Dependent Gaussian Processes

By Phillip Boyle, Marcus Frean. 2004

316 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Kernels for Vector-Valued Functions: a Review (2011, methodology): “moothing kernel.6 If the base process is a Gaussian process, it turns out that the convolved process is also a Gaussian process. We can therefore exploitconvolutions to construct covariance functions [8, 102, 43, 44, 14, 56, 2]. Inasimilarwaytothe linearmodelofcoregionalization,we considerQgroupsoff”
Gaussian Process Regression Networks (2011, background): “…an explosion of interest in extending the Gaussian process regression framework to account for ﬁxed correlations between output variables (Alvarez and Lawrence, 2011; Yu et al., 2009; Alvarez and Lawrence, 2008; Bonilla et al., 2008; Osborne et al., 2008; Teh et al., 2005; Boyle and Frean, 2004).”
Machine learning of linear differential equations using Gaussian processes (2017, methodology): “Moreover, systems of linear integro-differential equations can be addressed using multi-output Gaussian process regression [6,1,32].”
Statistical Learning by Imitation of Competing Constraints in Joint Space and Task Space (2009, background): “Retrieving multiple outputs and their associated correlations is on the contrary not straightforward for GPR or SVR, which requires to develop other strategies to deal with multiple outputs [33].”
Sparse Convolved Gaussian Processes for Multi-output Regression (2008, methodology): “In [2], the latent processes correspond to white Gaussian noises and the covariance matrix is given by eq.”
Online Sparse Multi-Output Gaussian Process Regression and Learning (2019, methodology): “An alternative method relies on convolving the latent GPs with different kernels to produce multiple outputs and introduce cross correlation among them [27]–[29].”
Gaussian process regression for multivariate spectroscopic calibration (2007, methodology): “This problem can be addressed using the indirect definition of the covariance function, for example by treating the Gaussian process as the output of stable linear filters [21].”
Gaussian Processes for Regression and Optimisation (2007, methodology): “This is an extension of the work of Boyle and Frean [6, 7], where dependent Gaussian processes were first defined.”
Spike and Slab Variational Inference for Multi-Task and Multiple Kernel Learning (2011, methodology): “methods [11, 12, 13] and multi-task Gaussian processes (GPs) [14, 15, 16, 17].”
Vector Field Learning via Spectral Filtering (2010, background): “Starting from the work of [7], related ideas have been developed in the context of regularization methods [8], Gaussian processes [9,10].”
Learning Social Etiquette: Human Trajectory Understanding In Crowded Scenes (2016, background): “Other methods [22,17,12] use Gaussian Processes to forecast human trajectories.”
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) (2005, unknown): “A related approach is taken by Boyle and Frean [2005] who introduce correlations between two processes by deriving them as different convolutions of the same underlying white noise process.”
Computationally Efficient Convolved Multiple Output Gaussian Processes (2011, methodology): “This idea was introduced to the machine learning audience by Boyle and Frean (2005).”
Efficient Multioutput Gaussian Processes through Variational Inducing Kernels (2010, methodology): “Using CPs for multi-output GPs was proposed by Higdon (2002) and introduced to the machine learning audience by Boyle and Frean (2005).”
Gaussian process regression with multiple response variables (2015, methodology): “Unlike the linear filtering method [2] where the covariance structure among different outputs is assumed to follow some specific forms, the proposed model is able to learn these dependencies from data, represented by the matrix B.”
Multi-output learning via spectral filtering (2012, methodology): “Starting from the work of Caruana (1997), related ideas have been developed in the context of regularization methods (Argyriou et al. 2008b; Jacob et al. 2008), Bayesian techniques—e.g. Gaussian processes (Boyle and Frean 2005; Chai et al. 2009; Alvarez et al. 2009), collaborative filtering…”
Remarks on multi-output Gaussian process regression (2018, methodology): “[57] developed a dependent GP model using multiple convolutions corresponding to different features of the outputs.”