# Gradient Descent From Scratch In Python

TLDRIn this tutorial, Vic teaches the concept of gradient descent, a fundamental technique for training neural networks. The video demonstrates implementing linear regression with gradient descent in Python, using a dataset to predict weather temperatures. Key topics include understanding the linear relationship, visualizing data, calculating loss with mean squared error, and iteratively updating weights and biases to minimize loss. The tutorial also covers the importance of choosing the right learning rate and weight initialization for effective convergence.

### Takeaways

- π The tutorial covers the concept of gradient descent, a fundamental algorithm used in training neural networks.
- π The process begins with data preparation using the pandas library to handle and visualize data, specifically weather-related data for temperature predictions.
- π The script explains the importance of a linear relationship in linear regression, demonstrated through a scatter plot comparing today's maximum temperature with tomorrow's predicted maximum temperature.
- π§ The principle of gradient descent is introduced as a method to minimize loss functions, using mean squared error (MSE) as an example to quantify prediction errors.
- π The concept of a loss function and its gradient is explored, with a visual representation of how varying weights affect the loss and the gradient's impact on the descent process.
- π§ The script walks through coding a linear regression model from scratch, including initializing parameters, making predictions, calculating loss and gradients, and updating parameters through the backward pass.
- π The iterative nature of gradient descent is highlighted, emphasizing the need for multiple epochs to converge to the optimal solution that minimizes loss.
- π The tutorial discusses the sensitivity of gradient descent to the learning rate, showing how too high or too low a rate can affect the convergence and performance of the model.
- π’ The importance of weight initialization is touched upon, noting that different initialization strategies can influence the speed and outcome of the gradient descent process.
- π The script concludes with a discussion on the final model's parameters, comparing the results obtained from the custom implementation with those from scikit-learn's linear regression.
- π The tutorial sets the stage for understanding more complex neural networks, indicating that the concepts learned about gradient descent are directly applicable to such models.

### Q & A

### What is the main topic of the video tutorial?

-The main topic of the video tutorial is gradient descent, specifically how to implement linear regression using gradient descent in Python.

### What is gradient descent and why is it important for neural networks?

-Gradient descent is an optimization algorithm used to minimize a function by iteratively moving in the direction of the steepest descent as defined by the negative of the gradient. It is important for neural networks because it is the method by which they learn from data and train their parameters.

### What library is mentioned in the script for reading data?

-The library mentioned for reading data is pandas, which helps in reading the data into a suitable format for processing.

### How does the script handle missing values in the data?

-The script fills in missing values in the data, as most machine learning algorithms do not work well with missing data.

### What is the goal of using gradient descent in the context of this tutorial?

-The goal is to use gradient descent to train a linear regression algorithm that can predict tomorrow's maximum temperature (TMax) using other columns from the data.

### What is a linear relationship in the context of linear regression?

-A linear relationship in the context of linear regression refers to a direct proportionality between the predictor variables and the predicted variable. It is often visualized using a scatter plot where a line can be drawn to represent the trend of the data points.

### What is the equation form used to represent the prediction in linear regression?

-The equation form used to represent the prediction in linear regression is \( \hat{y} = W_1 \times X_1 + b \), where \( \hat{y} \) is the predicted value, \( W_1 \) is the weight, \( X_1 \) is the predictor variable, and \( b \) is the bias.

### What is the mean squared error (MSE) and how is it used in gradient descent?

-Mean squared error (MSE) is a measure of the error between the predicted and actual values, calculated as the average of the squares of the differences between them. It is used in gradient descent to quantify the loss or error of the prediction, which the algorithm seeks to minimize.

### What is the role of the learning rate in gradient descent?

-The learning rate in gradient descent determines the size of the steps taken towards the minimum of the loss function. It is crucial for controlling the convergence of the algorithm, preventing it from taking too large or too small steps.

### What is the difference between batch gradient descent and stochastic gradient descent mentioned in the script?

-Batch gradient descent calculates the gradient by averaging the error across the entire dataset and updates the parameters once per iteration. Stochastic gradient descent, on the other hand, updates the parameters after every single training example or a small batch of examples, making it more suitable for large datasets.

### How does the script visualize the gradient and its relation to the loss function?

-The script visualizes the gradient by plotting different weight values against the loss, showing how the gradient changes as the weights change. It also plots the gradient itself to show how it varies with the weight values, indicating the rate of change of the loss function.

### What is the purpose of the partial derivative in the context of the gradient descent algorithm?

-The partial derivative in the context of gradient descent is used to calculate the rate at which the loss changes with respect to each parameter (weight and bias). It helps in determining how much each parameter contributes to the error and guides the update of these parameters to minimize the loss.

### How does the script handle the training of the linear regression model using gradient descent?

-The script handles the training by initializing parameters, making predictions using a forward pass, calculating the loss and gradient, and then updating the parameters in a backward pass. This process is repeated for a number of epochs until the loss converges to a minimum value.

