Simplified Cost function and Gradient- Logistic Regression

Cost Function

As seen in the previous lesson that the cost function for Logistic regression is as follow-

We can compress our cost function's two conditional cases into one case:

We can fully write out our entire cost function as follows:

A vectorized implementation is

Gradient Descent

Remember that the general form of gradient descent is:

We can work out the derivative part using calculus to get:

Notice that this algorithm is identical to the one we used in linear regression. We still have to simultaneously update all values in theta.