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An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization…
This paper deals with model order selection in context of correlated noise. More precisely, one considers sources embedded in an additive Complex Elliptically Symmetric (CES) noise, with unknown parameters. The main difficultly for…
Learned iterative shrinkage thresholding algorithm (LISTA), which adopts deep learning techniques to learn optimal algorithm parameters from labeled training data, can be successfully applied to small-scale multidimensional harmonic…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a…
A method is proposed to generate an optimal fit of a number of connected linear trend segments onto time-series data. To be able to efficiently handle many lines, the method employs a stochastic search procedure to determine optimal…
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…
We present an algorithm that efficiently computes nearly-optimal solutions to a class of combinatorial reconfiguration problems on weighted, undirected graphs. Inspired by societally relevant applications in networked infrastructure…
Source enumeration typically relies on subspace-based techniques that require accurate separation of signal and noise subspaces. However, prior works do not address coherent sources in small uniform linear arrays, where ambiguities arise in…
{\em Reoptimization} is a setting in which we are given an (near) optimal solution of a problem instance and a local modification that slightly changes the instance. The main goal is that of finding an (near) optimal solution of the…
In recent years, a number of fast algorithms for computing the determinant of a Toeplitz matrix were developed. The fastest algorithm we know so far is of order $k^2\log{n}+k^3$, where $n$ is the number of rows of the Toeplitz matrix and…
Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race,…
Matrix learning is at the core of many machine learning problems. A number of real-world applications such as collaborative filtering and text mining can be formulated as a low-rank matrix completion problem, which recovers incomplete…
We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…
We propose an iterative algorithm for low-rank matrix completion that can be interpreted as an iteratively reweighted least squares (IRLS) algorithm, a saddle-escaping smoothing Newton method or a variable metric proximal gradient method…