ecision function is.
We'll talk a bit more about the motivation of these two losses, starting with the logistic loss.


---

# Logistic Regression


.left-column[
$$\log\left(\frac{p(y=1|x)}{p(y=0|x)}\right) = w^T\textbf{x}$$

$$p(y|\textbf{x}) = \frac{1}{1+e^{-w^T\textbf{x}}}$$

`$$\min_{w \in ℝ^{p}} -\sum_{i=1}^n \log(\exp(-y_iw^T \textbf{x}_i) + 1)$$`


$$\hat{y} = \text{sign}(w^T\textbf{x} + b)$$
]
.right-column[
![:scale 100%](images/linear_classification_img_3.png)]


???
Logistic regression is prob