Logistic Regression

Hypothesis

$$\begin{gathered} z=w\cdot x+b \\ sigmoid(z)=\frac{1}{1+e^{-z}} \\ {f}_{w,b}(x)=sigmoid(z) \end{gathered}$$

Cost Function

$$\begin{gathered} L(w,b)=-y^{(i)}ln{x}^{(i)}+(y^{(i)}-1)ln(1-x^{(i)}) \\ J(w,b)=\frac{1}{m}{\sum }_{i=1}^{m}L(w,b)+\frac{\lambda }{2m}{\sum }_{j=1}^n{w}_j^2 \end{gathered}$$