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Regression
In regression the aim is find a line (or plane or hyperplane) that fits the given input
points:
In the following section we will explain how logistic regression is a very common
and useful classification technique.
Logistic regression
Logistic regression is used to determine the probability of an event. Conventionally,
the event is represented as a categorical dependent variable. The probability of the
event is expressed using the sigmoid (or "logit") function:
1
PP(YY haaaa = 1|XX = xx) =
1 + ee −(bb+wwTT xx)
The goal now is to estimate weights W = { w 1
, w 2
, ...w n
} and bias term b. In logistic
regression, the coefficients are estimated using either the maximum likelihood
estimator or stochastic gradient descent. If p is the total number of input data points,
the loss is conventionally defined as a cross-entropy term given by:
llllllll = ∑ YY ii log(YY haaaaii ) + (1 − YY ii )log (1 − YY haaaaii )
pp
ii=1
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