Gaussian process (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Gaussian process" in English language version.

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acs.org

pubs.acs.org

Shanks, B. L.; Sullivan, H. W.; Shazed, A. R.; Hoepfner, M. P. (2024). "Accelerated Bayesian Inference for Molecular Simulations using Local Gaussian Process Surrogate Models". Journal of Chemical Theory and Computation. 20 (9). arXiv:2310.19108. doi:10.1021/acs.jctc.3c01358.

ams.org

mathscinet.ams.org

Ledoux, Michel (1996), "Isoperimetry and Gaussian analysis", in Dobrushin, Roland; Groeneboom, Piet; Ledoux, Michel (eds.), Lectures on Probability Theory and Statistics: Ecole d'Eté de Probabilités de Saint-Flour XXIV–1994, Lecture Notes in Mathematics, vol. 1648, Berlin: Springer, pp. 165–294, doi:10.1007/BFb0095676, ISBN 978-3-540-62055-6, MR 1600888
Adler, Robert J. (1990). An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Vol. 12. Hayward, California: Institute of Mathematical Statistics. ISBN 0-940600-17-X. JSTOR 4355563. MR 1088478. {{cite book}}: |journal= ignored (help)
Berman, Simeon M. (1992). "Review of: Adler 1990 'An introduction to continuity...'". Mathematical Reviews. MR 1088478.

arxiv.org

Azmoodeh, Ehsan; Sottinen, Tommi; Viitasaari, Lauri; Yazigi, Adil (2014). "Necessary and sufficient conditions for Hölder continuity of Gaussian processes". Statistics & Probability Letters. 94: 230–235. arXiv:1403.2215. doi:10.1016/j.spl.2014.07.030.
Jidling, Carl; Wahlström, Niklas; Wills, Adrian; Schön, Thomas B. (2017-09-19). "Linearly constrained Gaussian processes". arXiv:1703.00787 [stat.ML].
Chen, Zexun; Wang, Bo; Gorban, Alexander N. (2019). "Multivariate Gaussian and Student-t process regression for multi-output prediction". Neural Computing and Applications. 32 (8): 3005–3028. arXiv:1703.04455. doi:10.1007/s00521-019-04687-8.
Saves, Paul; Diouane, Youssef; Bartoli, Nathalie; Lefebvre, Thierry; Morlier, Joseph (2023). "A mixed-categorical correlation kernel for Gaussian process". Neurocomputing. 550: 126472. arXiv:2211.08262. doi:10.1016/j.neucom.2023.126472.
Griffiths, Ryan-Rhys (2022). Applications of Gaussian Processes at Extreme Lengthscales: From Molecules to Black Holes (PhD thesis). University of Cambridge. arXiv:2303.14291. doi:10.17863/CAM.93643.
Shanks, B. L.; Sullivan, H. W.; Shazed, A. R.; Hoepfner, M. P. (2024). "Accelerated Bayesian Inference for Molecular Simulations using Local Gaussian Process Surrogate Models". Journal of Chemical Theory and Computation. 20 (9). arXiv:2310.19108. doi:10.1021/acs.jctc.3c01358.
Novak, Roman; Xiao, Lechao; Hron, Jiri; Lee, Jaehoon; Alemi, Alexander A.; Sohl-Dickstein, Jascha; Schoenholz, Samuel S. (2020). "Neural Tangents: Fast and Easy Infinite Neural Networks in Python". International Conference on Learning Representations. arXiv:1912.02803.

books.google.com

Amos Lapidoth (8 February 2017). A Foundation in Digital Communication. Cambridge University Press. ISBN 978-1-107-17732-1.

cam.ac.uk

inference.phy.cam.ac.uk

MacKay, David J.C. (2003). Information Theory, Inference, and Learning Algorithms (PDF). Cambridge University Press. p. 540. ISBN 9780521642989. The probability distribution of a function $y(\mathbf {x} )$ is a Gaussian processes if for any finite selection of points $\mathbf {x} ^{(1)},\mathbf {x} ^{(2)},\ldots ,\mathbf {x} ^{(N)}$ , the density $P(y(\mathbf {x} ^{(1)}),y(\mathbf {x} ^{(2)}),\ldots ,y(\mathbf {x} ^{(N)}))$ is a Gaussian

