Weekly Materials
Lecture slides, week 10
Professor's lecture slides (PDF)
Finger exercises part 1 (at the end of the lecture (with TA))
Hands-on tutorials and practice exercises
→
Finger exercises part 2 (at the end of the lecture (with TA))
Hands-on tutorials and practice exercises
→
Exercise 6
Distribution of Exercise sheet 6
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References & Resources
Finger Exercises
Finger exercises part 1 and 2 (at the end of the lecture (with TA))
Additional Notes
Week 10: Gaussian Processes
Learning Objectives
- Understand the theoretical foundations of Gaussian Processes (GPs)
- Master Gaussian Process regression techniques
- Learn about kernels and their role in GP modeling
- Handle noisy data in GP frameworks
- Apply GPs to financial modeling and option pricing
- Understand GP classification methods
Topics Covered
- Gaussian Process Regression: Theoretical foundations and practical implementation
- Kernels with Noise: Incorporating uncertainty and noise in GP models
- Option-Pricing Examples: Financial applications of Gaussian Processes
- GP Classification: Extending GPs to classification problems
- Bayesian Framework: Understanding the Bayesian perspective in GPs
- Hyperparameter Optimization: Tuning GP models for optimal performance
Schedule
- Lecture: Monday, November 17, 2025 (10:15 - 12:00)
- Practice Session: Monday, November 17, 2025 (16:30 - 18:00)
- TA Session: Two-part finger exercises and practical implementations
Key Concepts
- Gaussian Processes: Non-parametric Bayesian approach to regression
- Kernel Functions: RBF, Matern, periodic kernels and their properties
- Mean and Covariance Functions: Defining GP priors
- Marginal Likelihood: Model selection and hyperparameter optimization
- Uncertainty Quantification: Predictive distributions and confidence intervals
- Computational Complexity: Scaling GPs and approximation methods
Mathematical Foundations
- Multivariate Gaussian distributions
- Kernel methods and reproducing kernel Hilbert spaces
- Bayesian inference and posterior distributions
- Maximum likelihood estimation for hyperparameters
Practical Applications
- 1D and 2D Regression: Basic GP regression examples
- Financial Modeling: Option pricing using GP methods
- Noise Handling: Robust regression with noisy observations
- Multi-dimensional Problems: Scaling to higher dimensions
- Classification Tasks: GP classification with various kernels
Assignments
- Exercise 6: Distributed this week - GP implementation and applications
- Complete two-part finger exercises covering theory and practice
- Implement GP regression from scratch and compare with scikit-learn
Tools and Libraries
- GPy and GPFlow for advanced GP modeling
- scikit-learn for basic GP implementations
- Practical GP examples and case studies