Learning spatial patterns with variational Gaussian processes: Regression
A variational Gaussian process (VGP) model specialized in spatial data is introduced, capitalizing on recent advances in the machine learning field. The model is modular and customizable, being capable of handling different assumptions about the data. This work focusses on multivariate robust regres...
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| Published in | Computers & geosciences Vol. 161; p. 105056 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.04.2022
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| Abstract | A variational Gaussian process (VGP) model specialized in spatial data is introduced, capitalizing on recent advances in the machine learning field. The model is modular and customizable, being capable of handling different assumptions about the data. This work focusses on multivariate robust regression, using an adaptation of the ε-insensitive loss function. The VGP possibilitates end-to-end modeling: normal score transform, detection of the spatial pattern, and prediction. A methodology to deal with large datasets is presented. An open-source implementation is available.
•A variational Gaussian process model specialized in spatial data.•Stochastic variational inference is capable of handling large datasets.•Different models available as combinations of latent variables and likelihoods.•Robust multivariate regression with non-Gaussian marginals. |
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| AbstractList | A variational Gaussian process (VGP) model specialized in spatial data is introduced, capitalizing on recent advances in the machine learning field. The model is modular and customizable, being capable of handling different assumptions about the data. This work focusses on multivariate robust regression, using an adaptation of the ε-insensitive loss function. The VGP possibilitates end-to-end modeling: normal score transform, detection of the spatial pattern, and prediction. A methodology to deal with large datasets is presented. An open-source implementation is available.
•A variational Gaussian process model specialized in spatial data.•Stochastic variational inference is capable of handling large datasets.•Different models available as combinations of latent variables and likelihoods.•Robust multivariate regression with non-Gaussian marginals. |
| ArticleNumber | 105056 |
| Author | Gonçalves, Ítalo Gomes Guadagnin, Felipe Cordova, Diogo Peixoto |
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| Cites_doi | 10.1038/s41467-020-19160-7 10.1162/neco.2008.08-07-592 10.1080/01621459.2015.1044091 10.18637/jss.v063.i09 10.1007/s13253-020-00401-7 10.1016/j.asr.2019.11.011 10.1080/01621459.2017.1285773 10.1023/A:1012489924661 10.1007/s11004-012-9434-1 10.1016/j.neunet.2019.06.012 10.1007/s11222-017-9766-2 10.1016/j.cageo.2004.03.012 10.1016/j.cageo.2018.07.011 10.1080/01621459.2011.646928 10.1214/17-BA1056R 10.1214/19-STS755 |
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| References | Blei, Kucukelbir, McAuliffe (b4) 2017; 112 Vapnik (b39) 1995 Tresp (b38) 2001 Cohen, S., Mbuvha, R., Marwala, T., Deisenroth, M.P., 2020. Healing products of Gaussian process experts. In: Proceedings of the 37th International Conference on Machine Learning. Salimbeni, H., Deisenroth, M., 2017. Doubly stochastic variational inference for deep Gaussian processes. In: 31st Conference on Neural Information Processing Systems, NIPS 2017. Long Beach, CA, USA. Chilès, Delfiner (b7) 1999 Damianou, Lawrence (b11) 2013; vol. 31 Padoan, Bevilacqua (b28) 2015; 63 URL Burt, D.R., Rasmussen, C.E., Van Der Wilk, M., 2019. Rates of convergence for sparse variational Gaussian process regression. In: 36th International Conference on Machine Learning. Long Beach, California, p. 10. Gonçalves, Echer, Frigo (b16) 2020; 65 Abadi, Agarwal, Barham, Brevdo, Chen, Citro, Corrado, Davis, Dean, Devin, Ghemawat, Goodfellow, Harp, Irving, Isard, Jia, Jozefowicz, Kaiser, Kudlur, Levenberg, Mané, Monga, Moore, Murray, Olah, Schuster, Shlens, Steiner, Sutskever, Talwar, Tucker, Vanhoucke, Vasudevan, Viégas, Vinyals, Warden, Wattenberg, Wicke, Yu, Zheng (b1) 2015 Kingma, Ba (b23) 2015 Rullière, Durrande, Bachoc, Chevalier (b32) 2018 Bevilacqua, Gaetan, Mateu, Porcu (b3) 2012; 107 Hegde, P., Heinonen, M., Kaski, S., 2018. Variational zero-inflated Gaussian processes with sparse kernels. In: Conference on Uncertainty in Artificial Intelligence. Monterey, California, USA. Opper, Archambeau (b27) 2009; 21 Banerjee (b2) 2017; 12 Nguyen, Bonilla (b26) 2013; 31 Quiñonero Candela, Rasmussen, Herbrich (b6) 2005; 6 Hensman, Sheffield, Fusi, Lawrence (b20) 2013 Sollich (b35) 2002; 46 Dunlop, Girolami, Stuart, Teckentrup (b15) 2018; 19 Trapp, Peharz, Pernkopf, Rasmussen (b37) 2019 Cressie (b10) 1991 Desassis, Renard (b13) 2013; 45 Crameri, Shephard, Heron (b9) 2020; 11 Goovaerts (b17) 1997 Diggle, Ribeiro (b14) 2007 Rios, Tobar (b31) 2019; 118 Titsias (b36) 2009; vol. 5 Williams, Seeger (b40) 2000 , Katzfuss, Guinness, Gong, Zilber (b22) 2020; 25 . Pebesma (b29) 2004; 30 Datta, Banerjee, Finley, Gelfand (b12) 2016; 111 Moreno-Muñoz, P., Artés-Rodríguez, A., Álvarez, M.A., 2018. Heterogeneous multi-output Gaussian process prediction. In: Advances in Neural Information Processing Systems. Montreal, pp. 6711–6720. Wilson, A.G., Hu, Z., Salakhutdinov, R., Xing, E.P., 2016. Stochastic variational deep kernel learning. In: 29th Conference on Neural Information Processing Systems, NIPS 2016. Barcelona, Spain. Snelson, Rasmussen, Ghahramani (b34) 2004; 16 Hensman, Matthews, Ghahramani (b19) 2015; 38 Rasmussen, Williams (b30) 2006 Katzfuss, Guinness (b21) 2021; 36 Li, Zhang, Clarke, Liu, Zhu (b24) 2018; 120 Abadi (10.1016/j.cageo.2022.105056_b1) 2015 10.1016/j.cageo.2022.105056_b8 10.1016/j.cageo.2022.105056_b5 Kingma (10.1016/j.cageo.2022.105056_b23) 2015 Nguyen (10.1016/j.cageo.2022.105056_b26) 2013; 31 Bevilacqua (10.1016/j.cageo.2022.105056_b3) 2012; 107 Opper (10.1016/j.cageo.2022.105056_b27) 2009; 21 Blei (10.1016/j.cageo.2022.105056_b4) 2017; 112 Williams (10.1016/j.cageo.2022.105056_b40) 2000 Quiñonero Candela (10.1016/j.cageo.2022.105056_b6) 2005; 6 Vapnik (10.1016/j.cageo.2022.105056_b39) 1995 Sollich (10.1016/j.cageo.2022.105056_b35) 2002; 46 Tresp (10.1016/j.cageo.2022.105056_b38) 2001 Hensman (10.1016/j.cageo.2022.105056_b20) 2013 10.1016/j.cageo.2022.105056_b18 Li (10.1016/j.cageo.2022.105056_b24) 2018; 120 Datta (10.1016/j.cageo.2022.105056_b12) 2016; 111 Gonçalves (10.1016/j.cageo.2022.105056_b16) 2020; 65 10.1016/j.cageo.2022.105056_b33 Padoan (10.1016/j.cageo.2022.105056_b28) 2015; 63 Desassis (10.1016/j.cageo.2022.105056_b13) 2013; 45 Cressie (10.1016/j.cageo.2022.105056_b10) 1991 Trapp (10.1016/j.cageo.2022.105056_b37) 2019 Banerjee (10.1016/j.cageo.2022.105056_b2) 2017; 12 Snelson (10.1016/j.cageo.2022.105056_b34) 2004; 16 Pebesma (10.1016/j.cageo.2022.105056_b29) 2004; 30 Dunlop (10.1016/j.cageo.2022.105056_b15) 2018; 19 Hensman (10.1016/j.cageo.2022.105056_b19) 2015; 38 Rasmussen (10.1016/j.cageo.2022.105056_b30) 2006 Rullière (10.1016/j.cageo.2022.105056_b32) 2018 Diggle (10.1016/j.cageo.2022.105056_b14) 2007 Titsias (10.1016/j.cageo.2022.105056_b36) 2009; vol. 5 Katzfuss (10.1016/j.cageo.2022.105056_b21) 2021; 36 Damianou (10.1016/j.cageo.2022.105056_b11) 2013; vol. 31 Rios (10.1016/j.cageo.2022.105056_b31) 2019; 118 10.1016/j.cageo.2022.105056_b41 Chilès (10.1016/j.cageo.2022.105056_b7) 1999 Crameri (10.1016/j.cageo.2022.105056_b9) 2020; 11 Goovaerts (10.1016/j.cageo.2022.105056_b17) 1997 Katzfuss (10.1016/j.cageo.2022.105056_b22) 2020; 25 10.1016/j.cageo.2022.105056_b25 |
