Bayes Classifiers Nave Bayes Classification Patrick Mair Bayes - - PowerPoint PPT Presentation

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Sep 19, 2022 38 likes •98 views

Bayes Classifiers Nave Bayes Classification Patrick Mair Bayes Classifiers Weather data set Predictors: Outlook, Temperature, Humidity, Windy. Response: Play (yes/no) Starting point Cross classification: Predictor/Response

SLIDE 1

Bayes Classifiers

Naïve Bayes Classification Patrick Mair

SLIDE 2

Bayes Classifiers

Weather data set

Predictors: Outlook, Temperature, Humidity, Windy. Response: Play (yes/no)

Starting point

Cross classification: Predictor/Response

yes no sunny 2 3

vercast

4 rainy 3 2 yes no hot 2 2 mild 4 2 cool 3 1

Outlook/Play Temperature/Play

SLIDE 3

Bayes Classifiers

Conditional probabilities

Conditioned on response categories

yes no sunny 2/9 3/5

vercast

4/9 0/5 rainy 3/9 2/5 1 1 yes no hot 2/9 2/5 mild 4/9 2/5 cool 3/9 1/5 1 1

Outlook/Play Temperature/Play … Play

yes no 9/14 5/14

SLIDE 4

Bayes Classifiers

A new day, prediction “yes”; “no”

Outlook: sunny (p = 2/9; 3/5) Temperature: cool (p = 3/9; 1/5) Humidity: high (p = 3/9; 4/5) Windy: true (p = 3/9; 3/5) Play: ? (p = 9/14; 5/14)

Likelihood of yes/no Normalization

SLIDE 5

Bayes Classifiers

Bayes’ rule:

H: Hypothesis; e.g. play = yes. E: Evidence that bears on H; i.e. predictor combination. P(H|E)=? P(H)…prior probability P(H|E)…posterior probability

( ) ( ) ( ) ( )

| | P E H P H P H E P E =

SLIDE 6

Bayes Classifiers

Naïve Bayes

Based on Bayes’ rule Naïvely assumes independence in P(E|H)

Remarks

Calculation of P(E) not needed due to

normalization

No problem in handling missing values Normality assumption on numeric attributes