Regression with input-dependent noise: a Gaussian process treatment
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Kalman Filtering and Neural Networks
Kalman Filtering and Neural Networks
A family of algorithms for approximate bayesian inference
A family of algorithms for approximate bayesian inference
Heteroscedastic Gaussian process regression
ICML '05 Proceedings of the 22nd international conference on Machine learning
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Function factorization using warped Gaussian processes
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
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Stationarity is often an unrealistic prior assumption for Gaussian process regression. One solution is to predefine an explicit nonstationary covariance function, but such covariance functions can be difficult to specify and require detailed prior knowledge of the nonstationarity. We propose the Gaussian process product model (GPPM) which models data as the pointwise product of two latent Gaussian processes to nonparametrically infer nonstationary variations of amplitude. This approach differs from other nonparametric approaches to covariance function inference in that it operates on the outputs rather than the inputs, resulting in a significant reduction in computational cost and required data for inference. We present an approximate inference scheme using Expectation Propagation. This variational approximation yields convenient GP hyperparameter selection and compact approximate predictive distributions.