Gaussian Process

Creator

Creator

Created

Created

2024 Oct 1 0:25

Editor

Editor

Edited

Edited

2025 Jun 2 16:13

Refs

Refs

Bayesian Optimization

GP

Let

f(X) = (f(x₁), ..., f(xₙ))

. If

f(X)

follows a Gaussian distribution for any set of n points, then we say that

f: X → R

is a Gaussian process. A GP is characterized by its mean function

m(x)

and a covariance function

K(x, x′) ≥ 0

, which is any

f(x) \sim GP(m(x), K(x, \cdot))

where

m(x)

is the expected value of

f(x)

, and

K(x, x′) = \mathbb{E}[(f(x) - m(x))(f(x') - m(x'))^T]

.

p(f_X |X) = \mathcal{N}(f_X |µ_X , K_{X,X} )

where

\mu_X = (m(x_1), \dots, m(x_n))

and

K_{X,X}(i,j) = K(x_i, x_j)

.

Gaussian processes models

Visualization

www.infinitecuriosity.org

http://www.infinitecuriosity.org/vizgp/

Deep Neural Networks as Gaussian Processes

Deep Neural Networks as Gaussian Processes

We show how to make predictions using deep networks, without training deep networks.

https://openreview.net/forum?id=B1EA-M-0Z

Deep Neural Networks as Gaussian Processes

Lecture

Gaussian processes for fun and profit: Probabilistic machine learning in industry

Seminar by S.T. John, Senior Machine Learning Researcher, Secondmind Labs at the UCL Centre for AI. Recorded on the 4th November 2020. Abstract When companies, whether start-ups or big corporations, talk about "machine learning" they usually mean some kind of neural network model. Not always though: I will talk about why instead we put a lot of our efforts on probabilistic models built using Gaussian processes. When a Machine Learning course briefly covers Gaussian processes, you might go away thinking they're just basis function interpolation, only apply when the noise is Gaussian, and don't scale to larger datasets. Here I will discuss why these are misconceptions and show why Gaussian processes are both interesting and useful in practical applications. Bio Ti is a senior machine learning researcher in the probabilistic modelling team at Secondmind Labs, where they have been working on a broad range of customer and research projects involving Gaussian processes. Ti believes in making research output reusable by integrating it in common toolboxes and is core maintainer of the GPflow open source project for Gaussian process modelling.

Gaussian processes for fun and profit: Probabilistic machine learning in industry

https://youtu.be/uq8VxqeHPj8?si=mme8hPou0x5hGQni

Gaussian processes for fun and profit: Probabilistic machine learning in industry

gaussianprocess.org

https://gaussianprocess.org/gpml/chapters/RW.pdf

Backlinks

Optimization Algorithm MBTL Bayesian Optimization Active Learning

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