How does Naïve Bayes interact with probabilistic entropy decomposition in multi-feature systems?

Naïve Bayes assumes conditional independence, which allows entropy decomposition into additive feature-wise contributions.

Entropy H(X|C) is generally non-decomposable due to dependencies among features. Naïve Bayes enforces independence, enabling H(X|C) = Σ H(Xi|C). This simplifies probabilistic modeling but introduces approximation error when feature dependencies exist. The trade-off is between tractability and representational fidelity.