Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLinear Regression without Correspondences via Concave Minimization
65
0
0.0
(
0
)
Added by
Liangzu Peng
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 domains such as computer vision, data mining, communications and biology. In its simplest form, it is tantamount to solving a linear system of equations, for which the entries of the right hand side vector have been permuted. This type of data corruption renders the linear regression task considerably harder, even in the absence of other corruptions, such as noise, outliers or missing entries. Existing methods are either applicable only to noiseless data or they are very sensitive to initialization or they work only for partially shuffled data. In this paper we address these issues via an algebraic geometric approach, which uses symmetric polynomials to extract permutation-invariant constraints that the parameters $xi^* in Re^n$ of the linear regression model must satisfy. This naturally leads to a polynomial system of $n$ equations in $n$ unknowns, which contains $xi^*$ in its root locus. Using the machinery of algebraic geometry we prove that as long as the independent samples are generic, this polynomial system is always consistent with at most $n!$ complex roots, regardless of any type of corruption inflicted on the observations. The algorithmic implication of this fact is that one can always solve this polynomial system and use its most suitable root as initialization to the Expectation Maximization algorithm. To the best of our knowledge, the resulting method is the first working solution for small values of $n$ able to handle thousands of fully shuffled noisy observations in milliseconds.
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 methods such as $ell_1$ minimization and nuclear norm minimization are well understood through recent years research. However, rigorously characterizing the phase transition of total variation (TV) minimization in recovering sparse-gradient signal is still open. In this paper, we fully characterize the phase transition curve of the TV minimization. Our proof builds on Donoho, Johnstone and Montanaris conjectured phase transition curve for the TV approximate message passing algorithm (AMP), together with the linkage between the minmax Mean Square Error of a denoising problem and the high-dimensional convex geometry for TV minimization.
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 multiple access (NOMA) to a data sink in the uplink (UL). However, most existing works on WPCNs adopted the simplified linear energy-harvesting model and also cannot guarantee strict user quality-of-service requirements. To address these issues, we aim to minimize the total transmit energy consumption at the PS by jointly optimizing the resource allocation and IRS phase shifts over time, subject to the minimum throughput requirements of all devices. The formulated problem is decomposed into two subproblems, and solved iteratively in an alternative manner by employing difference of convex functions programming, successive convex approximation, and penalty-based algorithm. Numerical results demonstrate the significant performance gains achieved by the proposed algorithm over benchmark schemes and reveal the benefits of integrating IRS into WPCNs. In particular, employing different IRS phase shifts over UL and DL outperforms the case with static IRS beamforming.
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 and reduce resource consumption, we design optimal caching and power control algorithms for multi-hop wireless HetNets. We formulate a joint optimization framework to minimize the average transmission delay as a function of the caching variables and the signal-to-interference-plus-noise ratios (SINR) which are determined by the transmission powers, while explicitly accounting for backhaul connection costs and the power constraints. Using convex relaxation and rounding, we obtain a reduced-complexity formulation (RCF) of the joint optimization problem, which can provide a constant factor approximation to the globally optimal solution. We then solve RCF in two ways: 1) alternating optimization of the power and caching variables by leveraging biconvexity, and 2) joint optimization of power control and caching. We characterize the necessary (KKT) conditions for an optimal solution to RCF, and use strict quasi-convexity to show that the KKT points are Pareto optimal for RCF. We then devise a subgradient projection algorithm to jointly update the caching and power variables, and show that under appropriate conditions, the algorithm converges at a linear rate to the local minima of RCF, under general SINR conditions. We support our analytical findings with results from extensive numerical experiments.
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. When the encoder and the decoder know the statistical channel model, it is found that the optimal channel output processing function is the conditional expectation operator, thus hinting a potential role of regression, a classical topic in machine learning, for this model. Without utilizing the statistical channel model, a problem formulation inspired by machine learning principles is established, with suitable performance metrics introduced. A data-driven inference algorithm is proposed to solve the problem, and the effectiveness of the algorithm is validated via numerical experiments. Extensions to more general information transmission models are also discussed.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
