My understanding is that priors should be fitted to the data using observed target frequencies and a variant of Laplace smoothing to avoid assigning 0 probability to targets not yet observed.

It seems the implementation of partial_fit does not account for unobserved targets at the time of the first training batch when computing priors.

    import numpy as np
    import sklearn
    from sklearn.naive_bayes import MultinomialNB
    
    print('scikit-learn version:', sklearn.__version__)
    
    # Create toy training data
    X = np.random.randint(5, size=(6, 100))
    y = np.array([1, 2, 3, 4, 5, 6])
    
    # All possible targets
    classes = np.append(y, 7)
    
    clf = MultinomialNB()
    clf.partial_fit(X, y, classes=classes)

/home/skojoian/.local/lib/python3.6/site-packages/sklearn/naive_bayes.py:465: RuntimeWarning: divide by zero encountered in log
  self.class_log_prior_ = (np.log(self.class_count_) -
scikit-learn version: 0.20.2

This behavior is not very intuitive to me. It seems partial_fit requires classes for the right reason, but doesn't actually offset target frequencies to account for unobserved targets.