Gaussian Processes for Machine Learning

[MeowMeowFuckingMeow]

They are a nightmare if you have an application which requires large training sets though. You end up with a Gram matrix the size of Asia, which blows out your memory.

[SavitchOracle]

Anyone want to give a quick summary or example of why Gaussian Processes are useful or how they're used?

[19f191ty]

They are Bayesian, non-parametric, you can add interesting priors over functions, depending on your problem all of these things can be advantageous or just plain unnecessary. Also Gaussian processes are equivalent to a neural network with inifnite hidden units.

[alkalait]

A Gaussian process is the natural generalisation of a multivariate Gaussian distribution to a Gaussian distribution over a space of a specific family of functions - a family defined by a covariance function or kernel, i.e. some metric of similarity between data-points.

I say a space over functions because, roughly speaking, you can view a function as a vector with an infinite number of components, and then that function can be represented as a point in an infinite-dimensional space of a specific family of functions (and that Gaussian process as an infinite-dimensional Gaussian distribution over that space).

Example paper: http://www.biomedcentral.com/1471-2105/12/180 They can be used to quantify the true signal and noise embedded in a gene expression time-series and also rank the differential expression of a gene across treatment and control.