A. M. Alaa and M. Van-der-schaar, Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes, Advances in Neural Information Processing Systems, vol.30, pp.3424-3432, 2017.

M. A. Álvarez, L. Rosasco, and N. D. Lawrence, Kernels for Vector-Valued Functions: A Review. Foundations and Trends R in Machine Learning, vol.4, pp.195-266, 2012.

A. Banerjee, D. B. Dunson, and S. T. Tokdar, Efficient Gaussian process regression for large datasets, Biometrika, vol.100, issue.1, pp.75-89, 2013.

M. Bauer, M. Van-der-wilk, and C. E. Rasmussen, Understanding Probabilistic Sparse Gaussian Process Approximations, Advances in Neural Information Processing Systems, vol.29, pp.1533-1541, 2016.

C. Biernacki, G. Celeux, and G. Govaert, Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate gaussian mixture models, Computational Statistics and Data Analysis, vol.41, issue.3-4, pp.561-575, 2003.

H. Bijl, J. Van-wingerden, T. B. Schön, and M. Verhaegen, Online sparse Gaussian process regression using FITC and PITC approximations, IFAC-PapersOnLine, vol.48, issue.28, pp.703-708, 2015.

C. M. Bishop, Pattern Recognition and Machine Learning. Information Science and Statistics, 2006.

V. Edwin, K. M. Bonilla, C. Chai, and . Williams, Multi-task Gaussian Process Prediction, Advances in Neural Information Processing Systems, vol.20, pp.153-160, 2008.

R. M. Caruana and . Learning, Machine Learning, vol.28, pp.41-75, 1997.
URL : https://hal.archives-ouvertes.fr/in2p3-01171463

G. Casella, An Introduction to Empirical Bayes Data Analysis. The American Statistician, vol.39, pp.83-87, 1985.

C. Clingerman and E. Eaton, Lifelong Learning with Gaussian Processes, Michelangelo Ceci, Jaakko Hollmén, Ljup?o Todorovski, Celine Vens, and Sa?o D?eroski, vol.10535, pp.690-704, 2017.

M. Ciprian, A. J. Crainiceanu, and . Goldsmith, Bayesian Functional Data Analysis Using WinBUGS, Journal of statistical software, vol.32, issue.11, 2010.

A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of the Royal Statistical Society. Series B (Methodological), vol.39, issue.1, pp.35-9246, 1977.

D. Duvenaud, Automatic Model Construction with Gaussian Processes. Thesis, University of Cambridge, 2014.

F. Ferraty and P. Vieu, Nonparametric Functional Data Analysis: Theory and Practice, 2006.

K. Hayashi, T. Takenouchi, R. Tomioka, and H. Kashima, Self-measuring Similarity for Multi-task Gaussian Process, Transactions of the Japanese Society for Artificial Intelligence, vol.27, issue.3, pp.103-110, 2012.

J. Hensman, N. Fusi, and N. D. Lawrence, Gaussian Processes for Big Data, 2013.

T. Krishnan and . Mclachlan, The EM algorithm and extensions, 1997.

P. Moreno-muñoz, A. Artés-rodríguez, and M. A. Álvarez, Continual Multi-task Gaussian Processes, 2019.

J. Quiñonero-candela, C. E. Rasmussen, and C. K. Williams, Approximation Methods for Gaussian Process Regression, 2007.

B. Rakitsch, C. Lippert, K. Borgwardt, and O. Stegle, It is all in the noise: Efficient multi-task Gaussian process inference with structured residuals, Advances in Neural Information Processing Systems, vol.26, pp.1466-1474, 2013.

J. O. Ramsay and B. W. Silverman, Functional Data Analysis, 2005.

C. E. Rasmussen and C. K. Williams, Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning, 2006.

J. A. Rice and B. W. Silverman, Estimating the Mean and Covariance Structure Nonparametrically When the Data are Curves, Journal of the Royal Statistical Society. Series B (Methodological), vol.53, issue.1, pp.35-9246, 1991.

A. Schwaighofer, K. Volker-tresp, and . Yu, Learning Gaussian Process Kernels via Hierarchical Bayes, NIPS, p.8, 2004.

J. Q. Shi, B. Wang, R. Murray-smith, and D. M. Titterington, Gaussian Process Functional Regression Modeling for Batch Data, Biometrics, vol.63, issue.3, pp.714-723, 2007.

Q. Jian, Y. Shi, and . Cheng, Gaussian Process Function Data Analysis R Package 'GPFDA'. Manual of the GPFDA Package, p.33, 2014.

Q. Jian, T. Shi, and . Choi, Gaussian Process Regression Analysis for Functional Data, 2011.

J. Q. Shi, R. Murray-smith, and D. M. Titterington, Hierarchical Gaussian process mixtures for regression, Statistics and Computing, vol.15, issue.1, pp.1573-1375, 2005.

E. Snelson and Z. Ghahramani, Sparse Gaussian Processes using Pseudo-inputs. NIPS, 2006.

K. Swersky, J. Snoek, R. J. Burges, L. Bottou, M. Welling et al., Multi-Task Bayesian Optimization, Advances in Neural Information Processing Systems, vol.26, pp.2004-2012, 2013.

K. Wesley, O. Thompson, and . Rosen, A Bayesian Model for Sparse Functional Data, Biometrics, vol.64, issue.1, pp.54-63, 2008.

K. Michalis and . Titsias, Variational Learning of Inducing Variables in Sparse Gaussian Processes, AISTATS, issue.8, 2009.

C. Williams, S. Klanke, S. Vijayakumar, and K. M. Chai, Multi-task Gaussian Process Learning of Robot Inverse Dynamics, Advances in Neural Information Processing Systems 21, pp.265-272, 2009.

J. T. Wilson, V. Borovitskiy, A. Terenin, P. Mostowsky, and M. P. Deisenroth, Efficiently sampling functions from Gaussian process posteriors, Proceedings of the 37th International Conference on Machine Learning (ICML), p.2020

J. Yang, H. Zhu, T. Choi, and D. D. Cox, Smoothing and Mean-Covariance Estimation of Functional Data with a Bayesian Hierarchical Model, Bayesian Analysis, vol.11, issue.3, pp.649-670, 2016.

J. Yang, D. D. Cox, J. S. Lee, P. Ren, and T. Choi, Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes, Biometrics, vol.73, issue.4, pp.1082-1091, 2017.

K. Yu, A. Volker-tresp, and . Schwaighofer, Learning Gaussian Processes from Multiple Tasks, Proceedings of the 22Nd International Conference on Machine Learning, ICML '05, pp.1012-1019, 2005.

J. Zhu and S. Sun, Multi-task Sparse Gaussian Processes with Improved Multitask Sparsity Regularization, Pattern Recognition, pp.54-62, 2014.