nltk.probability.WittenBellProbDist

class nltk.probability.WittenBellProbDist[source]

Bases: ProbDistI

The Witten-Bell estimate of a probability distribution. This distribution allocates uniform probability mass to as yet unseen events by using the number of events that have only been seen once. The probability mass reserved for unseen events is equal to T / (N + T) where T is the number of observed event types and N is the total number of observed events. This equates to the maximum likelihood estimate of a new type event occurring. The remaining probability mass is discounted such that all probability estimates sum to one, yielding:

  • p = T / Z (N + T), if count = 0

  • p = c / (N + T), otherwise

__init__(freqdist, bins=None)[source]

Creates a distribution of Witten-Bell probability estimates. This distribution allocates uniform probability mass to as yet unseen events by using the number of events that have only been seen once. The probability mass reserved for unseen events is equal to T / (N + T) where T is the number of observed event types and N is the total number of observed events. This equates to the maximum likelihood estimate of a new type event occurring. The remaining probability mass is discounted such that all probability estimates sum to one, yielding:

  • p = T / Z (N + T), if count = 0

  • p = c / (N + T), otherwise

The parameters T and N are taken from the freqdist parameter (the B() and N() values). The normalizing factor Z is calculated using these values along with the bins parameter.

Parameters

  • freqdist (FreqDist) – The frequency counts upon which to base the estimation.

  • bins (int) – The number of possible event types. This must be at least as large as the number of bins in the freqdist. If None, then it’s assumed to be equal to that of the freqdist

prob(sample)[source]

Return the probability for a given sample. Probabilities are always real numbers in the range [0, 1].

Parameters

sample (any) – The sample whose probability should be returned.

Return type

float

max()[source]

Return the sample with the greatest probability. If two or more samples have the same probability, return one of them; which sample is returned is undefined.

Return type

any

samples()[source]

Return a list of all samples that have nonzero probabilities. Use prob to find the probability of each sample.

Return type

list

freqdist()[source]
discount()[source]

Return the ratio by which counts are discounted on average: c*/c

Return type

float

SUM_TO_ONE = True

True if the probabilities of the samples in this probability distribution will always sum to one.

generate()

Return a randomly selected sample from this probability distribution. The probability of returning each sample samp is equal to self.prob(samp).

logprob(sample)

Return the base 2 logarithm of the probability for a given sample.

Parameters

sample (any) – The sample whose probability should be returned.

Return type

float