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What is Laplace (additive) smoothing in Naive Bayes?

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Answer

  • It adds a small constant alpha to every count when estimating P(xj    c)P(x_{j}\; \mid \;c) so no probability is ever exactly zero.
  • Without smoothing, a single word never seen with class c in training would give P(document    c)  =  0P(\mathrm{document}\; \mid \;c)\; = \;0, killing the posterior.
  • Alpha=1 is Laplace smoothing; smaller alpha (e.g., 0.01) is Lidstone smoothing.
  • Choose it by cross-validation — it plays the role of a regularizer for the likelihood.
Check yourself — multiple choice
  • It smooths the decision boundary
  • It adds alpha to counts so P(xj    c)P(x_{j}\; \mid \;c) is never zero
  • It is only for continuous features
  • It replaces the priors

Additive smoothing avoids zero probabilities for unseen feature-class combos.

#naive-bayes#regularization

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