Gradient Descent From Scratch In Python

10 Jan 202342:38

TLDRIn this tutorial, Vic teaches the fundamentals of gradient descent, a key mechanism for training neural networks. The video demonstrates implementing linear regression with gradient descent in Python, using weather data to predict future temperatures. Key concepts like the forward and backward pass, loss calculation, and iterative optimization are covered, with an emphasis on the importance of selecting the right learning rate for effective convergence.


  • 📚 Gradient Descent is a fundamental algorithm used in training neural networks by optimizing parameters through learning from data.
  • 🔍 The tutorial begins with importing the pandas library for data handling and preparation, emphasizing the importance of dealing with missing values for effective machine learning.
  • 📈 The goal is to implement linear regression using gradient descent to predict future temperatures based on historical weather data.
  • 📊 A visualization of the data shows a potential linear relationship between today's maximum temperature and tomorrow's, which is essential for linear regression.
  • 🧠 The script explains the concept of a linear model with weights and biases, which are adjusted through gradient descent to minimize prediction errors.
  • 📉 Mean Squared Error (MSE) is introduced as the loss function to measure the error of predictions, which is crucial for guiding the gradient descent process.
  • 🔧 Gradient Descent involves iteratively updating the weights and biases to minimize loss, moving towards the lowest point on the loss curve.
  • 📈 The gradient, or the derivative of the loss function, indicates the direction and rate of change in loss with respect to the weights, guiding the update steps.
  • 🔎 The script demonstrates how to calculate the partial derivatives of the loss with respect to both weights and biases, which are key for parameter updates.
  • 🔄 Batch Gradient Descent is explained as the process of using all data points to calculate the average gradient and update the parameters accordingly.
  • 🔢 The importance of the learning rate in controlling the size of updates to the weights and biases is highlighted, with examples of how improper rates can lead to issues like divergence or slow convergence.

Q & A

  • What is the main topic of the video tutorial?

    -The main topic of the video tutorial is gradient descent, an important building block of neural networks, and its implementation in Python for linear regression.

  • What is the purpose of using the pandas library in the context of this tutorial?

    -The pandas library is used to help read and manipulate the data, including handling missing values, which is crucial before applying machine learning algorithms.

  • What is the significance of visualizing data points in a scatter plot for linear regression?

    -Visualizing data points in a scatter plot helps to identify the linear relationship between the predictor and the target variable, which is essential for understanding how linear regression works.

  • How is the linear regression equation represented in the script?

    -The linear regression equation is represented as \( \hat{y} = W_1 \times X_1 + b \), where \( \hat{y} \) is the predicted value, \( W_1 \) is the weight, \( X_1 \) is the predictor, and \( b \) is the bias.

  • What is the role of the mean squared error (MSE) in the context of gradient descent?

    -The mean squared error (MSE) is used to calculate the loss or error of the prediction, which is a critical part of the gradient descent process to understand how to adjust the parameters to minimize the error.

  • What does the gradient represent in the gradient descent algorithm?

    -The gradient represents the rate of change of the loss function with respect to the weights. It indicates how quickly the loss changes as the weights change, which is essential for determining the direction and magnitude of the parameter updates.

  • Why is the learning rate an important component in the gradient descent algorithm?

    -The learning rate is crucial because it controls the step size during the iterative process of gradient descent. It ensures that the algorithm does not overshoot the minimum loss point and helps in converging to the optimal solution.

  • 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, while stochastic gradient descent updates the parameters using the gradient from a single data point or a small batch of data points at a time.

  • How does the script describe the process of updating weights and biases in the gradient descent algorithm?

    -The script describes the process by first calculating the gradients and then using these gradients to update the weights and biases by subtracting the product of the gradient and the learning rate from the current parameters.

  • What is the significance of the partial derivative in the backward pass of the gradient descent algorithm?

    -The partial derivative in the backward pass is used to calculate how much each parameter (weight and bias) contributes to the error. It helps in determining the amount by which each parameter should be adjusted to minimize the loss.



📚 Introduction to Gradient Descent in Neural Networks

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.


📈 Understanding Linear Regression and Data 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.


🔍 Deeper Dive into Linear Regression Equation and Predictions

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.


🤖 Training a Linear Regression Model with scikit-learn

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.


📊 Mean Squared Error: Loss Function in Gradient Descent

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.


📉 Gradient and Its Role in Adjusting Weights for Minimum Loss

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.


🔧 Implementing Gradient Descent for Linear Regression

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.


🔧 Batch Gradient Descent and Model Parameter Updates

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.


