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Sum-Rate-Optimal Statistical Precoding for FDD Massive MIMO Downlink With Deterministic Equivalents

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2022年第7期71卷 7359-7370页

作者： Zhang, Yu-Xuan Lu, An-An Gao, Xiqi Southeast Univ Natl Mobile Commun Res Lab NCRL Nanjing 210096 Peoples R China Purple Mt Labs Nanjing 211111 Peoples R China

Statisticalprecoding is considered as a promising technique to release the channel state information (CSI) acquisition overhead. This article investigates a linear precoder design for frequency-division duplexing (FDD) massive MIMO downlink with only statistical CSI. We use a beam-based statistical channel model to capture the spatial correlation characteristics of the channels. The objective of the precoder design is to maximize the ergodic sum-rate under total power constraint. Based on the minorize-maximize (mm) algorithm, a stationary solution of the ergodic sum-rate maximization problem can be obtained. The stationary solution is shown to be the same as the optimal solution to a stochastic weighted minimum mean square error (SWmmSE) problem. Further, we establish the approximations for rate expressions with deterministic equivalent. The deterministic equivalents of ergodic rates are only related to the precoding matrices and statistical CSI. According to these closed-form rate expressions, we propose a linear precoder design algorithm and obtain tractable expressions for precoding matrices. Numerical comparisons with the existing precoding approach demonstrate the significant advantages of the developed algorithm.

关键词： Downlink Massive MIMO Precoding Uplink Transmission line matrix methods Training Signal to noise ratio Deterministic equivalent FDD linear precoder mm algorithm massive MIMO statistical CSI

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Distributed Precoding for Virtual Sum-Rate Maximization in Network Massive MIMO Systems

Distributed Precoding for Virtual Sum-Rate Maximization in N...

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IEEE Wireless Communications and Networking Conference (WCNC)

作者： Zhu, Wen-Jie Sun, Chen Gao, Xiqi Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China Purple Mt Labs Nanjing 211100 Peoples R China

ISBN: (纸本)9781665491228

This paper investigates the distributed precoding for network massive multi-input multi-output (MIMO) communications without data sharing between cells. In order to restrict the information exchange, which imposes significant requirements on signaling overhead, we first reformulate the original weighted sum-rate maximization problem into a cell-specific form. With this reformulated problem, we take a virtual weighted sum-rate, whose expression only depends on precoders in a single cell and some initial values, as the objective function of an approximated problem. A stationary point of this non-concave virtual weighted sum-rate maximization problem is then achieved iteratively through the minorize-maximize (mm) algorithm. After exchanging a virtual covariance matrix generated locally, each base station (BS) can solely optimize its precoding matrix in parallel without any exchange during the optimization procedure. Numerical results show that the proposed method performs well in the sense of achievable sum-rate.

关键词： Network massive MIMO distributed precoding mm algorithm

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Graphit: Iterative Reweighted 1 algorithm for Sparse Graph Inference in State-Space Models 48

Graphit: Iterative Reweighted 1 Algorithm for Sparse Graph I...

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48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023

作者： Chouzenoux, Émilie Elvira, Víctor Université Paris-Saclay CentraleSupélec Inria Cvn Gif-sur-Yvette France University of Edinburgh School of Mathematics United Kingdom

ISBN: (纸本)9781728163277

State-space models (SSMs) are a common tool for modeling multi-variate discrete-time signals. The linear-Gaussian (LG) SSM is widely applied as it allows for a closed-form solution at inference, if the model parameters are known. However, they are rarely available in real-world problems and must be estimated. Promoting sparsity of these parameters favours both interpretability and tractable inference. In this work, we propose GraphIT, a majorization-minimization (mm) algorithm for estimating the linear operator in the state equation of an LG-SSM under sparse prior. A versatile family of non-convex regularization potentials is proposed. The mm method relies on tools inherited from the expectation-maximization methodology and the iterated reweighted-l1 approach. In particular, we derive a suitable convex upper bound for the objective function, that we then minimize using a proximal splitting algorithm. Numerical experiments illustrate the benefits of the proposed inference technique. © 2023 IEEE.

关键词： graphical inference iterative reweighted scheme mm algorithm sparsity State-space model

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A new class of zero-truncated counting models and its application

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COmmUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： Tang, Xian-Ping Tian, Yu-Zhu Wu, Chun-Ho Wang, Yue Mian, Zhi-Bao Northwest Normal Univ Sch Math & Stat Lanzhou Peoples R China Gansu Prov Res Ctr Basic Disciplines Math & Stat Lanzhou Peoples R China Hang Seng Univ Hong Kong Sch Decis Sci Shatin Hong Kong Peoples R China Educ Univ Hong Kong Dept Math & Informat Technol Hong Kong Peoples R China Univ Hull Sch Comp Sci Kingston Upon Hull England

Count data is a type of data derived from the number of times an event occurs per unit of time, and zero-truncated count data refers to count data without zero, which often appears in various fields. In this paper, a new zero-truncated Bell (ZTBell) distribution is proposed on the basis of Bell distribution. We studied its statistical properties, exploring methods such as maximum likelihood estimation (MLE), expectation-maximization (EM) algorithm, and minimization-maximization (mm) algorithm for parameter estimation, as well as conducting likelihood ratio tests. In addition, we used the Bootstrap method to calculate the standard errors and confidence intervals of the parameters. The simulation results found that all of the MLE, mm algorithm and EM algorithm are effective. And, as the sample size increases, the estimates of the parameters are closer to the true values and the root mean square error is smaller. Finally, applying the model to a set of factory accident data, we found that the ZTBell distribution fits better than the other models and is close to the fitting results of the zero-truncated generalized Poisson distribution. But ZTBell distribution has only one parameter, so it's even simpler compared to the latter. Therefore, the ZTBell distribution can be a good alternative to other zero-truncated distributions, which provides more options available for statistical analysis in this domain.

