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Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood function is NP-hard to compute when the signal has dimension larger than one. To optimize this objective function we reformulate it as a concave minimization problem, which we solve via branch-and-bound. This is supported by a computable search space to branch, an effective lower bounding scheme via convex envelope minimization and a refined upper bound, all naturally arising from the concave minimization reformulation. The resulting algorithm outperforms state-of-the-art methods for fully shuffled data and remains tractable for up to $8$-dimensional signals, an untouched regime in prior work.
Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in diverse dom
Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery m
This paper considers an intelligent reflecting surface(IRS)-aided wireless powered communication network (WPCN), where devices first harvest energy from a power station (PS) in the downlink (DL) and then transmit information using non-orthogonal mult
A fundamental challenge in wireless heterogeneous networks (HetNets) is to effectively utilize the limited transmission and storage resources in the presence of increasing deployment density and backhaul capacity constraints. To alleviate bottlenecks
A general information transmission model, under independent and identically distributed Gaussian codebook and nearest neighbor decoding rule with processed channel output, is investigated using the performance metric of generalized mutual information