Gaussian process regression
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Bayesian non-parametric regression that gives predictions with uncertainty; also the surrogate in Bayesian optimisation.
LaTeX: f \sim \mathcal{GP}\big(m(x),\ k(x, x')\big),\quad k(x, x') = \sigma^2 \exp\!\left(-\frac{\lVert x - x' \rVert^2}{2\ell^2}\right)
Variables and notation#
f is a random function with mean m and covariance kernel k; sigma² is signal variance, ell length scale and x,x' inputs; GP denotes a Gaussian process.
Worked example#
For sigma²=1,ell=2 and inputs one unit apart, covariance=exp(−1/8)≈0.882497. At identical inputs it equals 1.
Related methods and when to use them#
GP regression gives a distribution over functions; ordinary linear regression restricts the function form. This equation specifies a prior/kernel, not the full posterior; observation noise and training-data conditioning are also needed.
Sources and further reading#
Key findings#
- Gaussian process regression was mentioned in 27 papers in the last 30 days (2026-10-07 to 2026-11-05), ranking #56 of the 248 equations and models mentioned.
- By journal category: Statistics (15), AI (6), Operations Research (3), Finance (2) and Economics (1).
- Most of them appeared in Journal of Multivariate Analysis (4), Computational Statistics & Data Analysis (2) and Spatial Statistics (2).
- Often mentioned together with Markov chain Monte Carlo (Metropolis-Hastings) (6), Random forest (4) and LASSO (3).
- Datasets named in the same papers: American Community Survey (2), World Development Indicators (World Bank) (1) and German Credit (UCI Statlog) (1).
- From Nov 2023 to Oct 2026, 1,340 archived papers mentioned Gaussian process regression in their title, abstract or keywords (the search of earlier months' full texts is still under way), most of them in Jul 2025 (54).
- From 2017 to 2026 (so far), Gaussian process regression was mentioned in 2,117 papers in the tracked journals, most of them in AI (959), statistics (626) and operations research (333).
- 423 of them were published in 2025, against 70 in 2017.
- Since 2023, the institutions with the most of these papers were Centre National de la Recherche Scientifique (37), Tsinghua University (25) and Chinese Academy of Sciences (20).
- The journals publishing most of them were Statistics and Computing (82), Spatial Statistics (65) and Artificial Intelligence Review (63).
- The most-cited of them is “A Comprehensive Survey of Continual Learning: Theory, Method and Application” (IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024), with 1,114 citations.
Mentions over 36 months#
| Trend | Nov 23–Oct 24 | Nov 24–Oct 25 | Nov 25–Oct 26 | 36 months |
|---|---|---|---|---|
| 461 | 437 | 442 | 1,340 |
Papers per year#
20172026 (so far)
| Category | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | 2025 | 2026 (so far) |
|---|---|---|---|---|---|---|---|---|---|---|
| AI | 29 | 43 | 30 | 49 | 59 | 81 | 101 | 249 | 180 | 138 |
| Statistics | 28 | 44 | 33 | 41 | 37 | 43 | 61 | 94 | 116 | 129 |
| Operations Research | 8 | 14 | 15 | 13 | 19 | 22 | 35 | 71 | 75 | 61 |
| Economics | 4 | 3 | 1 | 3 | 1 | 6 | 8 | 23 | 26 | 33 |
| Finance | 1 | 2 | 2 | 1 | 0 | 5 | 1 | 15 | 12 | 10 |
| Information Systems | 0 | 1 | 0 | 0 | 0 | 0 | 2 | 2 | 5 | 2 |
| Management | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 4 | 3 | 3 |
| Health Economics and Policy | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 2 | 3 | 1 |
| Higher Education and Research | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 2 |
| Marketing | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| Tourism and Hospitality | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 |
| All categories | 70 | 108 | 82 | 108 | 116 | 157 | 208 | 465 | 423 | 380 |
Where the papers come from#
| # | Journal | Papers |
|---|---|---|
| 1 | Statistics and Computing | 82 |
| 2 | Spatial Statistics | 65 |
| 3 | Artificial Intelligence Review | 63 |
| 4 | Expert Systems with Applications | 62 |
| 5 | Neural Computing and Applications | 60 |
| 6 | IEEE Transactions on Pattern Analysis and Machine Intelligence | 53 |
| 7 | Machine Learning | 46 |
| 8 | Transportation Research Part C Emerging Technologies | 41 |
| 9 | Knowledge-Based Systems | 40 |
| 10 | IEEE Transactions on Neural Networks and Learning Systems | 32 |
| # | Institution | Papers |
|---|---|---|
| 1 | Centre National de la Recherche Scientifique | 37 |
| 2 | Tsinghua University | 25 |
| 3 | Chinese Academy of Sciences | 20 |
| 4 | Hong Kong Polytechnic University | 18 |
| 5 | Tongji University | 18 |
| 6 | Central South University | 17 |
| 7 | National University of Singapore | 17 |
| 8 | King Abdullah University of Science and Technology | 15 |
| 9 | North Carolina State University | 15 |
| 10 | City University of Hong Kong | 14 |
| # | Country | Papers |
|---|---|---|
| 1 | China | 389 |
| 2 | United States | 298 |
| 3 | United Kingdom | 180 |
| 4 | Germany | 119 |
| 5 | France | 100 |
| 6 | Italy | 96 |
| 7 | Spain | 77 |
| 8 | Australia | 75 |
| 9 | Canada | 73 |
| 10 | Japan | 50 |
| # | Keyword | Papers |
|---|---|---|
| 1 | Gaussian processes | 124 |
| 2 | Gaussian process regression | 107 |
| 3 | uncertainty quantification | 78 |
| 4 | Bayesian optimization | 56 |
| 5 | surrogate models | 47 |
| 6 | computational efficiency | 40 |
| 7 | hyperparameter optimization | 40 |
| 8 | Kriging surrogate model | 33 |
| 9 | kriging | 32 |
| 10 | multi-objective optimization | 32 |
Most-cited papers#
Cite this page
Scholar4AI. (2026). Gaussian process regression. Journal and Conference Research Rankings. Retrieved November 5, 2026, from https://scholar4ai.com/equations/gaussian-process-regression
@misc{scholar4ai-equations-gaussian-process-regression,
author = {{Scholar4AI}},
title = {Gaussian process regression},
year = {2026},
howpublished = {\url{https://scholar4ai.com/equations/gaussian-process-regression}},
urldate = {2026-11-05},
note = {Journal and Conference Research Rankings; data from OpenAlex (CC0); licensed CC BY-NC 4.0}
}