Related papers: Optimal completions of a frame
Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific…
In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…
Tensor completion is a technique of filling missing elements of the incomplete data tensors. It being actively studied based on the convex optimization scheme such as nuclear-norm minimization. When given data tensors include some noises,…
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…
We consider potentially non-convex optimization problems, for which optimal rates of approximation depend on the dimension of the parameter space and the smoothness of the function to be optimized. In this paper, we propose an algorithm…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
When constructing finite frames for a given application, the most important consideration is the spectrum of the frame operator. Indeed, the minimum and maximum eigenvalues of the frame operator are the optimal frame bounds, and the frame…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
This paper aims to characterize the optimal frame for phase retrieval, defined as the frame whose condition number for phase retrieval attains its minimal value. In the context of the two-dimensional real case, we reveal the connection…
We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the $\ell_0$ norm. Specifically, the $\ell_0$ model has an objective function that is the sum of a convex fidelity term and a…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
We consider a convex constrained Gaussian sequence model and characterize necessary and sufficient conditions for the least squares estimator (LSE) to be minimax optimal. For a closed convex set $K\subset \mathbb{R}^n$ we observe…
In this paper we study the regularity of the optimal sets for the shape optimization problem \[ \min\Big\{\lambda_1(\Omega)+\dots+\lambda_k(\Omega)\ :\ \Omega\subset\mathbb{R}^d,\ \text{open}\ ,\ |\Omega|=1\Big\}, \] where…
In this paper, we analyze vertex-centered finite volume method (FVM) of any order for elliptic equations on rectangular meshes. The novelty is a unified proof of the inf-sup condition, based on which, we show that the FVM approximation…
It is generally believed that ensemble approaches, which combine multiple algorithms or models, can outperform any single algorithm at machine learning tasks, such as prediction. In this paper, we propose Bayesian convex and linear…
This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…
We provide theory for computing the lower semi-continuous convex envelope of functionals of the type f(x) plus an l2 misfit, and discuss applications to various non-convex optimization problems. The latter term is a data fit term whereas f…
In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this…
In this paper, we consider the design of robust linear precoders for MU-MISO systems where users have perfect Channel State Information (CSI) while the BS has partial CSI. In particular, the BS has access to imperfect estimates of the…