# Lect20 - Announcement HW4 on BNs due Tuesday Machine...

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Announcement HW4 on BNs due Tuesday Machine Learning Next Chapters 18 & 20 in text

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Naïve Bayes Symptoms (attributes) are conditionally independent of each other given the Disease (classification) Stringent assumptions / Impoverished expressiveness Works surprisingly (?) well in practice Common first choice NOTE the use of intentionally impoverished model (for tractability - recall coffee cup)
Naïve Bayes Symptom1 (T/F) Disease (1,2,3,…) Symptom2 (T/F) Symptom3 (T/F) P(d 1 ) P(d 2 ) P(d 3 )    P(s 1 |d 1 ) P(s 1 |d 2 ) P(s 1 |d 3 )    P(s 2 |d 1 ) P(s 2 |d 2 ) P(s 2 |d 3 )    P(s 3 |d 1 ) P(s 3 |d 2 ) P(s 3 |d 3 )    Infer likely disease: S d P i d i | max arg

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Naïve Bayes Diagnose by inference with: |D| Functions, each assigns probability over the Boolean hypercube Which are / are not probability models? Fourth is not normalized (why does that work?) Parameters are adjusted to best fit the world samples What are the parameters? A kind of machine learning We will consider the probability functions the log probability functions the decision boundaries j i j i d j i j i d i i d i d d s P d P S P d s P d P S P d S P d P S d P i i i i ) | ( ) ( max arg ) ( ) | ( ) ( max arg ) ( ) | ( ) ( max arg ) | ( max arg
Naïve Bayes Suppose we always reason from observed symptoms to diseases Characterize the boundaries Log(x) is monotonically increasing, so: Log of a product is… j i j i d d s P d P i ) | ( ) ( max arg j i j i d d s P d P Log i ) | ( ) ( max arg

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