Simplified Cost Function and Gradient Descent

Simplified Cost Function

Vectorized implementation:

$\begin{align*} & h = g(X\theta)\newline & J(\theta) = \frac{1}{m} \cdot \left(-y^{T}\log(h)-(1-y)^{T}\log(1-h)\right) \end{align*}$

Gradient Descent:

Vectorized implementation:

$\theta := \theta - \frac{\alpha}{m} X^{T} (g(X \theta ) - \vec{y})$

Notice the algorithm "looks" identical to linear regression though under the hood, it is using a different hypothesis function.

Resources:
- https://www.coursera.org/learn/machine-learning/lecture/MtEaZ/simplified-cost-function-and-gradient-descent
- https://www.coursera.org/learn/machine-learning/supplement/0hpMl/simplified-cost-function-and-gradient-descent