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We show that measures with finite support on the real line are the unique solution to an algorithm, named generalized minimal extrapolation, involving only a finite number of generalized moments (which encompass the standard moments, the Laplace transform, the Stieltjes transformation, etc). Generalized minimal extrapolation shares related geometric… (More)

- Yohann de Castro, Elisabeth Gassiat, Claire Lacour
- Journal of Machine Learning Research
- 2016

We consider stationary hidden Markov models with finite state space and nonparametric modeling of the emission distributions. It has remained unknown until very recently that such models are identifiable. In this paper, we propose a new penalized least-squares estimator for the emission distributions which is statistically optimal and practically tractable.… (More)

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm regularization procedure to localize the support and estimate the weights of a target discrete measure in this frame.… (More)

- Yohann de Castro
- ArXiv
- 2011

This article investigates a new parameter for the high-dimensional regression with noise: the distortion. This latter has attracted a lot of attention recently with the appearance of new deterministic constructions of “almost”-Euclidean sections of the L1-ball. It measures how far is the intersection between the kernel of the design matrix and the unit… (More)

- Y. DE CASTRO
- 2017

We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered with semidefinite… (More)

Abstract: We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered via… (More)

- Yohann de Castro
- IEEE Transactions on Information Theory
- 2014

We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the ℓ<sub>2</sub>-prediction error and ℓ<sub>1</sub>-risk of the lasso, and the Dantzig selector are optimal up to an explicit multiplicative constant. Thus, we can estimate a high-dimensional target… (More)

Motivated by electricity consumption metering, we extend existing nonnegative matrix factorization (NMF) algorithms to use linear measurements as observations, instead of matrix entries. The objective is to estimate multiple time series at a fine temporal scale from temporal aggregates measured on each individual series. Furthermore, our algorithm is… (More)

- Yohann de Castro, Thibault Espinasse, Paul Rochet
- Journal of Machine Learning Research
- 2017

In this paper, we aim at recovering an undirected weighted graph of N vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix W. Our approach is based on minimizing a cost function given by the Frobenius norm of the commutator AB−BA between symmetric matrices A and B. In the Erdős-Rényi model with no self-loops, we show… (More)

- Jean-Marc Azaïs, Yohann de Castro, Stéphane Mourareau
- ArXiv
- 2017

Abstract: This article introduces new testing procedures on the mean of a stationary Gaussian process. Our test statistics are exact and derived from the outcomes of total variation minimization on the space of complex valued measures. Two testing procedures are presented, the first one is based on thin grids (we show that this testing procedure is… (More)