Naive Bayes

first revise the bayse theorem:

The proof of bayse theorem

we can say probability of A given B is equal to probability of B given A into probability of A divided by probability of B.

The concept behind this algorightm

Look at this multiplication rule of independent events

For continuos attribute

so now i am going to explain every term of this formulae.

x is the feature and y is the class for eg: P(income=120 and age>13/No)

mew(u)=sample mean , sigma=sample variance xi=120 in this case don’t forget to watch example given below we will easily undetstand how things works in this algorithm.

For (Income=120k, Class=No):

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If Class=No

• sample mean = 110

• sample variance = 2975

P(Income=120K| Class=No)=( xi=120,u=mean,sigma=variance) and put it and find the probability of income =120k given class =no

Example of Naïve Bayes Classifier

naive Bayes Classifier: X  (Refund  No,Married,Income =120K)

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

Best way of solving any naive bayes ml model

so in first we are assuming play =yes and in second we are taking play=no and whoever has more probabaility we will consider as the probable outcome.

Some bonus revision

here and means you can understand intersection.