Related papers: Unlabeled Sensing with Random Linear Measurements
We study the unlabeled sensing problem that aims to solve a linear system of equations $A x =\pi(y) $ for an unknown permutation $\pi$. For a generic matrix $A$ and a generic vector $y$, we construct a system of polynomial equations whose…
The unlabeled sensing problem is to solve a noisy linear system of equations under unknown permutation of the measurements. We study a particular case of the problem where the permutations are restricted to be r-local, i.e. the permutation…
A recent line of research termed unlabeled sensing and shuffled linear regression has been exploring under great generality the recovery of signals from subsampled and permuted measurements; a challenging problem in diverse fields of data…
This paper introduces an algorithmic solution to a broader class of unlabeled sensing problems with multiple measurement vectors (MMV). The goal is to recover an unknown structured signal matrix, $\mathbf{X}$, from its noisy linear…
In this paper, we study the recovery of a signal from a set of noisy linear projections (measurements), when such projections are unlabeled, that is, the correspondence between the measurements and the set of projection vectors (i.e., the…
We study the problem of signal estimation from non-linear observations when the signal belongs to a low-dimensional set buried in a high-dimensional space. A rough heuristic often used in practice postulates that non-linear observations may…
This paper addresses a regression problem in which output label values are the results of sensing the magnitude of a phenomenon. A low value of such labels can mean either that the actual magnitude of the phenomenon was low or that the…
Unlabeled sensing is the problem of solving a linear system of equations, where the right-hand-side vector is known only up to a permutation. In this work, we study fields of rational functions related to symmetric polynomials and their…
A recent unlabeled sampling result by Unnikrishnan, Haghighatshoar and Vetterli states that with probability one over iid Gaussian matrices $A$, any $x$ can be uniquely recovered from an unknown permutation of $y = A x$ as soon as $A$ has…
In "Unlabeled Sensing", one observes a set of linear measurements of an underlying signal with incomplete or missing information about their ordering, which can be modeled in terms of an unknown permutation. Previous work on the case of a…
The assumption that response and predictor belong to the same statistical unit may be violated in practice. Unbiased estimation and recovery of true label ordering based on unlabeled data are challenging tasks and have attracted increasing…
We consider the unsupervised learning problem of assigning labels to unlabeled data. A naive approach is to use clustering methods, but this works well only when data is properly clustered and each cluster corresponds to an underlying…
Homomorphic sensing is a recent algebraic-geometric framework that studies the unique recovery of points in a linear subspace from their images under a given collection of linear maps. It has been successful in interpreting such a recovery…
Emerging applications of sensor networks for detection sometimes suggest that classical problems ought be revisited under new assumptions. This is the case of binary hypothesis testing with independent - but not necessarily identically…
Label Ranking (LR) corresponds to the problem of learning a hypothesis that maps features to rankings over a finite set of labels. We adopt a nonparametric regression approach to LR and obtain theoretical performance guarantees for this…
Unlabeled sensing is a linear inverse problem where the measurements are scrambled under an unknown permutation leading to loss of correspondence between the measurements and the rows of the sensing matrix. Motivated by practical tasks such…
Semi-supervised learning has received increasingly attention in statistics and machine learning. In semi-supervised learning settings, a labeled data set with both outcomes and covariates and an unlabeled data set with covariates only are…
Unravelling hidden patterns in datasets is a classical problem with many potential applications. In this paper, we present a challenge whose objective is to discover nonlinear relationships in noisy cloud of points. If a set of point…
This paper considers binary and multilabel classification problems in a setting where labels are missing independently and with a known rate. Missing labels are a ubiquitous phenomenon in extreme multi-label classification (XMC) tasks, such…
Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world…