Bayes Classifier
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Bayesian-Data Warehouse-Lecture Slides, Slides of Data Warehousing
Topics include in this course are Data Warehousing Concepts, Design and Development, Extraction, Transformation and Loading, OLAP Technology, Data Mining Techniques: Classification, Clustering and Decision Tree, Advanced Topics. This lecture includes: Bayesian, Ckassifier, Hypothesis, Tested, Evidence, Example, Promotion, Insurance, Instance, Counts, Probabilities
Typology: Slides
2011/2012
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Bayes Classifier HPHEP )()|( EHP )|( EP )( H testedbetohypothesistheiswhere^ H^ withassociatedevidencetheisE
Bayes Classifier: An Example
The Instance to be ClassifiedMagazine Promotion =
Yes Watch Promotion = Yes Life Insurance Promotion =^ No Credit Card Insurance =^ No Gender =?
Table 10.5 •^ Counts and Probabilities for Attribute Gender^ Magazine^
Watch^ Life Insurance^ Credit Card Promotion Promotion^ Promotion^ Insurance
Gender^ Male^ Female^ Male^
Female^ Male^ Female^ Male^ Female Yes^4 3
No^2 1
Ratio: yes/total^ 4/6^ 3/4^ 2/
2/4^ 2/6^ 3/4^ 2/^
Ratio: no/total^ 2/6^ 1/4^ 4/^
2/4^ 4/6^ 1/4^ 4/6^ 3/
Conditional Probabilities forGender = Male^ P ( magazine promotion = yes | gender = male
)^ =^ 4/ P ( watch promotion = yes | gender = male
)^ =^ 2/ P ( life insurance promotion = no | gender = male
)^ =^ 4/ P ( credit card insurance = no | gender = male
)^ =^ 4/ P(E | gender =male)^ = (4/6) (2/6) (4/6) (4/6) = 8/
The Probability for Gender=MaleGiven Evidence E^ P(gender = male) = 6/10P ( gender = male | E
)^ ^ 0.0593 /^ P ( E )
Zero-Valued Attribute Counts
attributefor thevaluespossible
ofnumber
totaltheofpartfractional
equalanisp
1)(usually 1 and 0
))(( pkn kd betweenvalueais k If an attribute has two possible values then p = 0.
Example• Let’s re-compute the conditional probabilityP(E | Gender = Female) for previousexample.• Let’s suppose k = 1 and we know p = 0.5(as there are two values for attributes)
5. 0135. 0110176.^01414
The Instance to be Classifiedwith Missing DataMagazine Promotion =
Yes Watch Promotion = UNKNOWN Life Insurance Promotion =^ No Credit Card Insurance =^ No Gender =?
Conditional Probabilities forGender = Male with missing data^ P ( magazine promotion = yes | gender = male
)^ =^ 4/ P ( watch promotion = unknown | gender = male
)^ = don’t use P ( life insurance promotion = no | gender = male
)^ =^ 4/ P ( credit card insurance = no | gender = male
)^ =^ 4/ P(E | gender =male)^ = (4/6) (4/6) (4/6) = 8/27Similarly P(E | gender =female)^ = (3/4) (1/4) (3/4) = 9/64So P(gender =male | E)^ = 0.1778/ P(E) P(gender =female | E)^ = 0.05625/ P(E)
Table 10.6 •^ Addition of Attribute Age to the Bayes Classifier Dataset^ Magazine^ Watch^ Life Insurance
Credit Card
Promotion^ Promotion^ Promotion
Insurance^ Age^ Gender
Yes^ No^ No^
No^45 Male Yes^ Yes^ Yes^
Yes^40 Female No^ No^ No^
No^42 Male Yes^ Yes^ Yes^
Yes^30 Male Yes^ No^ Yes^
No^38 Female No^ No^ No^
No^55 Female Yes^ Yes^ Yes^
Yes^35 Male No^ No^ No^
No^27 Male Yes^ No^ No^
No^43 Male Yes^ Yes^ Yes^
No^41 Female
Numeric Data Example
The Instance to be ClassifiedMagazine Promotion =
Yes Watch Promotion = Yes Life Insurance Promotion =^ No Credit Card Insurance =^ No Age = 45 Gender =?
Example
22 ]) 69. 7 ( 2 /[) 00. 3745 ( ) 69. 7
(^
emalegenderageP^ ^030.^0 )| 45 ( malegenderageP P(E | gender =male)^ = (4/6) (2/6)(4/6) (4/6) (0.030) = 0.003 P(gender =male | E)^ = (0.003) (6/10) / P(E) = 0.0018/ P(E)Similarly P(gender =female | E)^ = (0.004) (4/10) / P(E) = 0.0016/ P(E)HenceGender = male
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