Related papers: Interpolation and Extrapolation of Toeplitz Matric…
This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…
This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…
In several applications, one must estimate a real-valued (symmetric) Toeplitz covariance matrix, typically shifted by the conjugated diagonal matrices of phase progression and phase "calibration" errors. Unlike the Hermitian Toeplitz…
A new nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an…
This paper presents a new methodology for clustering multivariate time series leveraging optimal transport between copulas. Copulas are used to encode both (i) intra-dependence of a multivariate time series, and (ii) inter-dependence…
We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and…
A number of recent works have proposed to solve the line spectral estimation problem by applying off-the-grid extensions of sparse estimation techniques. These methods are preferable over classical line spectral estimation algorithms…
In this note, we propose an unbalanced version of the quantum mechanical version of optimal mass transport that was based on the Lindblad equation. We formulate a natural interpolation framework between density matrices and matrix-valued…
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…
Compressed sensing seeks to recover a sparse vector from a small number of linear and non-adaptive measurements. While most work so far focuses on Gaussian or Bernoulli random measurements we investigate the use of partial random circulant…
The problem of estimating the covariance matrix $\Sigma$ of a $p$-variate distribution based on its $n$ observations arises in many data analysis contexts. While for $n>p$, the classical sample covariance matrix $\hat{\Sigma}_n$ is a good…
How to construct a suitable measurement matrix is still an open question in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit considerable…
In this article, we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional Toeplitz covariance matrices, demonstrating in particular their asymptotic almost sure consistence. The…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
The aim of this article is to introduce and address the problem to smoothly interpolate (empirical) probability measures. To this end, we lift the concept of a spline curve from the setting of points in a Euclidean space that that of…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Convolutional and differential distance estimation schemes are considered and, for…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…
Interpolating between measures supported by polygonal or polyhedral domains is a problem that has been recently addressed by the semi-discrete optimal transport framework. Within this framework, one of the domains is discretized with a set…