doi.org

Kac, M.; Siegert, A.J.F (1947). "An Explicit Representation of a Stationary Gaussian Process". The Annals of Mathematical Statistics. 18 (3): 438–442. doi:10.1214/aoms/1177730391.
Seeger, Matthias (2004). "Gaussian Processes for Machine Learning". International Journal of Neural Systems. 14 (2): 69–104. CiteSeerX 10.1.1.71.1079. doi:10.1142/s0129065704001899. PMID 15112367. S2CID 52807317.
Dudley, R. M. (2010). "Sample Functions of the Gaussian Process". Selected Works of R.M. Dudley. Vol. 1. pp. 66–103. doi:10.1007/978-1-4419-5821-1_13. ISBN 978-1-4419-5820-4. {{cite book}}: |journal= ignored (help)
Ledoux, Michel (1996), "Isoperimetry and Gaussian analysis", in Dobrushin, Roland; Groeneboom, Piet; Ledoux, Michel (eds.), Lectures on Probability Theory and Statistics: Ecole d'Eté de Probabilités de Saint-Flour XXIV–1994, Lecture Notes in Mathematics, vol. 1648, Berlin: Springer, pp. 165–294, doi:10.1007/BFb0095676, ISBN 978-3-540-62055-6, MR 1600888
Dudley, R. M. (1967). "The sizes of compact subsets of Hilbert space and continuity of Gaussian processes". Journal of Functional Analysis. 1 (3): 290–330. doi:10.1016/0022-1236(67)90017-1.
Marcus, Michael B.; Shepp, Lawrence A. (1970). "Continuity of Gaussian processes". Transactions of the American Mathematical Society. 151 (2): 377–391. doi:10.1090/s0002-9947-1970-0264749-1. JSTOR 1995502.
Azmoodeh, Ehsan; Sottinen, Tommi; Viitasaari, Lauri; Yazigi, Adil (2014). "Necessary and sufficient conditions for Hölder continuity of Gaussian processes". Statistics & Probability Letters. 94: 230–235. arXiv:1403.2215. doi:10.1016/j.spl.2014.07.030.
Driscoll, Michael F. (1973). "The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process". Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete. 26 (4): 309–316. doi:10.1007/BF00534894. ISSN 0044-3719. S2CID 123348980.
Álvarez, Mauricio A.; Rosasco, Lorenzo; Lawrence, Neil D. (2012). "Kernels for vector-valued functions: A review" (PDF). Foundations and Trends in Machine Learning. 4 (3): 195–266. doi:10.1561/2200000036. S2CID 456491.
Chen, Zexun; Wang, Bo; Gorban, Alexander N. (2019). "Multivariate Gaussian and Student-t process regression for multi-output prediction". Neural Computing and Applications. 32 (8): 3005–3028. arXiv:1703.04455. doi:10.1007/s00521-019-04687-8.
Saves, Paul; Diouane, Youssef; Bartoli, Nathalie; Lefebvre, Thierry; Morlier, Joseph (2023). "A mixed-categorical correlation kernel for Gaussian process". Neurocomputing. 550: 126472. arXiv:2211.08262. doi:10.1016/j.neucom.2023.126472.
Platanios, Emmanouil A.; Chatzis, Sotirios P. (2014). "Gaussian Process-Mixture Conditional Heteroscedasticity". IEEE Transactions on Pattern Analysis and Machine Intelligence. 36 (5): 888–900. doi:10.1109/TPAMI.2013.183. PMID 26353224. S2CID 10424638.
Chatzis, Sotirios P. (2013). "A latent variable Gaussian process model with Pitman–Yor process priors for multiclass classification". Neurocomputing. 120: 482–489. doi:10.1016/j.neucom.2013.04.029.
Griffiths, Ryan-Rhys (2022). Applications of Gaussian Processes at Extreme Lengthscales: From Molecules to Black Holes (PhD thesis). University of Cambridge. arXiv:2303.14291. doi:10.17863/CAM.93643.
Shanks, B. L.; Sullivan, H. W.; Shazed, A. R.; Hoepfner, M. P. (2024). "Accelerated Bayesian Inference for Molecular Simulations using Local Gaussian Process Surrogate Models". Journal of Chemical Theory and Computation. 20 (9). arXiv:2310.19108. doi:10.1021/acs.jctc.3c01358.
Csato, L.; Opper, M. (2002). "Sparse on-line Gaussian processes". Neural Computation. 14 (3): 641–668. CiteSeerX 10.1.1.335.9713. doi:10.1162/089976602317250933. PMID 11860686. S2CID 11375333.
Lee, Se Yoon; Mallick, Bani (2021). "Bayesian Hierarchical Modeling: Application Towards Production Results in the Eagle Ford Shale of South Texas". Sankhya B. 84: 1–43. doi:10.1007/s13571-020-00245-8.
Ranftl, Sascha; Melito, Gian Marco; Badeli, Vahid; Reinbacher-Köstinger, Alice; Ellermann, Katrin; von der Linden, Wolfgang (2019-12-31). "Bayesian Uncertainty Quantification with Multi-Fidelity Data and Gaussian Processes for Impedance Cardiography of Aortic Dissection". Entropy. 22 (1): 58. Bibcode:2019Entrp..22...58R. doi:10.3390/e22010058. ISSN 1099-4300. PMC 7516489. PMID 33285833.

