Database Reference
In-Depth Information
Consider the bank marketing example presented in Section 7.1 on predicting if a
customer would subscribe to a term deposit. Let be a list of attributes {
job
,
marital
,
education
,
default
,
housing
,
loan
,
contact
,
poutcome
}.
According to
Equation 7.12
,
the problem is essentially to calculate
, where
.
7.2.2 Naïve Bayes Classifier
With two simplifications, Bayes' theorem can be extended to become a naïve Bayes
classifier.
The first simplification is to use the conditional independence assumption. That
is, each attribute is conditionally independent of every other attribute given a class
label . See
Equation 7.13
.
Therefore, this naïve assumption simplifies the computation of
.
The second simplification is to ignore the denominator . Because
appears in the denominator of for all values of
i
, removing
the denominator will have no impact on the relative probability scores and will
simplify calculations.
Naïve Bayes classification applies the two simplifications mentioned earlier and,
as a result,
is proportional to the product of
times
.
This is shown in
Equation 7.14
.
The mathematical symbol
indicates that the LHS
is directly proportional
to the RHS.
