Linear Regression using the Gradient Descent algorithm, NumPy, SymPy, and Matplotlib

Gradient Descent is an algorithm that finds the local extrema of a function. This is applicable to machine learning, because we want to find the optimal parameters that minimize our loss function. In machine learning, loss functions quantify the amount of error between the predicted values from a machine learning model and the actual expected values. In this notebook, we will perform linear regression by using gradient descent to find the optimal slope and y-intercept.

Gradient Descent Algorithm Formula $$X_{n+1} = X_n - lr * \frac{\partial}{\partial X} f(X_n)$$

Linear Regression Formula $$\hat{y} = w x + b$$

Loss Function $$MSE = \frac{1}{n} \sum_{i=1}^{n}(y_{i}-\hat{y})^2$$

jupyter notebook

Build the JupyterLab Docker image and start it

docker build -t gradient-descent .
docker run --rm -p 8888:8888 -v "$(pwd)":/home/jovyan/work gradient-descent

Open JupyterLab at the following URL: http://127.0.0.1:8888/lab

Start the Docker image

docker compose up --build -d

Open JupyterLab at the following URL: http://127.0.0.1:8888/lab

Clean up the Docker container

docker compose down --volumes --rmi local