Let's assume an Expectation Maximization algorithm for training a one to one word alignment model like the one discussed in class. The translation probabilities generated from an estimation step is given below. Using the probabilities below, calculate the probabilities of all 6 possible word alignments between the Spanish phrase: un pollito amarillo and the English phrase: a yellow chick. Please round the answer to three significant figures ($1.45 \times 10^{-4}$ or .000145). These calculations are part of the next expectation step. In combination, with the alignments of additional sentence pairs, they will be used to generate the next set of translation probabilities.
Translation Probabilities
Source Words (Spanish)
Target Words (English) el un amarillo pato pollito
the .88 0 .04 .02 .06
a 0 .82 .09 .09 0
yellow .05 .04 .78 .06 .07
chick .14 0 .10 0 .76
duck .02 .03 .05 .9 0
Answers: List each possible alignment, along with the total probability, e.g., one possible alignment is: un/yellow pollito/chick amarillo/a and the probability is based on the table above.
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