| References_xml | – volume: 16 start-page: 337 year: 2004 end-page: 344 ident: b34 article-title: Warped Gaussian processes publication-title: Adv. Neural Inf. Proc. Syst. contributor: fullname: Ghahramani – start-page: 483 year: 1997 ident: b17 article-title: Geoestatistics for Natural Resources Evaluation contributor: fullname: Goovaerts – year: 2015 ident: b23 article-title: Adam: A method for stochastic optimization publication-title: 3rd International Conference on Learning Representations, ICLR 2015 contributor: fullname: Ba – volume: 21 start-page: 786 year: 2009 end-page: 792 ident: b27 article-title: The variational gaussian approximation revisited publication-title: Neural Comput. contributor: fullname: Archambeau – start-page: 266 year: 2006 ident: b30 article-title: Gaussian Processes for Machine Learning contributor: fullname: Williams – volume: 11 start-page: 1 year: 2020 end-page: 10 ident: b9 article-title: The misuse of colour in science communication publication-title: Nature Commun. contributor: fullname: Heron – volume: 46 start-page: 21 year: 2002 end-page: 52 ident: b35 article-title: Bayesian methods for support vector machines: Evidence and predictive class probabilities publication-title: Mach. Learn. contributor: fullname: Sollich – volume: 107 start-page: 268 year: 2012 end-page: 280 ident: b3 article-title: Estimating space and space-time covariance functions for large data sets: A weighted composite likelihood approach publication-title: J. Amer. Statist. Assoc. contributor: fullname: Porcu – volume: 65 start-page: 677 year: 2020 end-page: 683 ident: b16 article-title: Sunspot cycle prediction using warped Gaussian process regression publication-title: Adv. Space Res. contributor: fullname: Frigo – start-page: 189 year: 1995 ident: b39 article-title: The Nature of Statistical Learning Theory contributor: fullname: Vapnik – volume: 120 start-page: 48 year: 2018 end-page: 59 ident: b24 article-title: An automatic variogram modeling method with high reliability fitness and estimates publication-title: Comput. Geosci. contributor: fullname: Zhu – start-page: 232 year: 2007 ident: b14 article-title: Model-Based Geostatistics contributor: fullname: Ribeiro – volume: vol. 5 start-page: 567 year: 2009 end-page: 574 ident: b36 article-title: Variational learning of inducing variables in sparse Gaussian processes publication-title: Aistats contributor: fullname: Titsias – volume: 6 start-page: 1935 year: 2005 end-page: 1959 ident: b6 article-title: A unifying view of sparse approximate Gaussian process regression publication-title: J. Mach. Learn. Res. contributor: fullname: Herbrich – start-page: 695 year: 1999 ident: b7 article-title: Geostatistics: Modeling Spatial Uncertainty contributor: fullname: Delfiner – volume: 25 start-page: 383 year: 2020 end-page: 414 ident: b22 article-title: Vecchia approximations of Gaussian-process predictions publication-title: J. Agric. Biol. Environ. Stat. contributor: fullname: Zilber – start-page: 654 year: 2001 end-page: 660 ident: b38 article-title: Mixtures of Gaussian processes publication-title: Adv. Neural Inf. Process. Syst. contributor: fullname: Tresp – volume: 19 start-page: 1 year: 2018 end-page: 46 ident: b15 article-title: How deep are deep Gaussian processes? publication-title: J. Mach. Learn. Res. contributor: