Likelihood for a test data (sequence of characters) given unigram models

Question

I would like to find the likelihood of a sequence of characters (the test data), given two unigram models.

The sequence (test data) is:

A B C B B

The models are:

       Model 1       Model 2
P(A)     0.3           0.4  
P(B)     0.4           0.5  
P(C)     0.3           0.1

Basically, I would like to know the likelihood, and if I can make a prediction as to which model the sequence belong and the underlying assumptions. I understand that given any unigram language model, the likelihood (or probability) of any sequence of characters is p(sequence of characters|Model).

What I have done so far was to find the MLE for each character:

P(A) =1/5 ; P(B) = 2/5 ; P(C) = 1/5

I don't know how to compute p(sequence of characters|Model). Should I multiply these to find the likelihood and establish which model it came from? How to handle the model probabilities given?

Thanks in advance :-)

Answer 1

Unigram models tend to rely on the naïve Bayes assumption: that is, they assume that every character is independent of everything else around it.

Under this assumption, the likelihood of A B C B B is just the product of the individual probabilities for each letter.

This assumption, as it turns out, isn't a very good one—which is why we move up to more powerful n-gram models.