How does Naïve Bayes behave under sparse feature collision in hashed vector spaces?

Feature hashing introduces collisions that can bias Naïve Bayes probability estimates in sparse spaces.

In hashed feature spaces, multiple distinct features map to the same index. Naïve Bayes aggregates counts for collided features, blending unrelated signals. While this increases efficiency, it introduces systematic noise in likelihood estimation. The impact depends on sparsity and hash space dimensionality.