Curve prediction and clustering with mixtures of Gaussian process functional regression models

Shi, Jian-Qing; Wang, B.

doi:10.1007/s11222-008-9055-1

Cited by 74 publications

(57 citation statements)

References 21 publications

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“…Parametrization (2.5) leads to convenient computations, as well as reliable inferences and predictions. In the current framework, the use of Gaussian process priors [20] or an allocation model [27] for the representation of the weight functions would lead to expensive computations due to the introduction of many extra latent/nuisance variables. The special case where the weights are assumed to be constant values th pkq ,I k p¨q " 1u implies that the fidelity of the computer models is constant across the input space, and hence it can be too restrictive in real world problems.…”

Section: Basic Formulationmentioning

confidence: 99%

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

Karagiannis

Lin

2014

Journal of Computational Physics

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractFor many real systems, several computer models may exist with different physics and predictive abilities.To achieve more accurate simulations/predictions, it is desirable for these models to be properly combined and calibrated. We propose the Bayesian calibration of computer model mixture method which relies on the idea of representing the real system output as a mixture of the available computer model outputs with unknown input dependent weight functions. The method builds a fully Bayesian predictive model as an emulator for the real system output by combining, weighting, and calibrating the available models in the Bayesian framework. Moreover, it fits a mixture of calibrated computer models that can be used by the domain scientist as a mean to combine the available computer models, in a flexible and principled manner, and perform reliable simulations. It can address realistic cases where one model may be more accurate than the others at different input values because the mixture weights, indicating the contribution of each model, are functions of the input. Inference on the calibration parameters can consider multiple computer models associated with different physics. The method does not require knowledge of the fidelity order of the models.We provide a technique able to mitigate the computational overhead due to the consideration of multiple computer models that is suitable to the mixture model framework. We implement the proposed method in a real world application involving the Weather Research and Forecasting large-scale climate model.

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Section: Basic Formulationmentioning

confidence: 99%

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

Karagiannis

Lin

2014

Journal of Computational Physics

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“…Through the literature there are different types of regression mixture models that have been used for sequential data modeling [10]. Among them, Hidden Markov Models [11], polynomial and spline regression models [12], [4], [5], mixtures of ARMA models [13] and mixtures of Gaussian processes [14] are commonly used models. These methods are suffering from the drawback of not automatically addressing the problem of model order selection, which is very important in regression.…”

Section: Introductionmentioning

confidence: 99%

The Mixture of Multi-kernel Relevance Vector Machines Model

Blekas

Likas

2012

2012 IEEE 12th International Conference on Data Mining

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Abstract-We present a new regression mixture model where each mixture component is a multi-kernel version of the Relevance Vector Machine (RVM). In the proposed model, we exploit the enhanced modeling capability of RVMs due to their embedded sparsity enforcing properties. Moreover, robustness is achieved with respect to the kernel parameters, by employing a weighted multi-kernel scheme. The mixture model is trained using the maximum a posteriori (MAP) approach, where the Expectation Maximization (EM) algorithm is applied offering closed form update equations for the model parameters. An incremental learning methodology is also presented to tackle the parameter initialization problem of the EM algorithm. The efficiency of the proposed mixture model is empirically demonstrated on the time series clustering problem using various artificial and real benchmark datasets and by performing comparisons with other regression mixture models.

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“…Completely specified by a mean and covariance function, the GP has a relatively simple structure and is able to attain a variety of shapes. Ramsmussen and Williams (2006) and Shi and Choi (2011) provide comprehensive reviews of the structure and properties of the Gaussian process for regression and classification. GP models have been applied in a variety of fields including geostatistics (Banerjee et al 2008), machine learning (Ramsmussen and Williams 2006), and ecology (Munch et al 2005).…”

Section: Introductionmentioning

confidence: 99%

Combining functional data with hierarchical Gaussian process models

Poynor

Munch

2017

Environ Ecol Stat

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Gaussian process models have been used in applications ranging from machine learning to fisheries management. In the Bayesian framework, the Gaussian process is used as a prior for unknown functions, allowing the data to drive the relationship between inputs and outputs. In our research, we consider a scenario in which response and input data are available from several similar, but not necessarily identical, sources. When little information is known about one or more of the populations it may be advantageous to model all populations together. We present a hierarchical Gaussian process model with a structure that allows distinct features for each source as well as shared underlying characteristics. Key features and properties of the model are discussed and demonstrated in a number of simulation examples. The model is then applied to a data set consisting of three populations of Rotifer Brachionus calyciflorus Pallas. Specifically, we model the log growth rate of the populations using a combination of lagged population sizes. The various lag combinations are formally compared to obtain the best model inputs. We then formally compare the leading hierarchical Gaussian process model with the inferential results obtained under the independent Gaussian process model.

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Curve prediction and clustering with mixtures of Gaussian process functional regression models

Cited by 74 publications

References 21 publications

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

The Mixture of Multi-kernel Relevance Vector Machines Model

Combining functional data with hierarchical Gaussian process models

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