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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)

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)

- Claire Boyer, Yohann de Castro, Joseph Salmon
- ArXiv
- 2016

In this paper, we study sparse spike deconvolution over the space of complex-valued measures when the input measure is a finite sum of Dirac masses. We introduce a modified version of the Beurling Lasso (BLasso), a semi-definite program that we refer to as the Concomitant Beurling Lasso (CBLasso). This new procedure estimates the target measure and the… (More)

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, Élisabeth Gassiat, Claire Lacour, David Dunson
- 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 esti-mator for the emission distributions which is statistically optimal and practically… (More)

- Sandrine Dallaporta, Yohann de Castro
- ArXiv
- 2016

Restricted Isometry Constants (RICs) are a pivotal notion in Compressed Sensing as these constants finely assess how a linear operator is conditioned on the set of sparse vectors and hence how it performs in stable and robust sparse regression (SRSR). While it is an open problem to construct deterministic matrices with apposite RICs, one can prove that such… (More)

- Yohann de Castro, Thibault Espinasse, Paul Rochet
- ArXiv
- 2016

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)