Concept - Curse of Dimensionality

On the slides (s.20): when classifying with Bayes rule over many attribute values $\mathbf{d}=[d_1,\dots ,d_n]$ (the features), estimating the joint likelihood $p(d_1,d_2,\dots ,d_n|h_i)$ needs too much data when $n$ is large. The slide names this the Curse of Dimensionality.

Remedy: assume Concept - Conditional Independence so that $p(d_1..d_n|h_i)={\prod }_{j}p(d_j|h_i)$, as in Concept - Naive Bayes (s.21-23). For text the dimension $n$ is the vocabulary/document length, so this problem is severe.

Related

Concept - Maximum A Posteriori, Concept - Conditional Independence, Concept - Naive Bayes

Source: 03 Text Classification - Chunk 01 (s.1-30)