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Zero probabilities spell disaster
We need to smooth probabilities
Discount nonzero probabilities
Give some probability mass to unseen things
There’s a wide space of approaches to smoothing probability distributions to deal with this problem, such as adding 1, ½ or to counts, Dirichlet priors, discounting, and interpolation
[See FSNLP ch. 6 or CS224N if you want more]
A simple idea that works well in practice is to use a mixture between the document multinomial and the collection multinomial distribution
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