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We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
The problem of mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence from observations of the sequence with a noise and missing observations is…
The rectangular multiparameter eigenvalue problem (RMEP) involves rectangular coefficient matrices (usually with more rows than columns) and may potentially have no solution in its original form. A minimal perturbation framework is proposed…
The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary sequence from observations of the sequence in special sets of points is considered. Formulas for…
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…
In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and sparsity can appear either at the group level or within certain groups. In such cases, an ideal model should be able to…
This paper focuses on the problem of the mean square optimal estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence. Estimates are based on observations of the sequence with…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
We study a class of spectral design problems in which a prior positive semidefinite information matrix is updated by a sum of rank-one matrices constructed from chosen design vectors subject to a bound on their Euclidean norm. The objective…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a…
This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence…
In this paper, a spectral method based on conformal mappings is proposed to solve Steklov eigenvalue problems and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov…
We proposed a novel dense line spectrum super-resolution algorithm, the DMRA, that leverages dynamical multi-resolution of atoms technique to address the limitation of traditional compressed sensing methods when handling dense point-source…
Reliable and efficient spectrum sensing through dynamic selection of a subset of spectrum sensors is studied. The problem of selecting K sensor measurements from a set of M potential sensors is considered where K << M. In addition, K may be…
The fundamental multidimensional line spectral estimation problem is addressed utilizing the Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) algorithm, multidimensional VALSE (MDVALSE) is…
The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…