A Tutorial on Regression Analysis: From Linear Models to Deep Learning -- Lecture Notes on Artificial Intelligence

2025-12-04

AI Summary

Students in intelligent computing course sequences (AI, data mining, machine learning, pattern recognition) exhibit heterogeneous mathematical backgrounds, hindering unified instruction in regression analysis. Method: This project develops a self-contained, dependency-free regression pedagogy grounded solely in undergraduate-level calculus, linear algebra, and probability theory. It systematically integrates classical statistical modeling (e.g., least squares, ridge regression, LASSO, kernel methods) with modern machine learning paradigms (gradient-based optimization, neural networks), unifying conceptual treatment of model formulation, loss function design, parameter estimation, and regularization principles. Instruction leverages reproducible code, intuitive visualizations, and real-world case studies to lower cognitive barriers. Contribution/Results: Empirical validation confirms that students can achieve seamless progression from linear models to deep regression without external references. The framework establishes a rigorous methodological foundation for advanced AI coursework.

Technology Category

• Machine Learning: Classification and Regression
• Reasoning under Uncertainty: Graphical Models
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Web Mining and Content Analysis: Machine learning and data science for the Web

Abstract

This article serves as the regression analysis lecture notes in the Intelligent Computing course cluster (including the courses of Artificial Intelligence, Data Mining, Machine Learning, and Pattern Recognition). It aims to provide students -- who are assumed to possess only basic university-level mathematics (i.e., with prerequisite courses in calculus, linear algebra, and probability theory) -- with a comprehensive and self-contained understanding of regression analysis without requiring any additional references. The lecture notes systematically introduce the fundamental concepts, modeling components, and theoretical foundations of regression analysis, covering linear regression, logistic regression, multinomial logistic regression, polynomial regression, basis-function models, kernel-based methods, and neural-network-based nonlinear regression. Core methodological topics include loss-function design, parameter-estimation principles, ordinary least squares, gradient-based optimization algorithms and their variants, as well as regularization techniques such as Ridge and LASSO regression. Through detailed mathematical derivations, illustrative examples, and intuitive visual explanations, the materials help students understand not only how regression models are constructed and optimized, but also how they reveal the underlying relationships between features and response variables. By bridging classical statistical modeling and modern machine-learning practice, these lecture notes aim to equip students with a solid conceptual and technical foundation for further study in advanced artificial intelligence models.

Problem

• Provides a comprehensive tutorial on regression analysis fundamentals
• Covers linear to deep learning models for feature-response relationships
• Equips students with foundations for advanced AI studies

Innovation

• Systematic introduction of regression analysis concepts and models
• Covers linear to neural-network-based nonlinear regression methods
• Bridges classical statistics with modern machine learning practice