There are two common ways to train the probabilities of the unknown word
model <UNK>. The first one is to turn the problem back into a closed vocabulary one by choosing a fixed vocabulary in advance: 1. Choose a vocabulary (word list) that is fixed in advance; 2. Convert in the training set any word that is not in this set (any OOV word) to the unknown word token <UNK> in a text normalization step; 3. Estimate the probabilities for <UNK> from its counts just like any other regular word in the training set.

The second alternative, in situations where we don’t have a prior vocabulary in advance, is to create such a vocabulary implicitly, replacing words in the training data by <UNK> based on their frequency.

Train the probabilities of unknown word model <UNK>

For words that occur in our test data but are not in our vocabulary (because they did not occur in any training documents),  ignore them—remove them from the test document and not include any probability for them at all.

University of Michigan - Ann Arbor

While training, we first consider maximum likelihood estimate.
We first concatenate all documents with category c into one big “category c” text. Then we use the frequency of wi in this concatenated document to give a maximum likelihood estimate of the probability:
$P(w_i|c) = \frac{count(w_i,c)}{\sum_{w\in V}count(w,c)}$

Training the naive Bayes Classifier

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

Whilie training, zero probabilities in the likelihood term for any class will cause the probability of the class to be zero, no matter the other evidence. A solution is the add-one (Laplace) smoothing:
$P(w_i|c) = \frac{count(w_i,c)+1}{\sum_{w\in V}{(count(w,c)+1)}}  = \frac{count(w_i,c)+1}{\sum_{w\in V}{count(w,c)}+|V|}$

Avoid zero posiblities

Unknown words

Some systems choose to completely ignore another class of words: stop words, very frequent words like the and a. But using a stop word list doesn’t improve performance, so in most cases, the entire vocabulary is used.

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