# Gaussian process regression

(1.3 hours to learn)

## Summary

Gaussian process regression is a Bayesian model for nonparametric regression. (That is, nonparametric in the sense that the complexity of the regression function grows with the amount of data.) The model places a prior directly on the output values without reference to an underlying parametric model.

## Context

This concept has the prerequisites:

- Gaussian processes
- Bayesian linear regression (Gaussian process regression is a kernelized version of Bayesian linear regression.)

## Core resources (read/watch one of the following)

## -Free-

→ Gaussian Processes for Machine Learning

A graduate-level machine learning textbook focusing on Gaussian processes.

## -Paid-

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 6.4-6.4.2, pages 303-311

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Bayesian Reasoning and Machine Learning

A textbook for a graudate machine learning course.

## -Paid-

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 15.1-15.2.3, pages 515-521

## See also

- In order to use GP regression in practice, it is usually necessary to learn the hyperparameters (such as the length scale) from data.
- Some other uses for Gaussian processes in machine learning:
- classification
- black-box optimization (where we only get to evaluate the function, and doing so is expensive)
- reinforcement learning