# introduce

Logistic regression is one of the most basic classification algorithms. Its model is
, where
.

its cost function
.

For the binary classification problem, the values of y are 0 and 1. Here, we
set y=1 probability. When it is greater than or equal to 0.5, we predict the result to be 1, and when it is less than 0.5, we predict the result to be 0.

# Use gradient descent algorithm

Iterative formula:
where
. The derivation process is shown in the figure below.

Vectorized expression:
.