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courses:rg:2011:deciphering_foreign_language [2012/01/07 13:25]
tran 		courses:rg:2011:deciphering_foreign_language [2012/01/07 13:41]
tran
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 \mathop {\arg \max }\limits_\theta  \prod\limits_f {\sum\limits_e {P(e) \times \sum\limits_a {P_\theta  (f,a|e)} } }  \mathop {\arg \max }\limits_\theta  \prod\limits_f {\sum\limits_e {P(e) \times \sum\limits_a {P_\theta  (f,a|e)} } } 
 </latex> </latex>
 +
 +==== Section 2 ====
 +Section 2 deals with a simple version of translation, Word Substitution Decipherment, where there is only one-to-one mapping between source string and cipher string (the position of string does not change.)
 +
 +The solution for this problem is pretty simple: Given a sequence of English tokens <latex>e=e_1,e_2,...,e_n</latex>, and the corresponding sequence of cipher tokens <latex>c=c_1,c_2,...,c_n</latex>, we need to estimate parameter <latex>\theta</latex>:
 +<latex>
 +\mathop {\arg \max }\limits_\theta  \prod\limits_c {P_\theta  (c)}  = \mathop {\arg \max }\limits_\theta  \prod\limits_c {\sum\limits_e {P(e) \times \prod\limits_{i = 1}^n {P_\theta  (c_i |e_i )} } } 
 +</latex>
 +
 +

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