fullname: Teckentrup – start-page: 661 year: 2000 end-page: 667 ident: b40 article-title: Using the nystrom method to speed up kernel machines publication-title: NIPS’00: Proceedings of the 13th International Conference on Neural Information Processing contributor: fullname: Seeger – volume: 118 start-page: 235 year: 2019 end-page: 246 ident: b31 article-title: Compositionally-warped Gaussian processes publication-title: Neural Netw. contributor: fullname: Tobar – volume: 30 start-page: 683 year: 2004 end-page: 691 ident: b29 article-title: Multivariable geostatistics in S: The gstat package publication-title: Comput. Geosci. contributor: fullname: Pebesma – start-page: 887 year: 1991 ident: b10 article-title: Statistics for Spatial Data contributor: fullname: Cressie – volume: 63 start-page: 1 year: 2015 end-page: 27 ident: b28 article-title: Analysis of random fields using compRandFld publication-title: J. Stat. Softw. contributor: fullname: Bevilacqua – year: 2015 ident: b1 article-title: TensorFlow: Large-scale machine learning on heterogeneous systems contributor: fullname: Zheng – volume: 45 start-page: 453 year: 2013 end-page: 470 ident: b13 article-title: Automatic variogram modeling by iterative least squares: Univariate and multivariate cases publication-title: Math. Geosci. contributor: fullname: Renard – volume: 112 start-page: 859 year: 2017 end-page: 877 ident: b4 article-title: Variational inference: A review for statisticians publication-title: J. Amer. Statist. Assoc. contributor: fullname: McAuliffe – volume: 111 start-page: 800 year: 2016 end-page: 812 ident: b12 article-title: Hierarchical nearest-neighbor Gaussian process models for large geostatistical datasets publication-title: J. Amer. Statist. Assoc. contributor: fullname: Gelfand – volume: 38 start-page: 351 year: 2015 end-page: 360 ident: b19 article-title: Scalable variational Gaussian process classification publication-title: J. Mach. Learn. Res. contributor: fullname: Ghahramani – year: 2018 ident: b32 article-title: Nested Kriging predictions for datasets with a large number of observations publication-title: Stat. Comput. contributor: fullname: Chevalier – volume: 12 start-page: 583 year: 2017 end-page: 614 ident: b2 article-title: High-dimensional Bayesian geostatistics publication-title: Bayesian Anal. contributor: fullname: Banerjee – year: 2019 ident: b37 article-title: Deep structured mixtures of Gaussian processes contributor: fullname: Rasmussen – volume: 36 start-page: 124 year: 2021 end-page: 141 ident: b21 article-title: A general framework for vecchia approximations of Gaussian processes publication-title: Statist. Sci. contributor: fullname: Guinness – volume: 31 start-page: 472 year: 2013 end-page: 480 ident: b26 article-title: Efficient variational inference for Gaussian process regression networks publication-title: J. Mach. Learn. Res. contributor: fullname: Bonilla – volume: vol. 31 start-page: 207 year: 2013 end-page: 215 ident: b11 article-title: Deep Gaussian processes publication-title: International Conference on Artificial Intelligence and Statistics contributor: fullname: Lawrence – start-page: 282 year: 2013 end-page: 290 ident: b20 article-title: Gaussian processes for big data publication-title: Uncertainty in Artificial Intelligence 29 contributor: fullname: Lawrence – start-page: 654 year: 2001 ident: 10.1016/j.cageo.2022.105056_b38 article-title: Mixtures of Gaussian processes publication-title: Adv. Neural Inf. Process. Syst. contributor: fullname: Tresp – volume: 11 start-page: 1 year: 2020 ident: 10.1016/j.cageo.2022.105056_b9 article-title: The misuse of colour in science communication