# Gradient Descent for Logistic Regression

### Implementation of Gradient Descent for optimizing Logistic Regression Cost Function

#### Assumptions:

- For the sake of simplicity, assume that there are only two features (the algorithm will generalize over training examples). Vectorized notations will take care of multiple features and training examples.
- Also, to make the notations simple, the derivative of the cost function with respect to a variable ‘x’ will be written as

#### Logistic Regression: Derivative calculation with two examples

Input: Parameters:

–> –>

#### Objective: Calculate the derivative of loss function w.r.t. &

Backpropagating Step By Step:

- Calculate or

- Calculate

- Calculate

#### Looping over m examples: Pseudocode

Initialize:

for i = 1 to m

= +

=

=

J/=m

/=m

/=m

db/=m

b = b- db

is the learning rate.

–

Written on November 29, 2017