🔧 Experimentation with Learning Rate and Weight Initialization

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.

🔚 Conclusion and Application to Neural Networks

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.



💡Gradient Descent

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. In the context of the video, it is the fundamental method by which neural networks learn from data and adjust their parameters to minimize the prediction error. The script discusses implementing linear regression using gradient descent, demonstrating how the algorithm iteratively improves predictions by adjusting weights and biases based on the calculated gradients.

💡Neural Networks

Neural Networks are a set of algorithms designed to recognize patterns and represent data in the form of interconnected nodes or 'neurons'. They are the foundation of deep learning, a subset of machine learning. The script mentions neural networks as the broader application of gradient descent, where the algorithm helps in training complex models by fine-tuning the network's parameters.

💡Linear Regression

Linear Regression is a statistical method for modeling the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data. The video script uses linear regression as an example to illustrate the application of gradient descent, with the goal of predicting future temperatures based on historical weather data.


Pandas is a Python library that provides data structures and data analysis tools for the Python programming language. In the script, Pandas is used to import and manipulate the dataset, which is essential for preparing the data for the gradient descent algorithm to learn from.

💡Data Imputation

Data Imputation is the process of filling in missing data. The script mentions filling in missing values in the dataset, which is a common preprocessing step in machine learning to ensure that the data is complete and ready for analysis.

💡Scatter Plot

A Scatter Plot is a type of plot that displays the values of two variables for a set of data. In the script, a scatter plot is used to visualize the relationship between the maximum temperature of the current day and the predicted maximum temperature for the next day, which helps in understanding the linear relationship necessary for linear regression.

💡Mean Squared Error (MSE)

Mean Squared Error is a measure of the average squared difference between the estimated values and the actual value. It is commonly used as a loss function in machine learning to measure how well a model's predictions match the actual data. The script explains MSE as part of the process to evaluate the error of predictions made by the gradient descent algorithm.

💡Learning Rate

The Learning Rate is a hyperparameter that controls the step size at each iteration while moving toward a minimum of a loss function. The script discusses the importance of selecting an appropriate learning rate for the gradient descent process to ensure that the algorithm converges to the optimal solution without overshooting or converging too slowly.

💡Batch Gradient Descent

Batch Gradient Descent is a form of gradient descent where the gradient of the loss function is calculated using the entire dataset before updating the parameters. The script contrasts this with other variants like stochastic gradient descent, and explains that batch gradient descent is used in the implementation of linear regression with gradient descent.


In the context of optimization and machine learning, Convergence refers to the point where the algorithm has found the minimum of the loss function or has reached a state where further iterations no longer significantly improve the model. The script describes the process of the gradient descent algorithm converging by iteratively reducing the loss until it stabilizes.


Regularization is a technique used to prevent overfitting by adding a penalty term to the loss function, which discourages large weights in the model. The script briefly mentions regularization as a technique that could be used to control the magnitude of the weights during the gradient descent process.


Introduction to gradient descent as a fundamental building block of neural networks.

Explanation of how neural networks learn from data and train parameters using gradient descent.

Demonstration of implementing linear regression with gradient descent in Python.

Importance of dealing with missing data for effective machine learning algorithms.

Overview of the dataset used for training, including weather data with 13,000 rows.

Objective to predict future temperatures using gradient descent for linear regression.

Visualization of the linear relationship between maximum temperatures and predictors.

Introduction of the linear regression equation and its components: weights and bias.

Use of multiple predictors in linear regression and their impact on predictions.

Training a linear regression model with scikit-learn and interpreting the results.

Calculation of mean squared error (MSE) as a measure of prediction error.

Graphical representation of loss and weight values to understand gradient descent.

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

Visualization of the gradient's impact on loss as weights change.

Introduction of the learning rate and its importance in controlling step size during updates.

Iterative process of gradient descent to converge towards the lowest loss.

Batch gradient descent versus stochastic gradient descent in the context of training algorithms.

Setup of the data for training, including conversion to numpy arrays and data splitting.

Initialization of weights and biases for the linear regression algorithm.

Writing the forward pass function to make predictions using weights and biases.

Calculation of loss and gradient to evaluate the accuracy of predictions.

Implementation of the backward pass to update parameters based on loss.

Development of a training loop to iteratively improve the model's performance.

Impact of learning rate on the convergence of the gradient descent algorithm.

Experimentation with weight and bias initialization for optimal algorithm performance.

Conclusion summarizing the importance of gradient descent in neural networks and future topics.