Infamous Logistic Regression

What exactly is logistic regression. For binary classification, logistic regression computes the posterior probability of class C1 as a logistic sigmoid acting on a linear function of the feature vector x: p(C1|x)=y(x)=σ(wTx).

σ (.) is the logistic sigmoid function. σ(a)=1/(1+exp(-a)) + d(σ)/d(a)=σ(1-σ).

Now the goal is to maximize the conditional likelihood p(t/w).

• we take the log to work with the equation and minimize the negative term.
• To find the minimum of the error, we use simple gradient descent.