• 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.

  • 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.

  • N. García Trillos, M. Gerlach, M. Hein, D. Slepčev "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).

  • 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;

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

  • 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.

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

  • 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.

  • N. García Trillos, D. Slepčev, J. von Brecht. “Estimating perimeter using graph cuts.” Advances in Applied Probability. Cambridge Press. Volume 49, Issue 4 December 2017 , pp. 1067-1090.

  • 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.

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

  • N. García Trillos, D. Slepčev. “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.


  • N. García Trillos, M. Jacobs, J. Kim "The multimarginal optimal transport formulation of adversarial multiclass classification" (2022) Preprint available at

  • L. Bungert, N. García Trillos, R. Murray "The Geometry of Adversarial Training in Binary Classification" (2021) Preprint available at

  • C.A. García Trillos and N. García Trillos "On the regularized risk of distributionally robust learning over deep neural networks" (2021) Preprint available at:

  • N. García Trillos, P. He, C. Li “Large sample spectral analysis of graph-based multi-manifold clustering” (2021) Preprint available at:

  • N. García Trillos, R. Murray "Adversarial classification: necessary conditions and geometric flows" 2020. Preprint available at:​​​

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