Welcome to LinearRegression-Exploration, a project led by Quan Hoang Ngoc during the first semester of 2023. This project explores the Mathematical Foundations of Computer Science with a focus on Linear Regression. It's designed to take you on a journey through the fundamental principles and applications of Linear Regression.
- Mastery of Linear Regression: We dive deep into the core concepts and principles of Linear Regression, building a strong foundation from the ground up.
- Algorithm Exploration: We explore and implement key algorithms such as Normal Equation (NE), Stochastic Gradient Descent (SGD), and Gradient Descent (GD).
- Dynamic Learning: We experiment with the alpha learning rate and measure the performance of our models using the R2 metric, helping to refine and optimize predictive models.
This project blends the precision of mathematics with the innovation of computer science, aiming to push the boundaries of traditional learning. It's not just about coding; it's about crafting a deeper understanding of predictive modeling. Every model we build is a step toward mastering Linear Regression, and every line of code contributes to the art of algorithmic development.
This repository is a practical guide and resource for understanding Linear Regression. It provides:
- Theoretical Foundations: A comprehensive explanation of Linear Regression concepts.
- Algorithm Implementations: Detailed steps to implement different algorithms such as NE, SGD, and GD.
- Learning Rate Experiments: An analysis of how the alpha learning rate affects model accuracy.
Understanding Linear Regression is essential for anyone working in data science or machine learning. This project is designed to help learners grasp the fundamental concepts and apply them effectively in real-world scenarios. It serves as both an educational tool and a practical guide for mastering Linear Regression.
This project is ideal for:
- Students and Educators: Those learning or teaching Linear Regression and its applications.
- Data Scientists and Machine Learning Practitioners: Professionals looking to enhance their knowledge and skills.
- Researchers and Developers: Anyone interested in applying Linear Regression techniques in practical projects.
- Interactive Notebooks: Step-by-step guides to implementing algorithms with clear explanations.
- Visualizations: Graphs and charts that demonstrate the impact of different learning rates and performance metrics.
- Sample Data: Provided datasets for hands-on learning and testing.
- Linear Regression Basics: We begin with the core principles of Linear Regression.
- Mathematical Derivations: Detailed derivations for a deeper understanding of each algorithm.
- Normal Equation (NE): A straightforward solution to Linear Regression.
- Stochastic Gradient Descent (SGD): A method optimized for handling large datasets.
- Gradient Descent (GD): An iterative approach to minimize the cost function.
- Experiments: Testing different alpha values to see their effects on model accuracy.
- R2 Metric: Evaluating model performance and predictive power.
- Graphs and Charts: Visual aids that help interpret the results and enhance understanding.
Through this project, we learned:
- The fundamental principles of Linear Regression.
- The advantages and challenges of different regression algorithms.
- How learning rates impact the performance of predictive models.
- The importance of visualization in data science and machine learning.
- Thorough Understanding: We gained a deep knowledge of Linear Regression.
- Successful Implementations: Implemented and compared multiple algorithms.
- Effective Visualization: Created visual tools that clarify complex concepts.
- Educational Resource: Provided a valuable learning resource for a wide audience.
This project serves as a comprehensive guide to understanding and applying Linear Regression. It combines theoretical knowledge with practical implementation, making it a valuable resource for anyone looking to master this essential data science technique.