相关论文: New Null Space Results and Recovery Thresholds for…

We study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers.…

The nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank-one factors needed to reconstruct it exactly. The problem of determining this rank and computing the corresponding nonnegative factors is difficult;…

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

Suppose that we observe entries or, more generally, linear combinations of entries of an unknown $m\times T$-matrix $A$ corrupted by noise. We are particularly interested in the high-dimensional setting where the number $mT$ of unknown…

We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity"…

Reduced-rank approach has been used for decades in robust linear estimation of both deterministic and random vector of parameters in linear model y=Hx+\sqrt{epsilon}n. In practical settings, estimation is frequently performed under…

This note demonstrates that we can stably recover all symmetric Toeplitz matrices $\pmb{X}_0\in\mathbb{R}^{n\times n}$ of rank at most $r$ from a number of rank-one subgaussian measurements on the order of $r\log^{2} n$ with an…

Recently, there was a substantial progress in the problem of sampling recovery on function classes with mixed smoothness. Mostly, it has been done by proving new and sometimes optimal upper bounds for both linear sampling recovery and for…

We study the role of the constraint set in determining the solution to low-rank, positive semidefinite (PSD) matrix sensing problems. The setting we consider involves rank-one sensing matrices: In particular, given a set of rank-one…

We present a subspace system identification method based on weighted nuclear norm approximation. The weight matrices used in the nuclear norm minimization are the same weights as used in standard subspace identification methods. We show…

Neutrino experiments are often limited by low statistics, sizable systematic uncertainties, and coarse observable binning, which can hinder discrimination among competing beyond-the-Standard-Model (BSM) explanations of anomalous signals. In…

We present a novel representation of rank constraints for non-square real matrices. We establish relationships with some existing results, which are particular cases of our representation. One of these particular cases, is a representation…

We present robust, model-marginalized limits on both the total neutrino mass ($\sum m_\nu$) and abundance ($N_{\rm eff}$) to minimize the role of parameterizations, priors and models when extracting neutrino properties from cosmology. The…

Many real world datasets subsume a linear or non-linear low-rank structure in a very low-dimensional space. Unfortunately, one often has very little or no information about the geometry of the space, resulting in a highly under-determined…

Nuclear-norm regularization plays a vital role in many learning tasks, such as low-rank matrix recovery (MR), and low-rank representation (LRR). Solving this problem directly can be computationally expensive due to the unknown rank of…

Rank minimization has attracted a lot of attention due to its robustness in data recovery. To overcome the computational difficulty, rank is often replaced with nuclear norm. For several rank minimization problems, such a replacement has…

The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The…

The outstanding performance of large foundational models across diverse tasks, from computer vision to speech and natural language processing, has significantly increased their demand. However, storing and transmitting these models poses…

Deployment of neural networks on resource-constrained devices demands models that are both compact and robust to adversarial inputs. However, compression and adversarial robustness often conflict. In this work, we introduce a dynamical…

Subspace clustering refers to the problem of segmenting a set of data points approximately drawn from a union of multiple linear subspaces. Aiming at the subspace clustering problem, various subspace clustering algorithms have been proposed…