How does Naïve Bayes relate to Bayes optimal risk minimization under 0-1 loss vs general loss functions?

Naïve Bayes is naturally aligned with Bayes optimal decision making under 0-1 loss, but requires modification for arbitrary loss functions.

Under 0-1 loss, the Bayes optimal classifier selects argmax P(C|X), which is exactly what Naïve Bayes approximates via factorized likelihoods. However, for general loss functions, the decision rule becomes minimizing expected risk, requiring integration over cost-weighted posteriors. Naïve Bayes must then be adjusted using cost-sensitive thresholds or utility-weighted posteriors.