))则是可见的
。
In the general Markov model, the state (x(t)) is directly visible to the
observer. By contrast, in Hidden Markov Model, the hidden state (x(t)) is
not directly visible, but the observation sequence (y(t)) dependent on the
state is visible.
Fig:
http://tinyurl.com/mvyut3s
上图中，随机过程x(t)是一个马尔可夫链，但不可见。 隐含状态x(t)决定了观察状态
y(t)，第i时刻的y(ti)只由x(ti)决定，它们之间是独立输出关系。
In the figure above, stochastic process x(t) is a Markov chain, but it is not
visible. The hidden state x(t) decides its corresponding observation sequence
y(t), and the observation sequence y(ti) at time i is decided solely by x(ti);
the observed outputs are independent of time.
因此隐马尔可夫模型是一个双重随机过程，有两个组成部分：
马尔可夫链：描述状态(x(t))的转移，用隐含状态转移概率描述。
一般随机过程：描述状态与观察序列间(y(t))的关系，用观察状态转移概率描述。
Therefore, Hidden Markov Model is a kind of doubly stochastic process composed
of two parts:
Markov chain: describing the transition between hidden states x(t)
by transition probabilities
General stochastic process: describing the relation between a state
and an observation sequence y(t) by emission
probabilities governing the distribution of the
observed variable at a particular given state
定义隐含状态转移概率矩阵为A，观察状态转移概率矩阵为B，初始状态概率矩阵为π，
那么可以用λ=(A,B,π)三元组来简洁的表示一个隐马尔可夫模型。
Denote the matrix of transition probabilities A, matrix of observation
probabilities B, and matrix of initial probabilities π. A hidden Markov model
can be concisely represented by a triple λ=(A,B,π).
http://www.findfunaax.com/notes/file/122
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