bayes classifier method examples

For continuous attributes:
– Discretize the range into bins
• one ordinal attribute per bin
• violates independence assumption
– Two-way split: (A < v) or (A > v)
• choose only one of the two splits as new attribute
– Probability density estimation:
• Assume attribute follows a normal distribution
• Use data to estimate parameters of distribution
(e.g., mean and standard deviation)
• Once probability distribution is known, can use it to estimate the
conditional probability P(Ai|c)

X = (Refund = No,Married,Income=120K)
Refund=Yes|No) = 3/7
P(Refund=No|No) = 4/7
P(Refund=Yes|Yes) = 0
P(Refund=No|Yes) = 1
P(Marital Status=Single|No) = 2/7
P(Marital Status=Divorced|No)=1/7
P(Marital Status=Married|No) = 4/7
P(Marital Status=Single|Yes) = 2/7
P(Marital Status=Divorced|Yes)=1/7
P(Marital Status=Married|Yes) = 0
For taxable income:
If class=No: sample mean=110
sample variance=2975
If class=Yes: sample mean=90
sample variance=25
P(X|Class=No) = P(Refund=No|Class=No)
× P(Married| Class=No)
× P(Income=120K| Class=No)
= 4/7 × 4/7 × 0.0072 = 0.0024
? P(X|Class=Yes) = P(Refund=No| Class=Yes)
× P(Married| Class=Yes)
× P(Income=120K| Class=Yes)
= 1 × 0 × 1.2 × 10-9 = 0
Since P(X|No)P(No) > P(X|Yes)P(Yes)
Therefore P(No|X) > P(Yes|X)
=> Class = No