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courses:rg:2011:deciphering_foreign_language [2012/01/07 13:25]
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courses:rg:2011:deciphering_foreign_language [2012/01/07 14:14]
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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> |
| | |
| | The key idea of section 2 is the Iterative EM algorithm, which is used to estimate <latex>\theta</latex> more effectively in term of saving memory and running time (complexity). |
| | |
| | If we use traditional EM, every time we update <latex>\theta</latex>, we also need to update pseudo-counts (in this case, conditional probabilities <latex>{P_\theta (c_i |e_i )</latex>.) It leads to O(|V|<sup>2</sup>) time. The heart of Iterative EM is that at every iteration, the algorithm run on a proportion of the most frequent words in vocabulary, and whenever the algorithm estimates <latex>P(c_i|e_i) > 0.5 </latex>, it fixes that probability equal to 1 in the following iteration, hence, the number of free parameters need to be estimated reduce after each iteration. |
| | |
| | __**Practical question:**__ How to initiate EM? How to start the first iteration? |
| | |
| | Some other notes related to this paper: |
| | Generative story: The generative process that generates data given some hidden variables. |
| | Chinese restaurant process |
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