Yohann De Castro

I am Professor of Mathematics at École Centrale Lyon and Institut Camille Jordan.
My main interest lies in Statistics, Inverse Problems, Machine Learning, and Signal Processing.
Part of my teaching duties inculdes Machine Learning, Statistics, and Optimization.

Quick Overview

Activities

Chercheur associé au CERMICS, École Ponts ParisTech;
Membre extérieur de l'équipe DANTE, INRIA Lyon;
Responsable élu du site École Centrale Lyon de l'Institut Camille Jordan;
Membre du bureau SciDoLySE: Science des Données à Lyon et Saint-Etienne.
Membre élu du conseil scientique de l'École Centrale Lyon;
Membre nommé du conseil scientique de l'Institut Camille Jordan;
Membre élu du conseil du Département Maths-Info de l'École Centrale Lyon;
Membre nommé du conseil des thèses de l'École Centrale Lyon;
Principal Investigator of IDEX Grant IMPULSION (2021);
Membre des ANR JCJC "CIPRESSI", "PIECES" et "GrandMa";

Teaching Duties

Course on Statistics (1A @ECL & 1A @Centrale Casablanca);
Course on Machine Learning (2A @ELC);
Course on Statistical Learning (3A @ECL joint with M2R Maths Avancées @ENSL)

Publications & Talks

Preprints/Papers can be found on HAL ArXiv

Papers & Proceedings

Sparse and Variational models in Statistics and Optimization

Towards off-the-grid algorithms for total variation regularized inverse problems, with R. Petit & V. Duval, Eighth International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), 2021 (to appear).
Dual optimal design and the Christoffel-Darboux polynomial with F. Gamboa & D. Henrion & J.-B. Lasserre, 2020, Optimization Letters (to appear).
SuperMix: Sparse Regularization for Mixtures, with S. Gadat & C. Marteau & C. Maugis-Rabusseau, Annals of Statistics, 2021, Vol. 49, No. 3, 1779-1809.
Multiple Testing and Variable Selection along Least Angle Regression's path, with J-M Azaïs, submitted, 2020. GitHub Repository
A Short Introduction to “Moment-SoS Hierarchies”, Deuxième Congès National de la SMF, 2018.
On Representer Theorems and Convex Regularization, with C. Boyer & A. Chambolle & V. Duval & F. de Gournay & P. Weiss, SIAM Journal on Optimization, 29(2), 1260–1281. A related conference paper published at iTWIST'18 is Convex Regularization and Representer Theorems, with C. Boyer & A. Chambolle & V. Duval & F. de Gournay & P. Weiss.
Testing Gaussian Process with Applications to Super-Resolution, with J.-M. Azaïs & S. Mourareau, Applied and Computational Harmonic Analysis, Volume 48, Pages 445-481, 2020. Python Notebook
Approximate Optimal Designs for Multivariate Polynomial Regression with F. Gamboa & D. Henrion & R. Hess & J.-B. Lasserre, Annals of Statistics, Volume 47, Issue 1, Pages 127–155, 2019. Matlab Code
Extended version of D-Optimal Design for Multivariate Polynomial Regression via the Christoffel function and Semidefinite Relaxations, with F. Gamboa & D. Henrion & R. Hess & J.-B. Lasserre, arXiv 1703.01777.
Sparse Recovery from Extreme Eigenvalues Deviation Inequalities, with S. Dallaporta, ESAIM P&S, Volume 23, Pages 430-463, 2019.
Adapting to Unknown Noise Level in Sparse Deconvolution, with C. Boyer & J. Salmon, Information & Inference: A Journal of the IMA, Volume 6, Issue 3, 1 September 2017, Pages 310–348.
Exact solutions to Super Resolution on semi-algebraic domains in higher dimensions, with F. Gamboa & D. Henrion & J.-B. Lasserre, IEEE Transactions on Information Theory, Volume 63, Issue 1, Jan. 2017, Pages 621-630. Matlab Code
Power of the Spacing test for Least-Angle Regression, with J.-M. Azaïs & S. Mourareau, Bernoulli Journal, Volume 24 n°1 (2018), Pages 465-492.
Randomized pick-freeze for sparse Sobol indices estimation in high dimension, with A. Janon, ESAIM P&S, Volume 19, 2015, Pages 725-745.
Non-uniform spline recovery from small degree polynomial approximation, with G. Mijoule, Journal of Mathematical Analysis and Applications, Volume 430, Issue 2, 15 October 2015, Pages 971–992.
Consistent estimation of the filtering and marginal smoothing distributions in nonparametric hidden Markov models, with É. Gassiat & S. Le Corff, IEEE Transactions on Information Theory, Volume 63, Issue 8, Aug. 2017, Pages 4758-4777.
A Rice method proof of the Null-Space Property over the Grassmannian, with J.-M. Azaïs & S. Mourareau, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, Volume 53, Number 4 (2017), Pages 1821-1838.
Spike Detection from Inaccurate Samplings, with J.-M. Azaïs & F. Gamboa, Applied and Computational Harmonic Analysis, Volume 38, Issue 2, March 2015, Pages 177–195.
Exact Reconstruction using Beurling Minimal Extrapolation, with F. Gamboa, Journal of Mathematical Analysis and Applications, Volume 395, Issue 1, Nov. 2012, Pages 336-354.
A remark on the lasso and the Dantzig selector, Statistics & Probability Letters, Volume 83, Issue 1, January 2013, Pages 304-314.
Optimal designs for Lasso and Dantzig selector using Expander Codes, IEEE Transactions on Information Theory, Volume 60, Issue 11, Nov. 2014, Pages 7293-7299.

