Related papers: Zeroth-order Low-rank Hessian Estimation via Matri…
In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element of arbitrary order $k$. We prove that the proposed Hessian recovery preserves polynomials of degree $k+1$ on general…
This work presents a novel matrix-based method for constructing an approximation Hessian using only function evaluations. The method requires less computational power than interpolation-based methods and is easy to implement in matrix-based…
In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…
We study an estimator with a convex formulation for recovery of low-rank matrices from rank-one projections. Using initial estimates of the factors of the target $d_1\times d_2$ matrix of rank-$r$, the estimator admits a practical…
Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and second-order methods where objective functions, gradients and Hessians are approximated by…
Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for both Newton solution of deterministic inverse problems, as…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…
Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…
We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…
Low rank model arises from a wide range of applications, including machine learning, signal processing, computer algebra, computer vision, and imaging science. Low rank matrix recovery is about reconstructing a low rank matrix from…
We consider the problem of estimating the uncertainty in statistical inverse problems using Bayesian inference. When the probability density of the noise and the prior are Gaussian, the solution of such a statistical inverse problem is also…
We revisit the problem of recovering a low-rank positive semidefinite matrix from rank-one projections using tools from optimal transport. More specifically, we show that a variational formulation of this problem is equivalent to computing…
Post-processing techniques are essential tools for enhancing the accuracy of finite element approximations and achieving superconvergence. Among these, recovery techniques stand out as vital methods, playing significant roles in both…
Existing results for low-rank matrix recovery largely focus on quadratic loss, which enjoys favorable properties such as restricted strong convexity/smoothness (RSC/RSM) and well conditioning over all low rank matrices. However, many…
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 considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are…
In this paper, we propose and analyze algorithms for zeroth-order optimization of non-convex composite objectives, focusing on reducing the complexity dependence on dimensionality. This is achieved by exploiting the low dimensional…
Matrix completion aims to recover an unknown low-rank matrix from a small subset of its entries. In many applications, the rank of the unknown target matrix is known in advance. In this paper, first we revisit a recently proposed rank-based…