https://www.youtube.com/watch?v=het9HFqo1TQ&list=PLoROMvodv4rMiGQp3WXShtMGgzqpfVfbU&index=4

The lecture covers two different regressions, locally weighted and logistic regression. Locally weighted regression comprises multiple bounds, with each local region having a different hypothesis. In locally weighted regression, a new term is introduced w^(i), which adjusts the weights with the functions:

Which is then multiplied in the cost function as such:

Where Theta transpose is just a matrix representation of the equation from the last lecture.

Another type of regression is Logistic Regression which is generally used for binary classification problems. Binary classification classifies two types of objects (i.e. y = 0 or y = 1).

Probabilistic Terms:

Loss function with n training example:

Log-likelihood:

Derivative proof of Log-Likelihood:

Stochastic Gradient Descent