Machine Learning: Regression Course Syllabus

Overview: This course provides a comprehensive introduction to regression techniques in machine learning, combining theoretical foundations with hands-on Python implementation. Over approximately 13.5 hours, learners will progress from simple linear regression to advanced regularization and non-parametric methods. Each module includes practical exercises using real-world datasets and Jupyter notebooks, culminating in a solid understanding of model evaluation, error analysis, and performance optimization. Ideal for learners with basic math and programming skills aiming to build robust predictive models.

Module 1: Simple Linear Regression

Estimated time: 2 hours

• Fit a line to data using gradient descent
• Apply closed-form solutions for linear regression
• Analyze residuals and model fit
• Understand the impact of outliers on regression models

Module 2: Multiple Regression

Estimated time: 2 hours

• Extend regression to multiple input features
• Incorporate polynomial terms for nonlinear relationships
• Interpret regression coefficients
• Improve prediction accuracy with feature engineering

Module 3: Assessing Performance

Estimated time: 2.5 hours

• Compute training and test errors
• Apply loss functions and error metrics
• Understand the bias-variance tradeoff
• Analyze model complexity and overfitting

Module 4: Ridge Regression

Estimated time: 2 hours

• Apply L2 regularization to prevent overfitting
• Implement ridge regression algorithms
• Use cross-validation to select regularization parameters
• Evaluate model performance with regularized coefficients

Module 5: Feature Selection and Lasso Regression

Estimated time: 2.5 hours

• Perform exhaustive and greedy feature selection
• Implement L1 regularization (Lasso) for sparsity
• Compare Lasso with other regularization methods
• Interpret sparse models for simplicity and insight

Module 6: Nearest Neighbors and Kernel Regression

Estimated time: 2 hours

• Apply k-nearest neighbors for regression
• Use kernel regression for flexible modeling
• Compare non-parametric methods to linear models
• Analyze performance on complex data patterns

Module 7: Summary and Final Review

Estimated time: 1 hour

• Review all regression techniques covered
• Recap model evaluation and error analysis
• Prepare for advanced topics in supervised learning

Prerequisites

• Basic knowledge of Python programming
• Familiarity with algebra and calculus
• Understanding of fundamental machine learning concepts

What You'll Be Able to Do After

• Implement simple and multiple linear regression models
• Apply ridge and lasso regression for regularization
• Evaluate models using cross-validation and error metrics
• Perform feature selection and interpret model coefficients
• Use non-parametric methods like kernel regression and k-nearest neighbors