N-Gram Model Formulas Estimating Probabilities - University of Texas at ...
N-Gram Model Formulas
? Word sequences ? Chain rule of probability ? Bigram approximation ? N-gram approximation
Perplexity
? Measure of how well a model "fits" the test data. ? Uses the probability that the model assigns to the
test corpus. ? Normalizes for the number of words in the test
corpus and takes the inverse.
? Measures the weighted average branching factor in predicting the next word (lower is better).
Estimating Probabilities
? N-gram conditional probabilities can be estimated from raw text based on the relative frequency of word sequences.
Bigram:
N-gram:
? To have a consistent probabilistic model, append a unique start () and end () symbol to every sentence and treat these as additional words.
Laplace (Add-One) Smoothing
? "Hallucinate" additional training data in which each possible N-gram occurs exactly once and adjust estimates accordingly.
Bigram:
N-gram:
where V is the total number of possible (N-1)-grams (i.e. the vocabulary size for a bigram model). ? Tends to reassign too much mass to unseen events, so can be adjusted to add 0 ................
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