What is the relationship between Naïve Bayes and Bayesian shrinkage estimators?

Updated May 17, 2026

Short answer

Naïve Bayes with smoothing acts as a Bayesian shrinkage estimator pulling probabilities toward a prior distribution.

Deep explanation

Shrinkage estimators reduce variance by pulling extreme estimates toward a central prior. In Naïve Bayes, Laplace or Dirichlet smoothing shrinks rare feature probabilities toward uniform priors. This reduces overfitting in sparse datasets and stabilizes likelihood estimation under limited data regimes.

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