Mathematical Statistics & Applied Probability

Three rates of convergence or separation via U-statistics in a dependent framework, with Q. Duchemin and C. Lacour, arXiv:2106.12796, submitted, 2021.
Minimax Estimation of Partially-Observed Vector AutoRegressions, with G. Dalle, arXiv:2106.09327, submitted, 2021.
Random Geometric Graph: Some recent developments and perspectives, with Q. Duchemin, submitted, 2021.
Forecasting Nonnegative Time Series via Sliding Mask Method (SMM) and Latent Clustered Forecast (LCF), with L. Mencarelli, arXiv:2102.05314, 2021.
Concentration inequality for U-statistics of order two for uniformly ergodic Markov chains, with Q. Duchemin and C. Lacour, arXiv 2011.11435v2, submitted.
Markov Random Geometric Graph (MRGG): A Growth Model for Temporal Dynamic Networks, with Q. Duchemin, arXiv:2006.07001, submitted.

GitHub Repository

Latent distance estimation for random geometric graphs, with E. Araya, NeurIPS 2019.
Adaptive Estimation of Nonparametric Geometric Graphs, with C. Lacour & T. M. Pham Ngoc, Mathematical Statistics and Learning, 2020 (to appear).
Nonnegative Matrix Factorization with Side Information for Time Series Recovery and Prediction, with J-M Azaïs & Y. Goude & G. Hébrail & J. Mei, IEEE Transactions on Knowledge and Data Engineering, Volume 31, Issue 3, March 1, Pages 493-506, 2019.
Nonnegative Matrix Factorization for Time Series Recovery From a Few Temporal Aggregates, with J-M Azaïs & Y. Goude & G. Hébrail & J. Mei, Proceedings of the 34th International Conference on Machine Learning (ICML 2017), PMLR 70:2382-2390, 2017.
Reconstructing undirected graphs from eigenspaces, with T. Espinasse & P. Rochet, Journal of Machine Learning Research, Volume 18, Issue 51, Pages 1−24, 2017.
Minimax adaptive estimation of non-parametric Hidden Markov Models, with É. Gassiat & C. Lacour, Journal of Machine Learning Research, Volume 17, Issue 111, Pages 1-43, 2016. Matlab Codes
Estimating the transition matrix of a Markov chain observed at random times, with F. Barsotti & T. Espinasse & P. Rochet, Statistics & Probability Letters, Volume 94, November 2014, Pages 98-105.
Quantitative Isoperimetric Inequalities on the Real Line, Annales Mathématiques Blaise Pascal, Volume 18 n°2 (2011), Pages 311-331.

Ph.D. Sutdents

Guillaume DALLE (IPEF, Starting September 2019) with Axel Parmentier; OR and ML for SNCF and Mobilités;
Quentin DUCHEMIN (DIM Math Innov, Starting September 2019) with Claire Lacour; Random Graphs;
Romain PETIT (DIM Math Innov, Starting September 2019) with Vincent Duval; Mixture models and off-the-grid methods;
Ernesto ARAYA (Orsay grant, 2017-2020); Random Graphs. Awarded a Chilean grant in 2019. Now Post-Doc @INRIA Lille;
Jiali MEI (ÉDF CIFRE, 2014-2017) with Jean-Marc Azaïs, Yannig Goude and Georges Hébrail; "Time series recovery and prediction with regression-enhanced nonnegative matrix factorization applied to electricity consumption". Prix Paul Caseau de l'académie des sciences, 2018. Now Senior Researcher @Shift.

Post-Docs

Nicolas Jouvin (2021), Sparse regularization on measures. Now Chargé de Recherche @INRAE;
Luca Mencarelli (2018-2020), Matrix factorization for Time Series;
Guillaume Mijoule (2018-2019), Semi-dicreste Optimal Transport.

Teaching

My office hours are on Thursday 1pm-3pm.

Machine Learning (2nd year -- Master 1), more detail at machine-learning-centrale.github.io .
Advanced Tools for Learning (3rd year -- Master 2) more detail at statistical-learning-centrale.github.io .

Vitae

Since 2019	Full Professor at École Centrale de Lyon (ICJ)
2018-2019	Senior Researcher at CERMICS
2017-2018	Invited Researcher at Inria Paris
2012-2018	Maître de Conférences Habilité at Institut de Mathématique d'Orsay	H.D.R
2008-2012	Ph.D. at Institut de Mathématiques de Toulouse	Ph.D. Thesis
2004-2009	Student at École Normale Supérieure

Contact

yohann.de-castro@ec-lyon.fr
+33 (0)4 72 18 67 90
Institut Camille Jordan
École Centrale de Lyon
36 Avenue Guy de Collongue
69134 Écully, France