Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification

1997/01/28 by Radford M. Neal, Neal, Radford M. · 10 citations
Computer Science · Engineering · Physics and Astronomy · #Control Systems and Identification #Data Analysis #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Scientific Research and Discoveries #Statistics and Probability (physics.data-an)

paper · pdf · doi:10.48550/arxiv.physics/9701026

openalex publication_date 1997/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an observed response, a Gaussian process model can easily be implemented using matrix computations that are feasible for datasets of up to about a thousand cases. Hyperparameters that define the covariance function of the Gaussian process can be sampled using Markov chain methods. Regression models where the noise has a t distribution and logistic or probit models for classification applications can be implemented by sampling as well for latent values underlying the observations. Software is now available that implements these methods using covariance functions with hierarchical parameterizations. Models defined in this way can discover high-level properties of the data, such as which inputs are relevant to predicting the response.

Citations

• Maximum likelihood estimation of models for residual covariance in spatial regression

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