Related papers: Structured Matrix Recovery via the Generalized Dan…
We prove an asymptotic normality guarantee for generalized low-rank matrix sensing -- i.e., matrix sensing under a general convex loss $\bar\ell(\langle X,M\rangle,y^*)$, where $M\in\mathbb{R}^{d\times d}$ is the unknown rank-$k$ matrix,…
In this paper, we propose a generalized expectation consistent signal recovery algorithm to estimate the signal $\mathbf{x}$ from the nonlinear measurements of a linear transform output $\mathbf{z}=\mathbf{A}\mathbf{x}$. This estimation…
Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local…
Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric…
Analyzing large samples of high-dimensional data under dependence is a challenging statistical problem as long time series may have change points, most importantly in the mean and the marginal covariances, for which one needs valid tests.…
Matrix sensing has many real-world applications in science and engineering, such as system control, distance embedding, and computer vision. The goal of matrix sensing is to recover a matrix $A_\star \in \mathbb{R}^{n \times n}$, based on a…
One goal of geometric measure theory is to understand how measures in the plane or higher dimensional Euclidean space interact with families of lower dimensional sets. An important dichotomy arises between the class of rectifiable measures,…
There has recently been renewed recognition of the need to understand the consistency properties that must be preserved when a generalized matrix inverse is required. The most widely known generalized inverse, the Moore-Penrose…
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…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to…
Continuing the analysis in a unified scheme for treating generalized superselection sectors based upon the notion of selection criteria for states of relevance in quantum physics, we extend the Doplicher-Roberts superselection theory for…
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…
In this paper, we introduce structured sparsity estimators in Generalized Linear Models. Structured sparsity estimators in the least squares loss are introduced by Stucky and van de Geer (2018) recently for fixed design and normal errors.…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
We take a geometrical viewpoint and present a unifying view on supervised deep learning with the Bregman divergence loss function - this entails frequent classification and prediction tasks. Motivated by simulations we suggest that there is…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
This paper considers reconstructing a spectrally sparse signal from a small number of randomly observed time-domain samples. The signal of interest is a linear combination of complex sinusoids at $R$ distinct frequencies. The frequencies…