1. Loss Function and Its Solution
Model linear regression model are as follows:
Logistic regression model definition (needs the Sigmoid function):
The above-described linear regression model brought to g (x) to give a final logistic regression model:
Assuming equal probability of the expressions of class 1, class 0 NATURAL equal probability equal to 1 minus the probability of the class is equal to, the following:
The above two equations integrated into a following formula:
Then the likelihood function is
m represents the number of samples, in order to facilitate the calculation, to give logarithmic
Seeking a maximum value of the above formula, the introduction of factor -1 / m, for the sake of conversion of the minimum value of the formula:
This is the log loss function logistic regression, in which
By then we gradient descent update theta
Where α is the learning step.
The following presents how the partial derivative derived above:
Derivative of the sigmoid function as:
g(x)' = g(x)*(1-g(x))
derivation of the derivative of the sigmoid function: the Click here Wallpaper