Related papers: Information Recovery from Pairwise Measurements
In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in…
In matrix recovery from random linear measurements, one is interested in recovering an unknown $M$-by-$N$ matrix $X_0$ from $n<MN$ measurements $y_i=Tr(A_i^T X_0)$ where each $A_i$ is an $M$-by-$N$ measurement matrix with i.i.d random…
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…
Community recovery is a central problem that arises in a wide variety of applications such as network clustering, motion segmentation, face clustering and protein complex detection. The objective of the problem is to cluster data points…
Classical results in sparse recovery guarantee the exact reconstruction of $s$-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since…
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)…
The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely…
We study the problem of community recovery from coarse measurements of a graph. In contrast to the problem of community recovery of a fully observed graph, one often encounters situations when measurements of a graph are made at…
We study the problem of learning latent community structure from multiple correlated networks, focusing on edge-correlated stochastic block models with two balanced communities. Recent work of Gaudio, R\'acz, and Sridhar (COLT 2022)…
We consider the problem of clustering a graph $G$ into two communities by observing a subset of the vertex correlations. Specifically, we consider the inverse problem with observed variables $Y=B_G x \oplus Z$, where $B_G$ is the incidence…
We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…
The notion of {\em recoverable value} was advocated in work of Feige, Immorlica, Mirrokni and Nazerzadeh [Approx 2009] as a measure of quality for approximation algorithms. There this concept was applied to facility location problems. In…
This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of…
Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n << m) and e is an…
We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…
We study the problem of recovering the relative positions of objects moving along the real line based only on pairwise collision data. While interaction-based sensing systems arise naturally in a variety of practical settings, a systematic…
We study metric learning from preference comparisons under the ideal point model, in which a user prefers an item over another if it is closer to their latent ideal item. These items are embedded into $\mathbb{R}^d$ equipped with an unknown…
Scientific and commercial data is often incomplete. Recovery of the missing information is an important pre-processing step in data analysis. Real-world data can in many cases be represented as a superposition of two or more different types…
Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…