gaussianprocess.org

Rasmussen, C.E.; Williams, C.K.I (2006). Gaussian Processes for Machine Learning. MIT Press. ISBN 978-0-262-18253-9.

harvard.edu

ui.adsabs.harvard.edu

Ranftl, Sascha; Melito, Gian Marco; Badeli, Vahid; Reinbacher-Köstinger, Alice; Ellermann, Katrin; von der Linden, Wolfgang (2019-12-31). "Bayesian Uncertainty Quantification with Multi-Fidelity Data and Gaussian Processes for Impedance Cardiography of Aortic Dissection". Entropy. 22 (1): 58. Bibcode:2019Entrp..22...58R. doi:10.3390/e22010058. ISSN 1099-4300. PMC 7516489. PMID 33285833.

jstor.org

Adler, Robert J. (1990). An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Vol. 12. Hayward, California: Institute of Mathematical Statistics. ISBN 0-940600-17-X. JSTOR 4355563. MR 1088478. {{cite book}}: |journal= ignored (help)
Marcus, Michael B.; Shepp, Lawrence A. (1970). "Continuity of Gaussian processes". Transactions of the American Mathematical Society. 151 (2): 377–391. doi:10.1090/s0002-9947-1970-0264749-1. JSTOR 1995502.

mathunion.org

Dudley, R. M. (1975). "The Gaussian process and how to approach it" (PDF). Proceedings of the International Congress of Mathematicians. Vol. 2. pp. 143–146.

nih.gov

pubmed.ncbi.nlm.nih.gov

Seeger, Matthias (2004). "Gaussian Processes for Machine Learning". International Journal of Neural Systems. 14 (2): 69–104. CiteSeerX 10.1.1.71.1079. doi:10.1142/s0129065704001899. PMID 15112367. S2CID 52807317.
Platanios, Emmanouil A.; Chatzis, Sotirios P. (2014). "Gaussian Process-Mixture Conditional Heteroscedasticity". IEEE Transactions on Pattern Analysis and Machine Intelligence. 36 (5): 888–900. doi:10.1109/TPAMI.2013.183. PMID 26353224. S2CID 10424638.
Csato, L.; Opper, M. (2002). "Sparse on-line Gaussian processes". Neural Computation. 14 (3): 641–668. CiteSeerX 10.1.1.335.9713. doi:10.1162/089976602317250933. PMID 11860686. S2CID 11375333.
Ranftl, Sascha; Melito, Gian Marco; Badeli, Vahid; Reinbacher-Köstinger, Alice; Ellermann, Katrin; von der Linden, Wolfgang (2019-12-31). "Bayesian Uncertainty Quantification with Multi-Fidelity Data and Gaussian Processes for Impedance Cardiography of Aortic Dissection". Entropy. 22 (1): 58. Bibcode:2019Entrp..22...58R. doi:10.3390/e22010058. ISSN 1099-4300. PMC 7516489. PMID 33285833.

ncbi.nlm.nih.gov

Ranftl, Sascha; Melito, Gian Marco; Badeli, Vahid; Reinbacher-Köstinger, Alice; Ellermann, Katrin; von der Linden, Wolfgang (2019-12-31). "Bayesian Uncertainty Quantification with Multi-Fidelity Data and Gaussian Processes for Impedance Cardiography of Aortic Dissection". Entropy. 22 (1): 58. Bibcode:2019Entrp..22...58R. doi:10.3390/e22010058. ISSN 1099-4300. PMC 7516489. PMID 33285833.

projecteuclid.org

Dudley, R. M. (2010). "Sample Functions of the Gaussian Process". Selected Works of R.M. Dudley. Vol. 1. pp. 66–103. doi:10.1007/978-1-4419-5821-1_13. ISBN 978-1-4419-5820-4. {{cite book}}: |journal= ignored (help)
Marcus, M.B.; Shepp, Lawrence A. (1972). "Sample behavior of Gaussian processes". Proceedings of the sixth Berkeley symposium on mathematical statistics and probability, vol. II: probability theory. Vol. 6. Univ. California, Berkeley. pp. 423–441.

