Related papers: Theoretical Guarantees for the Subspace-Constraine…
We study the recovery of sparse vectors from subsampled random convolutions via $\ell_1$-minimization. We consider the setup in which both the subsampling locations as well as the generating vector are chosen at random. For a subgaussian…
Multi-index models provide a popular framework to investigate the learnability of functions with low-dimensional structure and, also due to their connections with neural networks, they have been object of recent intensive study. In this…
We consider the problem of simultaneously finding lower-dimensional subspace structures in a given $m$-tuple of possibly corrupted, high-dimensional data sets all of the same size. We refer to this problem as simultaneous robust subspace…
Given a real-valued function $f$ defined over a manifold $M$ embedded in $\mathbb{R}^d$, we are interested in recovering structural information about $f$ from the sole information of its values on a finite sample $P$. Existing methods…
Recently, tensor low-rank representation (TLRR) has become a popular tool for tensor data recovery and clustering, due to its empirical success and theoretical guarantees. However, existing TLRR methods consider Gaussian or gross sparse…
In the remote state estimation problem, an observer tries to reconstruct the state of a dynamical system at a remote location, where no direct sensor measurements are available. The observer only has access to information sent through a…
The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR…
We give the first dimensionality reduction methods for the overconstrained Tukey regression problem. The Tukey loss function $\|y\|_M = \sum_i M(y_i)$ has $M(y_i) \approx |y_i|^p$ for residual errors $y_i$ smaller than a prescribed…
This paper is concerned with estimating the column space of an unknown low-rank matrix $\boldsymbol{A}^{\star}\in\mathbb{R}^{d_{1}\times d_{2}}$, given noisy and partial observations of its entries. There is no shortage of scenarios where…
Let us consider a case where all of the elements in some continuous slices are missing in tensor data. In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements. The key problem…
The problem of testing whether a signal lies within a given subspace, also named matched subspace detection, has been well studied when the signal is represented as a vector. However, the matched subspace detection methods based on vectors…
Remote sensing hyperspectral sensors collect large volumes of high dimensional spectral and spatial data. However, due to spectral and spatial redundancy the true hyperspectral signal lies on a subspace of much lower dimension than the…
In this paper, we adopt a componentwise perturbation analysis for $\star$-Sylvester equations. Based on the small condition estimation (SCE), we devise the algorithms to estimate normwise, mixed and componentwise condition numbers for…
We study the problem of outlier robust high-dimensional mean estimation under a finite covariance assumption, and more broadly under finite low-degree moment assumptions. We consider a standard stability condition from the recent robust…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…
Orthogonal group synchronization aims to recover orthogonal group elements from their noisy pairwise measurements. It has found numerous applications including computer vision, imaging science, and community detection. Due to the orthogonal…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…
An estimated state-space model can possibly be improved by further iterations with estimation data. This contribution specifically studies if models obtained by subspace estimation can be improved by subsequent re-estimation of the B, C,…
In this paper, we introduce the tamed stochastic gradient descent method (TSGD) for optimization problems. Inspired by the tamed Euler scheme, which is a commonly used method within the context of stochastic differential equations, TSGD is…