Gradient Descent From Scratch In Python

This paragraph introduces the concept of gradient descent, a fundamental algorithm used in training neural networks. The speaker, Vic, explains that gradient descent is essential for learning from data and adjusting parameters. The tutorial's aim is to implement linear regression using Python and gradient descent, with a focus on predicting maximum temperatures based on historical weather data. The initial steps involve importing necessary libraries like pandas for data handling and matplotlib for visualization.

The speaker delves into the linear regression algorithm, emphasizing its requirement for a linear relationship between the predictors and the target variable. A visual representation of this relationship using a scatter plot is discussed, with the TMax column as a predictor and TMax for the next day as the target. The paragraph explains the process of drawing a line of best fit using matplotlib and how this line can be used for predictions, leading to a basic understanding of the linear relationship in the context of the data.

Vic explains the linear regression equation in detail, discussing how predictions are made by multiplying the predictor value by a weight and adding a bias. The paragraph covers the automatic learning process of W (weight) and B (bias) through linear regression. It also introduces the concept of using multiple predictors, extending the linear equation to include additional variables and their corresponding weights.

The paragraph describes the process of training a linear regression model using the scikit-learn library. It outlines the steps to initialize the linear regression class and fit it to the data, which involves training the algorithm to predict TMax for the next day based on the current day's data. The speaker also discusses plotting the data points and the regression line, and explains how to interpret the model's coefficients for weight and bias to understand the prediction line.

Vic introduces the concept of mean squared error (MSE) as a loss function to measure the error or loss of predictions in gradient descent. The paragraph explains how MSE is calculated and its importance in improving predictions. It also discusses the process of graphing different weight values against loss to visualize the optimal weight that minimizes loss, which is a key step in understanding how gradient descent works to find the best parameters.

The speaker explains the gradient, which indicates how quickly the loss changes with respect to the weights. The paragraph discusses the calculation of the gradient and its visualization, showing how the gradient's magnitude changes with different weight values. It emphasizes the goal of gradient descent to find the weight value that results in the lowest loss, which corresponds to the point where the gradient is zero or near zero.

Vic outlines the steps to implement gradient descent for linear regression, starting with data preparation by converting pandas dataframes into numpy arrays. The paragraph details the initialization of weights and biases, the creation of a forward pass for prediction, and the calculation of loss and gradient. It also covers the backward pass, which updates the parameters based on the loss, and the iterative training loop that runs until the loss is minimized or the algorithm converges.

The paragraph explains the concept of batch gradient descent, where the gradient is averaged across the entire dataset to update the parameters. It discusses the importance of the learning rate in controlling the step size during updates to avoid overshooting the minimum loss point. The speaker also describes the process of updating weights and biases using the calculated gradients and the impact of the learning rate on the convergence of the algorithm.

Vic discusses the importance of experimenting with the learning rate and weight initialization in gradient descent. The paragraph highlights how different learning rates can affect the convergence of the algorithm, with too high a rate causing the loss to diverge to infinity and too low a rate resulting in slow learning. It also touches on the impact of weight initialization on the descent process and the potential use of regularization techniques like ridge regression.

In conclusion, the speaker summarizes the key concepts learned in the tutorial, such as the forward and backward passes, which are directly applicable to neural networks. The paragraph emphasizes the significance of gradient descent as a building block for understanding and implementing neural networks, and hints at the continuation of the topic in future tutorials.