Concept - Conditional Independence

Chain rule (s.22): $p (d_{1}, \dots, d_{n} ∣ h_{i}) = p (d_{1} ∣ h_{i}) p (d_{2} ∣ h_{i}, d_{1}) p (d_{3} ∣ h_{i}, d_{1}, d_{2}) \dots p (d_{n} ∣ h_{i}, d_{1}, \dots, d_{n - 1})$ .

Naive Bayes assumption (s.22): attributes are independent, given the class: $p (d_{2} ∣ h_{i}, d_{1}) = p (d_{2} ∣ h_{i})$ , …, $p (d_{n} ∣ h_{i}, d_{1} .. d_{n - 1}) = p (d_{n} ∣ h_{i})$ , so $p (d_{1}, \dots, d_{n} ∣ h_{i}) = p (d_{1} ∣ h_{i}) p (d_{2} ∣ h_{i}) \dots p (d_{n} ∣ h_{i})$

Realism (s.21): often violated in practice; even then it usually works well (text classification, diagnosis).

Concept - Naive Bayes, Concept - Curse of Dimensionality, Concept - Probability Basics

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

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Concept - Conditional Independence

Concept - Conditional Independence

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Khaled Notes

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Concept - Conditional Independence

Concept - Conditional Independence

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