publication-title: Nature Commun. doi: 10.1038/s41467-020-19160-7 contributor: fullname: Crameri – volume: 6 start-page: 1935 year: 2005 ident: 10.1016/j.cageo.2022.105056_b6 article-title: A unifying view of sparse approximate Gaussian process regression publication-title: J. Mach. Learn. Res. contributor: fullname: Quiñonero Candela – start-page: 483 year: 1997 ident: 10.1016/j.cageo.2022.105056_b17 contributor: fullname: Goovaerts – ident: 10.1016/j.cageo.2022.105056_b18 – volume: 31 start-page: 472 year: 2013 ident: 10.1016/j.cageo.2022.105056_b26 article-title: Efficient variational inference for Gaussian process regression networks publication-title: J. Mach. Learn. Res. contributor: fullname: Nguyen – volume: 21 start-page: 786 year: 2009 ident: 10.1016/j.cageo.2022.105056_b27 article-title: The variational gaussian approximation revisited publication-title: Neural Comput. doi: 10.1162/neco.2008.08-07-592 contributor: fullname: Opper – ident: 10.1016/j.cageo.2022.105056_b8 – start-page: 695 year: 1999 ident: 10.1016/j.cageo.2022.105056_b7 contributor: fullname: Chilès – volume: 111 start-page: 800 year: 2016 ident: 10.1016/j.cageo.2022.105056_b12 article-title: Hierarchical nearest-neighbor Gaussian process models for large geostatistical datasets publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.2015.1044091 contributor: fullname: Datta – year: 2015 ident: 10.1016/j.cageo.2022.105056_b23 article-title: Adam: A method for stochastic optimization contributor: fullname: Kingma – volume: vol. 5 start-page: 567 year: 2009 ident: 10.1016/j.cageo.2022.105056_b36 article-title: Variational learning of inducing variables in sparse Gaussian processes contributor: fullname: Titsias – volume: 63 start-page: 1 year: 2015 ident: 10.1016/j.cageo.2022.105056_b28 article-title: Analysis of random fields using compRandFld publication-title: J. Stat. Softw. doi: 10.18637/jss.v063.i09 contributor: fullname: Padoan – start-page: 266 year: 2006 ident: 10.1016/j.cageo.2022.105056_b30 contributor: fullname: Rasmussen – volume: 19 start-page: 1 year: 2018 ident: 10.1016/j.cageo.2022.105056_b15 article-title: How deep are deep Gaussian processes? publication-title: J. Mach. Learn. Res. contributor: fullname: Dunlop – volume: 25 start-page: 383 year: 2020 ident: 10.1016/j.cageo.2022.105056_b22 article-title: Vecchia approximations of Gaussian-process predictions publication-title: J. Agric. Biol. Environ. Stat. doi: 10.1007/s13253-020-00401-7 contributor: fullname: Katzfuss – volume: 65 start-page: 677 year: 2020 ident: 10.1016/j.cageo.2022.105056_b16 article-title: Sunspot cycle prediction using warped Gaussian process regression publication-title: Adv. Space Res. doi: 10.1016/j.asr.2019.11.011 contributor: fullname: Gonçalves – volume: 112 start-page: 859 year: 2017 ident: 10.1016/j.cageo.2022.105056_b4 article-title: Variational inference: A review for statisticians publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.2017.1285773 contributor: fullname: Blei – volume: 46 start-page: 21 year: 2002 ident: 10.1016/j.cageo.2022.105056_b35 article-title: Bayesian methods for support vector machines: Evidence and predictive class probabilities publication-title: Mach. Learn. doi: 10.1023/A:1012489924661 contributor: fullname: Sollich – start-page: 887 year: 1991 ident: 10.1016/j.cageo.2022.105056_b10 contributor: fullname: Cressie – year: 2015 ident: 10.1016/j.cageo.2022.105056_b1 contributor: fullname: Abadi – volume: 45 start-page: 453 year: 2013 ident: 10.1016/j.cageo.2022.105056_b13 article-title: Automatic variogram modeling by iterative least squares: Univariate and multivariate cases publication-title: Math. Geosci. doi: 10.1007/s11004-012-9434-1 contributor: fullname: Desassis – start-page: 282 year: 2013 ident: 10.1016/j.cageo.2022.105056_b20 article-title: Gaussian processes for big data contributor: fullname: Hensman – start-page: 189 year: 1995 ident: 10.1016/j.cageo.2022.105056_b39 contributor: fullname: Vapnik – volume: 118 start-page: 235 year: 2019 ident: 10.1016/j.cageo.2022.105056_b31 article-title: Compositionally-warped Gaussian processes publication-title: Neural Netw. doi: 10.1016/j.neunet.2019.06.012 contributor: fullname: Rios – ident: 10.1016/j.cageo.2022.105056_b25 – year: 2018 ident: 10.1016/j.cageo.2022.105056_b32 article-title: Nested Kriging predictions for datasets with a large number of observations publication-title: Stat. Comput. doi: 10.1007/s11222-017-9766-2 contributor: fullname: Rullière – volume: 30 start-page: 683 year: 2004 ident: 10.1016/j.cageo.2022.105056_b29 article-title: Multivariable geostatistics in S: The gstat package publication-title: Comput. Geosci. doi: 10.1016/j.cageo.2004.03.012 contributor: fullname: Pebesma – ident: 10.1016/j.cageo.2022.105056_b5 – volume: 120 start-page: 48 year: 2018 ident: 10.1016/j.cageo.2022.105056_b24 article-title: An automatic variogram modeling method with high reliability fitness and estimates publication-title: Comput. Geosci. doi: 10.1016/j.cageo.2018.07.011 contributor: fullname: Li – ident: 10.1016/j.cageo.2022.105056_b33 – start-page: 232 year: 2007 ident: 10.1016/j.cageo.2022.105056_b14 contributor: fullname: Diggle – volume: 38 start-page: 351 year: 2015 ident: 10.1016/j.cageo.2022.105056_b19 article-title: Scalable variational Gaussian process classification publication-title: J. Mach. Learn. Res. contributor: fullname: Hensman – ident: 10.1016/j.cageo.2022.105056_b41 – volume: 16 start-page: 337 year: 2004 ident: 10.1016/j.cageo.2022.105056_b34 article-title: Warped Gaussian processes publication-title: Adv. Neural Inf. Proc. Syst. contributor: fullname: Snelson – volume: 107 start-page: 268 year: 2012 ident: 10.1016/j.cageo.2022.105056_b3 article-title: Estimating space and space-time covariance functions for large data sets: A weighted composite likelihood approach publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.2011.646928 contributor: fullname: Bevilacqua – year: 2019 ident: 10.1016/j.cageo.2022.105056_b37 contributor: fullname: Trapp – volume: 12 start-page: 583 year: 2017 ident: 10.1016/j.cageo.2022.105056_b2 article-title: High-dimensional Bayesian geostatistics publication-title: Bayesian Anal. doi: 10.1214/17-BA1056R contributor: fullname: Banerjee – volume: vol. 31 start-page: 207 year: 2013 ident: 10.1016/j.cageo.2022.105056_b11 article-title: Deep Gaussian processes contributor: fullname: Damianou – volume: 36 start-page: 124 year: 2021 ident: 10.1016/j.cageo.2022.105056_b21 article-title: A general framework for vecchia approximations of Gaussian processes publication-title: Statist. Sci. doi: 10.1214/19-STS755 contributor: fullname: Katzfuss – start-page: 661 year: 2000 ident: 10.1016/j.cageo.2022.105056_b40 article-title: Using the nystrom method to speed up kernel machines contributor: fullname: Williams |
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| Snippet | A variational Gaussian process (VGP) model specialized in spatial data is introduced, capitalizing on recent advances in the machine learning field. The model... |
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| SubjectTerms | Gaussian process Kriging Machine learning Variational inference |
| Title | Learning spatial patterns with variational Gaussian processes: Regression |
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