psu.edu

citeseerx.ist.psu.edu

Seeger, Matthias (2004). "Gaussian Processes for Machine Learning". International Journal of Neural Systems. 14 (2): 69–104. CiteSeerX 10.1.1.71.1079. doi:10.1142/s0129065704001899. PMID 15112367. S2CID 52807317.
Smola, A.J.; Schoellkopf, B. (2000). "Sparse greedy matrix approximation for machine learning". Proceedings of the Seventeenth International Conference on Machine Learning: 911–918. CiteSeerX 10.1.1.43.3153.
Csato, L.; Opper, M. (2002). "Sparse on-line Gaussian processes". Neural Computation. 14 (3): 641–668. CiteSeerX 10.1.1.335.9713. doi:10.1162/089976602317250933. PMID 11860686. S2CID 11375333.

scikit-learn.org

The documentation for scikit-learn also has similar examples.

semanticscholar.org

api.semanticscholar.org

Seeger, Matthias (2004). "Gaussian Processes for Machine Learning". International Journal of Neural Systems. 14 (2): 69–104. CiteSeerX 10.1.1.71.1079. doi:10.1142/s0129065704001899. PMID 15112367. S2CID 52807317.
Driscoll, Michael F. (1973). "The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process". Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete. 26 (4): 309–316. doi:10.1007/BF00534894. ISSN 0044-3719. S2CID 123348980.
Álvarez, Mauricio A.; Rosasco, Lorenzo; Lawrence, Neil D. (2012). "Kernels for vector-valued functions: A review" (PDF). Foundations and Trends in Machine Learning. 4 (3): 195–266. doi:10.1561/2200000036. S2CID 456491.
Platanios, Emmanouil A.; Chatzis, Sotirios P. (2014). "Gaussian Process-Mixture Conditional Heteroscedasticity". IEEE Transactions on Pattern Analysis and Machine Intelligence. 36 (5): 888–900. doi:10.1109/TPAMI.2013.183. PMID 26353224. S2CID 10424638.
Csato, L.; Opper, M. (2002). "Sparse on-line Gaussian processes". Neural Computation. 14 (3): 641–668. CiteSeerX 10.1.1.335.9713. doi:10.1162/089976602317250933. PMID 11860686. S2CID 11375333.

springer.com

Talagrand, Michel (2014). Upper and lower bounds for stochastic processes: modern methods and classical problems. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. Springer, Heidelberg. ISBN 978-3-642-54074-5.

ucl.ac.uk

web4.cs.ucl.ac.uk

Barber, David (2012). Bayesian Reasoning and Machine Learning. Cambridge University Press. ISBN 978-0-521-51814-7.

ufl.edu

cnel.ufl.edu

Liu, W.; Principe, J.C.; Haykin, S. (2010). Kernel Adaptive Filtering: A Comprehensive Introduction. John Wiley. ISBN 978-0-470-44753-6. Archived from the original on 2016-03-04. Retrieved 2010-03-26.

web.archive.org

Liu, W.; Principe, J.C.; Haykin, S. (2010). Kernel Adaptive Filtering: A Comprehensive Introduction. John Wiley. ISBN 978-0-470-44753-6. Archived from the original on 2016-03-04. Retrieved 2010-03-26.

whiterose.ac.uk

eprints.whiterose.ac.uk

Álvarez, Mauricio A.; Rosasco, Lorenzo; Lawrence, Neil D. (2012). "Kernels for vector-valued functions: A review" (PDF). Foundations and Trends in Machine Learning. 4 (3): 195–266. doi:10.1561/2200000036. S2CID 456491.

worldcat.org

search.worldcat.org

Driscoll, Michael F. (1973). "The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process". Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete. 26 (4): 309–316. doi:10.1007/BF00534894. ISSN 0044-3719. S2CID 123348980.
Ranftl, Sascha; Melito, Gian Marco; Badeli, Vahid; Reinbacher-Köstinger, Alice; Ellermann, Katrin; von der Linden, Wolfgang (2019-12-31). "Bayesian Uncertainty Quantification with Multi-Fidelity Data and Gaussian Processes for Impedance Cardiography of Aortic Dissection". Entropy. 22 (1): 58. Bibcode:2019Entrp..22...58R. doi:10.3390/e22010058. ISSN 1099-4300. PMC 7516489. PMID 33285833.