Publications

Accepted/Published:

 

  • N. Garcia Trillos, Z. Kaplan, T. Samakhoana and D. Sanz-Alonso "On the consistency of graph-based Bayesian learning and the scalability of sampling algorithms." To appear in the Journal of Machine Learning Research (JMLR). 2020. Preprint available in ArXiv: https://arxiv.org/abs/1710.07702

  • N. Garcia Trillos. “Variational limits of k-nn graph-based functionals on data clouds.” SIMODS, 1(1):93-120, 2019.

  • N. Garcia 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. Garcia 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. Garcia Trillos and D. Sanz-Alonso. “Continuum limits of posteriors in graph bayesian inverse problems.” SIAM Journal on Mathematical Analysis, 50(4):4020-4040, 2018.

  •  N. Garcia Trillos and D. Slepcev. “A variational approach to the consistency of spectral clustering.” Applied and Computational Harmonic Analysis,  45(2):239-281, 2018.

  •  N. Garcia Trillos and R. Murray. “A new analytical approach to consistency and overtting in regularized empirical risk minimization.” European Journal of Applied Mathematics, 28(6):886-921, 2017.

  • N. Garcia 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.

  • N. Garcia 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.

  • A. Ramdas, N. Garcia 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. Garcia Trillos, D. Slepcev, J. Von Brecht, T. Laurent, and X. Bresson. “Consistency of Cheeger and ratio graph cuts.” The Journal of Machine Learning Research, 17(1):6268-6313, 2016.

  • N. Garcia Trillos and D. Slepcev. “Continuum limit of total variation on point clouds.” Archive for rational mechanics and analysis, 220(1):193-241, 2016.

  • N. Garcia 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.

Preprints:

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

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

  • N. Garcia Trillos, R. Murray,  “A maximum principle argument for the uniform convergence of graph Laplacian regressors.” Preprint available in ArXiv: https://arxiv.org/abs/1901.10089

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

© 2020 by Nicolas Garcia Trillos.