Sparse Convolved Gaussian Processes for Multi-output Regression

By Mauricio A Álvarez, Neil D. Lawrence. 2008

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Citations in the corpus

Kernels for Vector-Valued Functions: a Review (2011, methodology): “In [2], the authors show how through making speciﬁc conditional independence assumptions, inspired by the model structure in the process convolution formulation (for which the LMC is a special case), it is possible to arrive at a series of efﬁcient approximations that represent the covariance…”
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).”
Continual Multi-task Gaussian Processes (2019, methodology): “Given D output functions F and Q latent functions U , we build our joint prior to be p ( F , U ) = p ( F|U ) p ( U| ψ ) , where again, we use ψ to refer the subset of hyperparameters involved in the MOGP prior.”
Latent Force Models (2009, methodology): “We are not the first to suggest the use of convolution processes for multi-output regression, they were proposed by (Higdon, 2002) and built on by (Boyle and Frean, 2005) — the ideas in these papers have also recently been made more computationally practical through sparse approximations suggested b”
A survey of adaptive sampling for global metamodeling in support of simulation-based complex engineering design (2017, methodology): “Some commonly used symmetric multi-response modeling approaches include, for example, the artificial neural networks (ANNs) that are extended to support multi-response by defining how inputs are shared across responses (Caruana 1995; Collobert and Weston 2008), the multi-response Gaussian process fr”
Incremental Variational Sparse Gaussian Process Regression (2016, background): “� This general maximum likelihood scheme for ﬁnding the inducing points is adopted with variations in [23, 26, 8, 2].”
Online Sparse Multi-Output Gaussian Process Regression and Learning (2019, background): “In [28] and [29], the sparse approximation [35] was integrated into the convolved multi-”
Computationally Efficient Convolved Multiple Output Gaussian Processes (2011, methodology): “We show how through making specific conditional independence assumptions, inspired by the model structure (Álvarez and Lawrence, 2009), we arrive at a efficient approximation similar in form to the partially independent training conditional model (PITC, see Quiñonero-Candela and Rasmussen, 2005).”
Efficient Multioutput Gaussian Processes through Variational Inducing Kernels (2010, methodology): “Before we propose our variational sparse inference method for multioutput GP regression in Section 4, we review the sparse method proposed by Álvarez and Lawrence (2009).”
Inferring solutions of differential equations using noisy multi-fidelity data (2016, background): “An equally important direction involves solving systems of linear partial differential equations, which can be addressed using multi-output GP regression [26, 27].”
Remarks on multi-output Gaussian process regression (2018, methodology): “Finally, to reduce the computational complexity of calculating K−1 M for cases with large-scale training data, some sparse approximations that use m (m N) inducing points to approximate the large covariance matrix, or use the variational inference to approximate the lower bound of p(y), have been ap”
It is all in the noise: Efficient multi-task Gaussian process inference with structured residuals (2013, methodology): “In contrast to existing work extending Gaussian process multi task models by deﬁning more complex covariance structures [2, 9, 8], our model utilizes the gradient of the marginal likelihood for parameter estimation and does not require expected maximization, variational approximation or MCMC…”
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].”