A certain little-known human language consists of only nouns and verbs. A sentence begins with a noun with probability 75% and with a verb with probability 25%. If a given word in a sentence is a noun, there is a 75% probability that the next word is a verb and a 25% probability that the next word is a noun. If a given word is a verb, there is a 75% probability that the next word in the sentence is a noun and a 25% probability that is a verb. We can model this language using a Markov chain with two states: noun and verb. Question 1: There are only four words in the language: awk, yacc, grep, and perl. Each of these words can be either a noun or a verb. Of all noun occurrences, 10% are the word awk, 20% are the word yacc, 40% are the word grep, and 30% are the word perl. Of all verb occurrences, 20% are the word awk, 30% are the word yacc, 45% are the word grep, and 5% are the word perl. Using the Markov model described above and the Variable Elimination algorithm, find the probability that the fourth word of the following sentence is a noun: Perl yacc awk awk. Remember that you can express this sentence with the following Bayes' net:   So in other words, the question is what is P(Q4 = noun | O1 = perl, O2 = yacc, O3 = awk, O4 = awk)? a) around 20.65% b) around 67.55% c) around 34.23% d) around 60.96%   Question 2: Finally, consider observing the sentence "Yacc grep." What is the most likely part-of-speech state sequence (i.e. sequence of nouns and verbs) that could have resulted in this sentence? As an exercise for now, just use a brute-force search over all 4 possible sequences, i.e. compute all 4 and choose the one with the highest probability. In the next lecture, we will see how to do this more efficiently using the Viterbi algorithm. a) Noun Noun b) Noun Verb c) Verb Noun d) Verb Verb

A certain little-known human language consists of only nouns and verbs. A sentence begins with a noun with probability 75% and with a verb with probability 25%. If a given word in a sentence is a noun, there is a 75% probability that the next word is a verb and a 25% probability that the next word is a noun. If a given word is a verb, there is a 75% probability that the next word in the sentence is a noun and a 25% probability that is a verb.

We can model this language using a Markov chain with two states: noun and verb.

Question 1:

There are only four words in the language: awk, yacc, grep, and perl. Each of these words can be either a noun or a verb. Of all noun occurrences, 10% are the word awk, 20% are the word yacc, 40% are the word grep, and 30% are the word perl. Of all verb occurrences, 20% are the word awk, 30% are the word yacc, 45% are the word grep, and 5% are the word perl.

Using the Markov model described above and the Variable Elimination algorithm, find the probability that the fourth word of the following sentence is a noun: Perl yacc awk awk.

Remember that you can express this sentence with the following Bayes' net:

So in other words, the question is what is P(Q₄ = noun | O₁ = perl, O₂ = yacc, O₃ = awk, O₄ = awk)?

a) around 20.65%

b) around 67.55%

c) around 34.23%

d) around 60.96%

Question 2:

Finally, consider observing the sentence "Yacc grep." What is the most likely part-of-speech state sequence (i.e. sequence of nouns and verbs) that could have resulted in this sentence?

As an exercise for now, just use a brute-force search over all 4 possible sequences, i.e. compute all 4 and choose the one with the highest probability. In the next lecture, we will see how to do this more efficiently using the Viterbi algorithm.

a) Noun Noun

b) Noun Verb

c) Verb Noun

d) Verb Verb