Computationally Efficient Convolved Multiple Output Gaussian Processes

By Mauricio A Álvarez, Neil D. Lawrence. 2011

346 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Probabilistic & Bayesian Methods

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Citations in the corpus

Neural Ordinary Differential Equations (2018, neutral): “Missing data can be addressed using generative time-series models (Álvarez and Lawrence, 2011; Futoma et al., 2017; Mei and Eisner, 2017; Soleimani et al., 2017a) or data imputation (Che et al., 2018).”
Gaussian Processes for Big Data (2013, methodology): “The ability to increase the number of inducing variables and the applicability to unlimited data make our method suitable for multiple output GPs [´Alvarez and Lawrence, 2011].”
Gaussian Process Regression Networks (2011, methodology): “We follow Alvarez and Lawrence (2011) and reverse training and testing replicas to create SET 2 .”
Gaussian process regression for forecasting battery state of health (2017, background): “…we note various diﬀerent eﬃcient/approximate schemes have been proposed in the literature, based on approximating input data with pseudo points [24], exploiting grid structure [25] and exploiting the recursivity of the estimation problem in online settings [22, 26, 27]; and these could be used…”
Hidden Parameter Markov Decision Processes: A Semiparametric Regression Approach for Discovering Latent Task Parametrizations (2013, background): “[23, 14, 24]), though most of these are focused on learning a convolution kernel to model several related outputs on a single task, rather than parameterizing several related tasks.”
GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation (2014, background): “A more realistic assumption is a full covariance Gaussian process such as the convolution processes of [12, 7, 1].”
Learning Treatment-Response Models from Multivariate Longitudinal Data (2017, methodology): “The structure used in the random-effects component is similar to the linear models of coregionalization (Seeger et al., 2005; ´Alvarez and Lawrence, 2009), which is used to jointly model multiple correlated signals.”
Recent Advances in Bayesian Optimization (2022, methodology): “In [213], unknown functions with varying idelities are jointly modeled as a convolved Gaussian process [5], then a multi-output random feature approximation is introduced to calculate PES.”
Remarks on multi-output Gaussian process regression (2018, methodology): “[56] pointed out that if we take the smoothing kernel to be the Dirac delta function, i.”
Multitask Gaussian Processes for Multivariate Physiological Time-Series Analysis (2015, methodology): “[23], some of these techniques have been used to investigate sparse MTGPs which reduce the complexity to O(mn ñ2).”
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].”
Scalable Inference for Gaussian Process Models with Black-Box Likelihoods (2015, methodology): “The former (multiple output problem) has been addressed, notably, by [19] and [20] using the convolution process formalism.”
Sparse Multi-Output Gaussian Processes for Medical Time Series Prediction (2017, background): “Convolution processes (CPs) have also been adapted to model multiple correlated outputs through the convolution of smooth kernels and latent processes (Álvarez and Lawrence, 2011).”