or a log odd function is defined as below, where ߙ and ߚ are two

rs for a univariate regression,

log

݌ሺݔሻ

1 െ݌ሺݔሻ^ൌߙ൅ߚݔ

(3.20)

8. The Naïve Bayes discrimination model for the data shown in Figure 3.6.

ogit function can be changed to the following format, where ߠൌ

led a slop parameter and ߜൌെߚߙ

⁄

is called a threshold

r

݌ሺݔሻൌ

1

1 ൅݁^{ିఏሺ௫ିఋሻ}

(3.21)

e 3.9 shows some logistic function with different parameter

When ߠൌ1 and ߜൌ0, the logit function is degenerated to the

function, which has been widely used in neural network

ms [Bishop, 1996] and will be discussed later in this chapter.

mmonly used objective function to model a data set using the

egression algorithm is a likelihood function show below, where

is defined by a Bernoulli function [Uspensky, 1937],

ൌෑܲሺݔ௡|ݕ௡ሻ

ே

௡ୀଵ

ൌෑ݌ሺݔ௡ሻ^௬೙ሺ1 െ݌ሺݔ௡ሻሻ^ଵି௬೙

ே

௡ୀଵ

(3.22)