dorsal/arxiv
View SchemaMonte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification
| Authors | Radford M. Neal |
|---|---|
| Categories | |
| ArXiv ID | physics/9701026 |
| URL | https://arxiv.org/abs/physics/9701026 |
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.
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"abstract": "Gaussian processes are a natural way of defining prior distributions over\nfunctions of one or more input variables. In a simple nonparametric regression\nproblem, where such a function gives the mean of a Gaussian distribution for an\nobserved response, a Gaussian process model can easily be implemented using\nmatrix computations that are feasible for datasets of up to about a thousand\ncases. Hyperparameters that define the covariance function of the Gaussian\nprocess can be sampled using Markov chain methods. Regression models where the\nnoise has a t distribution and logistic or probit models for classification\napplications can be implemented by sampling as well for latent values\nunderlying the observations. Software is now available that implements these\nmethods using covariance functions with hierarchical parameterizations. Models\ndefined in this way can discover high-level properties of the data, such as\nwhich inputs are relevant to predicting the response.",
"arxiv_id": "physics/9701026",
"authors": [
"Radford M. Neal"
],
"categories": [
"physics.data-an"
],
"title": "Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification",
"url": "https://arxiv.org/abs/physics/9701026"
},
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