Learn 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)
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)
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)
  • Yohann De Castro, Élisabeth Gassiat, Sylvain Le Corff
  • 2017
In this paper, we consider the filtering and smoothing recursions in nonparametric finite state space hidden Markov models (HMMs) when the parameters of the model are unknown and replaced by estimators. We provide an explicit and time uniform control of the filtering and smoothing errors in total variation norm as a function of the parameter estimation(More)
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)
We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the &#x2113;<sub>2</sub>-prediction error and &#x2113;<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)
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)
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)
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)