Related papers: Unlabeled Sensing with Random Linear Measurements
Consider the recovery of an unknown signal ${x}$ from quantized linear measurements. In the one-bit compressive sensing setting, one typically assumes that ${x}$ is sparse, and that the measurements are of the form…
In this paper, we study statistical properties of semi-supervised learning, which is considered as an important problem in the community of machine learning. In the standard supervised learning, only the labeled data is observed. The…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless…
This paper addresses detecting anomalous patterns in images, time-series, and tensor data when the location and scale of the pattern is unknown a priori. The multiscale scan statistic convolves the proposed pattern with the image at various…
In this study, we consider a variant of unlabelled sensing where the measurements are sparsely permuted, and additionally, a few correspondences are known. We present an estimator to solve for the unknown vector. We derive a theoretical…
Cross-channel unlabeled sensing addresses the problem of recovering a multi-channel signal from measurements that were shuffled across channels. This work expands the cross-channel unlabeled sensing framework to signals that lie in a union…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
A weakly-supervised learning framework named as complementary-label learning has been proposed recently, where each sample is equipped with a single complementary label that denotes one of the classes the sample does not belong to. However,…
We demonstrate the first algorithms for the problem of regression for generalized linear models (GLMs) in the presence of additive oblivious noise. We assume we have sample access to examples $(x, y)$ where $y$ is a noisy measurement of…
Unlabeled sensing is a linear inverse problem with permuted measurements. We propose an alternating minimization (AltMin) algorithm with a suitable initialization for two widely considered permutation models: partially shuffled/$k$-sparse…
In supervised learning, we typically leverage a fully labeled dataset to design methods for function estimation or prediction. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is…
Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…
We study the problem of learning mixtures of low-rank models, i.e. reconstructing multiple low-rank matrices from unlabelled linear measurements of each. This problem enriches two widely studied settings -- low-rank matrix sensing and mixed…
Is it possible to perform linear regression on datasets whose labels are shuffled with respect to the inputs? We explore this question by proposing several estimators that recover the weights of a noisy linear model from labels that are…
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…
We consider the estimation problem in high-dimensional semi-supervised learning. Our goal is to investigate when and how the unlabeled data can be exploited to improve the estimation of the regression parameters of linear model in light of…
This paper focuses on learning efficient sensor allocations that ensure observability of unknown high-dimensional linear systems using only a small number of sensors. Existing methods either require an impractically large number of sensors…
Signal amplitude estimation and detection from unlabeled quantized binary samples are studied, assuming that the order of the time indexes is completely unknown. First, maximum likelihood (ML) estimators are utilized to estimate both the…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…