The document provides a practical overview of Gaussian processes, highlighting key literature and implementations such as Bayesian linear regression. It discusses various aspects including kernel tricks, predictive distribution, and handling nonlinearity through feature design. Additionally, it emphasizes hyperparameters and their influence on predictions in the context of Gaussian processes.

1. Gaussian Processes
Practical overview
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2. ● Rassmussen & Williams, 2006
● Hensman, Matthews, Ghahramani, 2015
● GPy
● GPFlow
Literature and implementations

3. Weight space view
Simple case: Bayesian linear regression

4. Simple case: Bayesian linear regression

5. Simple case: Bayesian linear regression
(a) - prior
(b) - predictive mean and std
(c) - likelihood
(d) - posterior
Weight space view

6. Adding features
How to deal with nonlinearity?
Let’s design features!
Weight space view

7. Predictive distribution: we have to invert NxN matrix
Alternative form: nxn inversion, faster for n<N
Weight space view

8. Kernel trick

9. GP is a collection of random variables, any finite number of which have a
joint Gaussian distribution.
x is not time (in general case)!
Function-space view

10. Bayesian linear regression

11. Kernels

12. Algorithm [Rasmussen & Williams, 2006]
Making predictions

13. Varying hyperparameters

14. Kernels

15. Classification

16. Thanks for attention
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