Gaussian process

Nonparametric Bayesian statistics | Normal distribution | Stochastic processes

In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g. time or space. The concept of Gaussian processes is named after Carl Friedrich Gauss because it is based on the notion of the Gaussian distribution (normal distribution). Gaussian processes can be seen as an infinite-dimensional generalization of multivariate normal distributions. Gaussian processes are useful in statistical modelling, benefiting from properties inherited from the normal distribution. For example, if a random process is modelled as a Gaussian process, the distributions of various derived quantities can be obtained explicitly. Such quantities include the average value of the process over a range of times and the error in estimating the average using sample values at a small set of times. While exact models often scale poorly as the amount of data increases, multiple approximation methods have been developed which often retain good accuracy while drastically reducing computation time. (Wikipedia).

(ML 19.1) Gaussian processes - definition and first examples

Definition of a Gaussian process. Elementary examples of Gaussian processes.

From playlist Machine Learning

(ML 19.2) Existence of Gaussian processes

Statement of the theorem on existence of Gaussian processes, and an explanation of what it is saying.

From playlist Machine Learning

(ML 19.3) Examples of Gaussian processes (part 1)

Illustrative examples of several Gaussian processes, and visualization of samples drawn from these Gaussian processes. (Random planes, Brownian motion, squared exponential GP, Ornstein-Uhlenbeck, a periodic GP, and a symmetric GP).

From playlist Machine Learning

(ML 19.4) Examples of Gaussian processes (part 2)

From playlist Machine Learning

What is Gaussian elimination?

Gaussian elimination example is discussed and the general algorithm explained. Such ideas are important in the solution of systems of equations.

From playlist Intro to Linear Systems

PUSHING A GAUSSIAN TO THE LIMIT

Integrating a gaussian is everyones favorite party trick. But it can be used to describe something else. Link to gaussian integral: https://www.youtube.com/watch?v=mcar5MDMd_A Link to my Skype Tutoring site: dotsontutoring.simplybook.me or email dotsontutoring@gmail.com if you have ques

From playlist Math/Derivation Videos

Gaussian Integral 7 Wallis Way

Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using a technique that is very similar to the

From playlist Gaussian Integral

Gaussian Processes - Part 1

From playlist COMP0168 (2020/21)

(PP 6.1) Multivariate Gaussian - definition

Introduction to the multivariate Gaussian (or multivariate Normal) distribution.

From playlist Probability Theory

(ML 19.9) GP regression - introduction

Introduction to the application of Gaussian processes to regression. Bayesian linear regression as a special case of GP regression.

From playlist Machine Learning

ML Tutorial: Gaussian Processes (Richard Turner)

Machine Learning Tutorial at Imperial College London: Gaussian Processes Richard Turner (University of Cambridge) November 23, 2016

From playlist Machine Learning Tutorials

Aretha Teckentrup: Numerical analysis of Gaussian process regression

LMS Computer Science Colloquium 2021

From playlist LMS Computer Science Colloquium Nov 2021

Inference in Time Series

From playlist COMP0168 (2020/21)

06 Inference in Time Series

Slides and more information: https://mml-book.github.io/slopes-expectations.html

From playlist There and Back Again: A Tale of Slopes and Expectations (NeurIPS-2020 Tutorial)

Some thoughts on Gaussian processes for emulation of deterministic computer models: Michael Stein

Uncertainty quantification (UQ) employs theoretical, numerical and computational tools to characterise uncertainty. It is increasingly becoming a relevant tool to gain a better understanding of physical systems and to make better decisions under uncertainty. Realistic physical systems are

From playlist Effective and efficient gaussian processes

03 Numerical Integration

Slides and more information: https://mml-book.github.io/slopes-expectations.html

From playlist There and Back Again: A Tale of Slopes and Expectations (NeurIPS-2020 Tutorial)

Numerical Integration

From playlist COMP0168 (2020/21)

(PP 6.3) Gaussian coordinates does not imply (multivariate) Gaussian

An example illustrating the fact that a vector of Gaussian random variables is not necessarily (multivariate) Gaussian.

From playlist Probability Theory

Gaussian process

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