# Parametric Gaussian process regression for big data

@article{Raissi2019ParametricGP, title={Parametric Gaussian process regression for big data}, author={Maziar Raissi}, journal={Computational Mechanics}, year={2019}, pages={1-8} }

This work introduces the concept of parametric Gaussian processes (PGP), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. The resulting framework is capable of encoding massive amount of data into a small number of “hypothetical” data points. Moreover, parametric Gaussian processes are well aware of their imperfections and are capable of properly quantifying the uncertainty in their predictions associated with such limitations. The effectiveness…

## 27 Citations

Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2018

The method circumvents the need for spatial discretization of the differential operators by proper placement of Gaussian process priors and is an attempt to construct structured and data-efficient learning machines, which are explicitly informed by the underlying physics that possibly generated the observed data.

Forecasting of Commercial Sales with Large Scale Gaussian Processes

- Computer Science2017 IEEE International Conference on Data Mining Workshops (ICDMW)
- 2017

This paper argues that there has not been enough discussion in the field of applications of Gaussian Process for the fast moving consumer goods industry, and shows value of this type of models as a decision-making tool for management.

Hidden physics models: Machine learning of nonlinear partial differential equations

- Computer ScienceJ. Comput. Phys.
- 2018

Machine Learning of Space-Fractional Differential Equations

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2019

This work provides a user-friendly and feasible way to perform fractional derivatives of kernels, via a unified set of d-dimensional Fourier integral formulas amenable to generalized Gauss-Laguerre quadrature.

The pitfalls of using Gaussian Process Regression for normative modeling

- Computer SciencebioRxiv
- 2021

It is shown that the uncertainty directly from Gaussian Processes Regression is irrelevant to the cohort heterogeneity in general.

The pitfalls of using Gaussian Process Regression for normative modeling

- Computer SciencePloS one
- 2021

It is shown that the uncertainty directly from Gaussian Processes Regression is irrelevant to the cohort heterogeneity in general.

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

- Computer ScienceJ. Mach. Learn. Res.
- 2018

This work puts forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time by approximate the unknown solution as well as the nonlinear dynamics by two deep neural networks.

Machine Learning of Space-Fractional Differential Equations | SIAM Journal on Scientific Computing | Vol. 41, No. 4 | Society for Industrial and Applied Mathematics

- Computer Science, Mathematics
- 2019

The proposed method has several benefits compared to previous works on data-driven discovery of differential equations; the user is not required to assume a “dictionary” of derivatives of various orders and directly controls the parsimony of the models being discovered.

Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations

- Computer Science, MathematicsArXiv
- 2018

This work approximate the unknown solution by a deep neural network which essentially enables the author to benefit from the merits of automatic differentiation in partial differential equations.

Shared Gaussian Process Latent Variable Model for Incomplete Multiview Clustering

- Computer ScienceIEEE Transactions on Cybernetics
- 2020

A shared Gaussian process (GP) latent variable model for incomplete multiview clustering to gain the merits of two worlds by learning a set of intentionally aligned representative auxiliary points in individual views jointly to not only compensate for missing instances but also implement the group-level constraint.

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