nltk language model (ngram) calculate the prob of a word from context

Question

I am using Python and NLTK to build a language model as follows:

from nltk.corpus import brown
from nltk.probability import LidstoneProbDist, WittenBellProbDist
estimator = lambda fdist, bins: LidstoneProbDist(fdist, 0.2)
lm = NgramModel(3, brown.words(categories='news'), estimator)
# Thanks to miku, I fixed this problem
print lm.prob("word", ["This is a context which generates a word"])
>> 0.00493261081006
# But I got another program like this one...
print lm.prob("b", ["This is a context which generates a word"]) 

But it doesn't seem to work. The result is as follows:

>>> print lm.prob("word", "This is a context which generates a word")
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/local/lib/python2.6/dist-packages/nltk/model/ngram.py", line 79, in prob
    return self._alpha(context) * self._backoff.prob(word, context[1:])
  File "/usr/local/lib/python2.6/dist-packages/nltk/model/ngram.py", line 79, in prob
    return self._alpha(context) * self._backoff.prob(word, context[1:])
  File "/usr/local/lib/python2.6/dist-packages/nltk/model/ngram.py", line 82, in prob
    "context %s" % (word, ' '.join(context)))
TypeError: not all arguments converted during string formatting

Can anyone help me out? Thanks!

Answer 1

I know this question is old but it pops up every time I google nltk's NgramModel class. NgramModel's prob implementation is a little unintuitive. The asker is confused. As far as I can tell, the answers aren't great. Since I don't use NgramModel often, this means I get confused. No more.

The source code lives here: https://github.com/nltk/nltk/blob/master/nltk/model/ngram.py. Here is the definition of NgramModel's prob method:

def prob(self, word, context):
    """
    Evaluate the probability of this word in this context using Katz Backoff.

    :param word: the word to get the probability of
    :type word: str
    :param context: the context the word is in
    :type context: list(str)
    """

    context = tuple(context)
    if (context + (word,) in self._ngrams) or (self._n == 1):
        return self[context].prob(word)
    else:
        return self._alpha(context) * self._backoff.prob(word, context[1:])

(note: 'self[context].prob(word) is equivalent to 'self._model[context].prob(word)')

Okay. Now at least we know what to look for. What does context need to be? Let's look at an excerpt from the constructor:

for sent in train:
    for ngram in ingrams(chain(self._lpad, sent, self._rpad), n):
        self._ngrams.add(ngram)
        context = tuple(ngram[:-1])
        token = ngram[-1]
        cfd[context].inc(token)

if not estimator_args and not estimator_kwargs:
    self._model = ConditionalProbDist(cfd, estimator, len(cfd))
else:
    self._model = ConditionalProbDist(cfd, estimator, *estimator_args, **estimator_kwargs)

Alright. The constructor creates a conditional probability distribution (self._model) out of a conditional frequency distribution whose "context" is tuples of unigrams. This tells us 'context' should not be a string or a list with a single multi-word string. 'context' MUST be something iterable containing unigrams. In fact, the requirement is a little more strict. These tuples or lists must be of size n-1. Think of it this way. You told it to be a trigram model. You better give it the appropriate context for trigrams.

Let's see this in action with a simpler example:

>>> import nltk
>>> obs = 'the rain in spain falls mainly in the plains'.split()
>>> lm = nltk.NgramModel(2, obs, estimator=nltk.MLEProbDist)
>>> lm.prob('rain', 'the') #wrong
0.0
>>> lm.prob('rain', ['the']) #right
0.5
>>> lm.prob('spain', 'rain in') #wrong
0.0
>>> lm.prob('spain', ['rain in']) #wrong
'''long exception'''
>>> lm.prob('spain', ['rain', 'in']) #right
1.0

(As a side note, actually trying to do anything with MLE as your estimator in NgramModel is a bad idea. Things will fall apart. I guarantee it.)

As for the original question, I suppose my best guess at what OP wants is this:

print lm.prob("word", "generates a".split())
print lm.prob("b", "generates a".split())

...but there are so many misunderstandings going on here that I can't possible tell what he was actually trying to do.