相关论文: Recovery Sets of Subspaces from a Simplex Code
We assume i.i.d. data sampled from a mixture distribution with K components along fixed d-dimensional linear subspaces and an additional outlier component. For p>0, we study the simultaneous recovery of the K fixed subspaces by minimizing…
Designing computational experiments involving $\ell_1$ minimization with linear constraints in a finite-dimensional, real-valued space for receiving a sparse solution with a precise number $k$ of nonzero entries is, in general, difficult.…
This paper aims to recover a multi-subspace matrix from permuted data: given a matrix, in which the columns are drawn from a union of low-dimensional subspaces and some columns are corrupted by permutations on their entries, recover the…
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
In this paper, we introduce a model of a distributed storage system that is locally recoverable from any single server failure. Unlike the usual local recovery model of codes for distributed storage, this model accounts for the fact that…
The rapid developing area of compressed sensing suggests that a sparse vector lying in an arbitrary high dimensional space can be accurately recovered from only a small set of non-adaptive linear measurements. Under appropriate conditions…
Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…
A $k$-server Private Information Retrieval (PIR) code is a binary linear $[m,s]$-code admitting a generator matrix such that for every integer $i$ with $1\le i\le s$ there exist $k$ disjoint subsets of columns (called recovery sets) that…
Representing meaning in the form of high dimensional vectors is a common and powerful tool in biologically inspired architectures. While the meaning of a set of concepts can be summarized by taking a (possibly weighted) sum of their…
Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. While parameter…
The problem of recovering a vector from the absolute values of its inner products against a family of measurement vectors has been well studied in mathematics and engineering. A generalization of this phase retrieval problem also exists in…
We study the Service Rate Region of Reed-Muller codes in the context of distributed storage systems. The service rate region is a convex polytope comprising all achievable data access request rates under a given coding scheme. It represents…
We assume data independently sampled from a mixture distribution on the unit ball of the D-dimensional Euclidean space with K+1 components: the first component is a uniform distribution on that ball representing outliers and the other K…
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.…
Various types of recovery algorithms for batch codes have been investigated, such as asynchronous recovery or recovery as afforded by batch codes obtained from Almost Affinely Disjoint (AAD) families. In this paper, we offer the first…
This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this…
The paper considers recovery of signals from incomplete observations and a problem of determination of the allowed quantity of missed observations, i.e. the problem of determination of the size of the uniqueness sets for a given data…
In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible…
We propose distributed solutions to the problem of Robust Subspace Recovery (RSR). Our setting assumes a huge dataset in an ad hoc network without a central processor, where each node has access only to one chunk of the dataset.…
The problem of reconstructing a sequence from the set of its length-$k$ substrings has received considerable attention due to its various applications in genomics. We study an uncoded version of this problem where multiple random sources…