Hidden Markov model and its training (1)

 

 

 

Markov hypothesis , That is, each state in the random process S： The probability distribution of is only related to its previous state S-1 of .

 

Independent output hypothesis ,

Hidden Markov model at every moment t Will output symbols Ot:, and Ot Follow St Relevant and only St relevant  

  Plug in （5.3） obtain

  Given a sufficient number of observations , How to estimate the parameters of hidden Markov model

 

 

 

  Directly obtained . The premise of supervised training is that a large amount of manually labeled data is required . It's a pity , Many applications can't do this , For example, acoustic model training in speech recognition . People cannot determine the sequence of states that produce a certain speech , Therefore, it is impossible to label the data of the training model . In other applications , Although labeling data is feasible , But the cost is very high .
For example, the training model of Chinese English machinetranslation , It requires a large number of Chinese and English language materials , And the Chinese and English