Simplified Cost Function and Gradient Descent

Note: [6:53 - the gradient descent equation should have a 1/m factor]

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

Cost(hθ(x),y)=−ylog(hθ(x))−(1−y)log(1−hθ(x))

Notice that when y is equal to 1, then the second term (1−y)log(1−h

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.

A vectorized implementation is:

θ:=θ−αmXT(g(Xθ)−y⃗ )