### Outlines

### π Introduction to Gradient Descent and Linear Regression

In this introductory segment, Vic introduces the concept of gradient descent as a fundamental building block in neural networks. The focus is on how neural networks use gradient descent to learn from data and train their parameters. The tutorial will implement linear regression using Python and gradient descent, with the aim of predicting maximum temperatures based on historical weather data. The data set consists of 13,000 rows, covering several years of daily records including maximum and minimum temperatures, rainfall, and next day's temperatures. Vic emphasizes the importance of handling missing data and understanding the linear relationship between predictors and the target variable.

### π Understanding Linear Regression and Data Visualization

This paragraph delves deeper into the linear regression algorithm, which requires a linear relationship between the predictors and the target variable. Vic uses a scatter plot to visualize the relationship between today's maximum temperature and tomorrow's predicted maximum temperature. A line is drawn to represent the best fit through the data points, illustrating the concept of a linear relationship. The segment also covers the basic equation of linear regression, where the predicted value is calculated as the product of the temperature and a weight, plus a bias. The goal is to use gradient descent to find the optimal weight and bias values for accurate predictions.

### π§ Implementing Linear Regression with Scikit-learn

Vic demonstrates how to use the scikit-learn library to implement linear regression. The tutorial shows the process of importing the linear regression class, initializing it, and fitting it to the data to train the algorithm. After training, the model's coefficients, including the weights and bias, are used to plot a line on the scatter plot, representing the model's prediction. The segment also introduces the concept of mean squared error (MSE) as a loss function to measure the accuracy of predictions, emphasizing its importance in the gradient descent process.

### π Exploring the Gradient Descent Optimization Process

This section explains the optimization process in gradient descent. Vic discusses how to graph different weight values against loss to understand the relationship between them. The goal is to find the weight value that minimizes the loss. The concept of the gradient, which indicates how quickly the loss changes with respect to the weights, is introduced. The tutorial includes a visualization of the loss function and the gradient, showing how the gradient descent algorithm adjusts weights to minimize loss.

### π§ Gradient Calculation and Parameter Update Strategy

Vic explains how to calculate the gradient and use it to update the weights and biases in the linear regression model. The tutorial covers the process of finding the partial derivatives of the loss with respect to the weights and bias, which are crucial for adjusting the model's parameters. The segment also introduces the concept of a learning rate, which is used to control the size of the steps taken during the parameter update process to avoid overshooting the optimal values.

### π Batch Gradient Descent for Linear Regression

This paragraph describes the process of implementing batch gradient descent for linear regression. The algorithm uses all data points to calculate the gradient and update the parameters simultaneously. The tutorial explains how to set up the data, initialize weights and biases, and create functions for making predictions, calculating loss, and updating parameters. The training loop is introduced, which iteratively runs the algorithm to minimize the loss until the model converges.

### π§ Fine-Tuning Gradient Descent with Learning Rate and Initialization

Vic discusses the importance of fine-tuning the gradient descent algorithm by adjusting the learning rate and the initialization of weights and biases. The tutorial shows the impact of different learning rates on the convergence of the algorithm and how improper settings can lead to issues like infinite loss or slow learning. The segment also explores different weight initialization strategies and their effects on the descent process and model convergence.

### π Conclusion and Future Outlook on Neural Networks

In the concluding segment, Vic summarizes the key concepts learned in the tutorial about gradient descent and its application in linear regression. The tutorial concludes with a comparison of the final model's parameters with those obtained from scikit-learn, highlighting the relevance of the concepts to neural networks. Vic expresses hope that the tutorial was informative and hints at future tutorials that will expand on these concepts in the context of neural networks.

### Mindmap

### Keywords

### π‘Gradient Descent

### π‘Neural Networks

### π‘Linear Regression

### π‘Pandas

### π‘Data Visualization

### π‘Scikit-learn

### π‘Mean Squared Error (MSE)

### π‘Learning Rate

### π‘Batch Gradient Descent

### π‘Convergence

### π‘Overfitting

### Highlights

Introduction to gradient descent, a fundamental algorithm in machine learning and neural networks.

Using Python to implement linear regression with gradient descent.

Importing the pandas library for data manipulation and analysis.

Reading and preparing data with pandas, including handling missing values.

Understanding the goal of predicting future temperatures using historical data.

Visualizing data with matplotlib to examine the linear relationship between variables.

Drawing a line of best fit on a scatter plot to understand linear regression.

The mathematical formulation of linear regression and the role of weights and bias.

Training a linear regression model using scikit-learn library.

Plotting the regression line and comparing it to the initial line of best fit.

Calculating the mean squared error (MSE) to measure the prediction error.

The concept of loss function and its importance in gradient descent.

Graphical representation of loss and gradient to understand the optimization process.

Calculating the gradient and its role in adjusting weights to minimize loss.

The iterative process of gradient descent to find the optimal weight values.

Implementing batch gradient descent to update parameters using the entire dataset.

Writing a training loop to iteratively improve the model's predictions.

The impact of learning rate on the convergence of the gradient descent algorithm.

Experimenting with different weight initializations and their effect on training.

Comparing the final model's parameters with those obtained from scikit-learn.

Conclusion summarizing the importance of gradient descent in neural networks.