• Corpus ID: 232076304

# Hierarchical Inducing Point Gaussian Process for Inter-domain Observations

@inproceedings{Wu2021HierarchicalIP,
title={Hierarchical Inducing Point Gaussian Process for Inter-domain Observations},
author={Luhuan Wu and Andrew Miller and Lauren Anderson and Geoff Pleiss and David M. Blei and John P. Cunningham},
booktitle={AISTATS},
year={2021}
}
• Published in AISTATS 28 February 2021
• Computer Science
We examine the general problem of interdomain Gaussian Processes (GPs): problems where the GP realization and the noisy observations of that realization lie on different domains. When the mapping between those domains is linear, such as integration or differentiation, inference is still closed form. However, many of the scaling and approximation techniques that our community has developed do not apply to this setting. In this work, we introduce the hierarchical inducing point GP (HIP-GP), a…
5 Citations

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## References

SHOWING 1-10 OF 44 REFERENCES
Inter-domain Gaussian Processes for Sparse Inference using Inducing Features
• Computer Science
NIPS
• 2009
A general inference framework for inter-domain Gaussian Processes (GPs) is presented and it is shown how previously existing models fit into this framework and will be used to develop two new sparse GP models.
Scalable Gaussian Processes with Grid-Structured Eigenfunctions (GP-GRIEF)
• Computer Science
ICML
• 2018
A kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in $\mathcal{O}(p)$ time and enables type-I or II Bayesian inference on large-scale datasets is introduced.
A Framework for Interdomain and Multioutput Gaussian Processes
• Computer Science
ArXiv
• 2020
This work presents a mathematical and software framework for scalable approximate inference in GPs, which combines interdomain approximations and multiple outputs, and provides a unified interface for many existing multioutput models, as well as more recent convolutional structures.
Sparse Orthogonal Variational Inference for Gaussian Processes
• Computer Science
AISTATS
• 2020
A new interpretation of sparse variational approximations for Gaussian processes using inducing points is introduced, which can lead to more scalable algorithms than previous methods and report state-of-the-art results on CIFAR-10 among purely GP-based models.
Scalable Gaussian Processes with Billions of Inducing Inputs via Tensor Train Decomposition
• Computer Science
AISTATS
• 2018
The key idea of theTT-GP is to use Tensor Train decomposition for variational parameters, which allows to train GPs with billions of inducing inputs and achieve state-of-the-art results on several benchmarks.
Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)
• Computer Science
ICML
• 2015
A new structured kernel interpolation (SKI) framework is introduced, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs) and naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability.
Exact Gaussian Processes on a Million Data Points
• Computer Science
NeurIPS
• 2019
A scalable approach for exact GPs is developed that leverages multi-GPU parallelization and methods like linear conjugate gradients, accessing the kernel matrix only through matrix multiplication, and is generally applicable, without constraints to grid data or specific kernel classes.
MCMC for Variationally Sparse Gaussian Processes
• Computer Science
NIPS
• 2015
A Hybrid Monte-Carlo sampling scheme which allows for a non-Gaussian approximation over the function values and covariance parameters simultaneously, with efficient computations based on inducing-point sparse GPs.
Thoughts on Massively Scalable Gaussian Processes
• Computer Science
ArXiv
• 2015
The MSGP framework enables the use of Gaussian processes on billions of datapoints, without requiring distributed inference, or severe assumptions, and reduces the standard GP learning and inference complexity to O(n), and the standard test point prediction complexity to \$O(1).
Gaussian Processes for Big Data
• Computer Science
UAI
• 2013
Stochastic variational inference for Gaussian process models is introduced and it is shown how GPs can be variationally decomposed to depend on a set of globally relevant inducing variables which factorize the model in the necessary manner to perform Variational inference.