相关论文: Noisy Low Rank Column-wise Sensing

There has been a recent surge of interest in studying permutation-based models for ranking from pairwise comparison data. Despite being structurally richer and more robust than parametric ranking models, permutation-based models are less…

Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…

Several key questions remain unanswered regarding overparameterized learning models. It is unclear how (stochastic) gradient descent finds solutions that generalize well, and in particular the role of small random initializations. Matrix…

This paper is concerned with low-rank matrix optimization, which has found a wide range of applications in machine learning. This problem in the special case of matrix sensing has been studied extensively through the notion of Restricted…

Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in…

Non-parametric entropy estimation on sequential data is a fundamental tool in signal processing, capturing information flow within or between processes to measure predictability, redundancy, or similarity. Methods based on longest common…

We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…

Unlabeled sensing is a linear inverse problem with permuted measurements. We propose an alternating minimization (AltMin) algorithm with a suitable initialization for two widely considered permutation models: partially shuffled/$k$-sparse…

High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint…

We consider the problem of estimating the factors of a low-rank $n \times d$ matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known)…

The Gaussian kernel is one of the most important kernels, applicable to many research fields, including scientific computing and data science. In this paper, we present asymptotic analysis of the Gaussian kernel matrix in high dimension…

The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…

Affine matrix rank minimization problem is a fundamental problem with a lot of important applications in many fields. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank…

A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…

We study the problem of recovering the latent ground truth labeling of a structured instance with categorical random variables in the presence of noisy observations. We present a new approximate algorithm for graphs with categorical…

This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…

Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by…

This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex…