ML | Cost function in Logistic Regression
In the case of Linear Regression, the Cost function is –
But for Logistic Regression,
It will result in a non-convex cost function. But this results in cost function with local optima’s which is a very big problem for Gradient Descent to compute the global optima.
So, for Logistic Regression the cost function is
If y = 1
Cost = 0 if y = 1, hθ(x) = 1
hθ(x) -> 0
Cost -> Infinity
If y = 0
To fit parameter θ, J(θ) has to be minimized and for that Gradient Descent is required.
Gradient Descent – Looks similar to that of Linear Regression but the difference lies in the hypothesis hθ(x)