Keith Neo Home Page - Gaussian Process Prior Models

Basic Idea of Gaussian Process Prior Models

Regression using Gaussian process prior models have shown extreme good performance in System Identification. With assumption of the Gaussian distribution placed on the prior, the joint probability distribution of the posterior is also Gaussian with specific-defined mean and covariance. Well-known for its excellent prediction on time-series data, Gaussian process can also be extended to perform data analysis on multiple-dimension cases, such as state-space identification.

Demonstration of an Example

To demonstrate a simple example on how Gaussian process regression is useful on noisy data, consider figure 1 (see below). A self-generated nonlinear function is shown, with additive Gaussian white noise. Applying Gaussian regression, by placing a Gaussian distribution over an infinite space of functions, the posterior is assumed to be the fit to the data as if it was noise free. Note that, upon applying Gaussian process, no attempt is being made at all to propagate a Gaussian distribution (or any other distribution) into the nonlinear function. Finally, figure 2 illustrates the prediction of the fit, together with confidence intervals, which are 2 x standard deviations (of 95% confidence intervals).

I have been using Gaussian process prior models in data analysis as well as system identification for nonlinear dynamics systems. Over this time, there are some simple GP codes which I have developed. Check out at the Source Codes page.

Figure 1. Data containing Gaussian white noise data

Figure 2. Posterior Prediction of the fit to the data with confidence intervals

Keith Neo Kian Seng

Gaussian Process Prior Models

Quick Link

Research Link

Basic Idea of Gaussian Process Prior Models

Demonstration of an Example