Publications

Accepted/Published:
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  • D. Bigoni, Y. Chen, N. García Trillos, Y. Marzouk, D. Sanz-Alonso, "Data-Driven Forward Discretizations for Bayesian Inversion." To appear in Inverse Problems 2020. https://doi.org/10.1088/1361-6420/abb2fa

  • N. García Trillos, R. Murray,  “A maximum principle argument for the uniform convergence of graph Laplacian regressors.”  SIAM Journal on Mathematics of Data Science, 2(3), 705-739. (35 pages). 2020. https://doi.org/10.1137/19M1245372

  • N. García Trillos, Z. Kaplan, T. Samakhoana and D. Sanz-Alonso "On the consistency of graph-based Bayesian learning and the scalability of sampling algorithms." The Journal of Machine Learning Research. 21(28):1−47, 2020. https://jmlr.org/papers/v21/17-698.html

  • N. García Trillos, M. Gerlach, M. Hein, D. Slepcev "Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator." Foundations of Computational Mathematics 20, pages 827–887(2020). https://doi.org/10.1007/s10208-019-09436-w

  • N. García Trillos, D. Sanz-Alonso, R. Yang, “Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis” Journal of Machine Learning Research 20 (2019) 1-37 9; http://jmlr.org/papers/v20/19-261.html

  • N. García Trillos, Z. Kaplan, D. Sanz-Alonso “Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning” Entropy 2019, 21(5), 511; https://doi.org/10.3390/e21050511

  • N. García Trillos and D. Sanz-Alonso. “Continuum limits of posteriors in graph bayesian inverse problems.” SIAM Journal on Mathematical Analysis, 50(4):4020-4040, 2018. https://doi.org/10.1137/17M1138005

  • N. García Trillos and D. Slepcev. “A variational approach to the consistency of spectral clustering.” Applied and Computational Harmonic Analysis,  45(2):239-281, 2018. https://doi.org/10.1016/j.acha.2016.09.003

  • N. García Trillos and R. Murray. “A new analytical approach to consistency and overfitting in regularized empirical risk minimization.” European Journal of Applied Mathematics, 28(6):886-921, 2017. https://doi.org/10.1017/S0956792517000201

  • N. García Trillos, D. Slepcev, J. von Brecht. “Estimating perimeter using graph cuts.” Advances in Applied Probability. Cambridge Press. Volume 49, Issue 4 December 2017 , pp. 1067-1090.  https://doi.org/10.1017/apr.2017.34

  • N. García Trillos, D. Sanz-Alonso. “The Bayesian formulation and well-posedness of fractional elliptic inverse problems” Inverse Problems, Volume 33, Number 6  Published 24 May 2017. https://doi.org/10.1088/1361-6420/aa711e

  • A. Ramdas, N. García Trillos, M. Cuturi. On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests. Entropy 2017, 19(2), 47; https://doi.org/10.3390/e19020047

  • N. García Trillos, D. Slepcev. “On the Rate of Convergence of Empirical Measures in ∞-transportation Distance.” Canadian Journal of Mathematics. Volume 67, Issue 6 01 December 2015 , pp. 1358-1383.  https://doi.org/10.4153/CJM-2014-044-6

Preprints:

  • J. Calder, N. García Trillos, M. Lewicka "Lipschitz regularity of graph Laplacians on random data clouds" 2020. Preprint available at: https://arxiv.org/abs/2007.06679

  • N. García Trillos, F. Morales, J. Morales "Traditional and accelerated gradient descent for neural architecture search" 2020. Preprint available at: https://arxiv.org/abs/2006.15218

  • N. García Trillos, J. Morales "Semi-discrete optimization through semi-discrete optimal transport: a framework for neural architecture search" 2020. Preprint available at: https://arxiv.org/abs/2006.15221

  • N. García Trillos, R. Murray, M. Thorpe, "From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds" 2020. Preprint available at: https://arxiv.org/abs/2004.09304

  • J. Calder, N. García Trillos, "Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs" 2019. Preprint available in ArXiv: https://arxiv.org/abs/1910.13476

  • N. García Trillos, F. Hoffmann, B. Hosseini, "Geometric structure of graph Laplacian embeddings." 2019. Preprint available in ArXiv:  https://arxiv.org/abs/1901.10651

  • N. García Trillos , R. Murray, and D. Sanz-Alonso. “Spatial extreme values via variational techniques” 2018. Preprint available in ArXiv: https://arxiv.org/abs/1808.03218

© Nicolas Garcia Trillos.