关键词： Bootstrap Count data EM algorithm mm algorithm ZTBell

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Heteroscedastic Laplace mixture of experts regression models and applications

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Applied Mathematics(A Journal of Chinese Universities) 2021年第1期36卷 60-69页

作者： WU Liu-cang ZHANG Shu-yu LI Shuang-shuang Faculty of Science Kunming University of Science and TechnologyKunming 650093China College of Mathematics and Informatics Fujian Normal UniversityFuzhou 350117China

Mixture of Experts(MoE)regression models are widely studied in statistics and machine learning for modeling heterogeneity in data for regression,clustering and *** distribution is one of the most important statistical tools to analyze thick and tail *** Mixture of Linear Experts(LMoLE)regression models are based on the Laplace distribution which is more *** to modelling variance parameter in a homogeneous population,we propose and study a new novel class of models:heteroscedastic Laplace mixture of experts regression models to analyze the heteroscedastic data coming from a heterogeneous population in this *** issues of maximum likelihood estimation are *** particular,Minorization-Maximization(mm)algorithm for estimating the regression parameters is *** of the estimators of the regression coefficients are evaluated through Monte Carlo *** from the analysis of two real data sets are presented.

关键词： mixture of experts regression models heteroscedastic mixture of experts regression models,Laplace distribution mm algorithm

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Point Cloud Registration algorithm Based on Cauchy Mixture Model

IEEE PHOTONICS JOURNAL

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IEEE PHOTONICS JOURNAL 2021年第1期13卷 1-13页

作者： Wang, Chang Yang, Yunxiu Shu, Qin Yu, Chunxiao Cui, Zhongma Sichuan Univ Coll Elect Engn Chengdu 610065 Peoples R China Southwest Inst Tech Phys Chengdu 610041 Peoples R China Beijing Inst Remote Sensing Equipment Beijing 100854 Peoples R China

In this paper, the Cauchy mixture distribution is used for rigid and affine registration. The Cauchy function has a wider effective range than the general window function, so it has a greater information utilization ratio than most registration algorithms. This means that the method can quickly match point clouds without initial registration and corresponding points. On the other hand, the computational complexity of Cauchy mixture model is lower than that of widely used Gaussian mixture model. This means that the introduction of Cauchy mixture model will save computing resources. However, the log-likelihood function of the Cauchy mixture distribution is a nonlinear function that is difficult to solve. This paper proposes an optimization method for the Cauchy mixture model, and discusses the advantages of the Cauchy mixture model in rigid and affine registration. In the experiment, compared with several other algorithms, our method quickly and accurately registers point clouds.

关键词： Affine cauchy distribution mm algorithm point cloud registration

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ORTHOGONAL TRACE-SUM MAXIMIZATION: APPLICATIONS, LOCAL algorithmS, AND GLOBAL OPTIMALITY

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2021年第2期42卷 859-882页

作者： Won, Joong-Ho Zhou, Hua Lange, Kenneth Seoul Natl Univ Dept Stat Seoul 08826 South Korea Univ Calif Los Angeles Dept Biostat Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Computat Med Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Human Genet Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Stat Los Angeles CA 90095 USA

This paper studies the problem of maximizing the sum of traces of matrix quadratic forms on a product of Stiefel manifolds. This orthogonal trace-sum maximization (OTSM) problem generalizes many interesting problems such as generalized canonical correlation analysis (CCA), Procrustes analysis, and cryo-electron microscopy of the Nobel prize fame. For these applications finding global solutions is highly desirable, but it has been unclear how to find even a stationary point, let alone test its global optimality. Through a close inspection of Ky Fan's classical result [Proc. Natl. Acad. Sci. USA, 35 (1949), pp. 652-655] on the variational formulation of the sum of largest eigenvalues of a symmetric matrix, and a semidefinite programming (SDP) relaxation of the latter, we first provide a simple method to certify global optimality of a given stationary point of OTSM. This method only requires testing whether a symmetric matrix is positive semidefinite. A by-product of this analysis is an unexpected strong duality between Shapiro and Botha [SIAM J. Matrix Anal. Appl., 9 (1988), pp. 378-383] and Zhang and Singer [Linear Algebra Appl., 524 (2017), pp. 159-181]. After showing that a popular algorithm for generalized CCA and Procrustes analysis may generate oscillating iterates, we propose a simple fix that provably guarantees convergence to a stationary point. The combination of our algorithm and certificate reveals novel global optima of various instances of OTSM.

关键词： Stiefel manifold canonical correlation analysis Procrustes analysis cryo-EM semidefinite programming MAXBET MAXDIFF mm algorithm Kurdyka-Lojasiewicz inequality

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Statistical Methods for Single Cell Gene Expression: Differential Expression, Curve Estimation and Graphical Modelling

Statistical Methods for Single Cell Gene Expression: Differe...

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作者： Saha, Satabdi Michigan State University

学位级别：Ph.D., Doctor of Philosophy

This dissertation elucidates a set of statistical methods developed for analysis of single cell gene expression datasets. Gene expression profiling of single cells has led to unprecedented progress in understanding normal physiology, disease progression and developmental processes. However, despite many improvements in high throughput sequencing, various technical factors including cell-cycle heterogeneity, library size differences, amplification bias, and low RNA capture per cell lead to high noise in scRNA-seq experiments. A primary characteristic of these datasets is the presence of high number of zeroes which represents the undetectable level of expression for a transcript. Statistical methods capable of modelling novel single cell experiments are developed and new estimation strategies are proposed and validated using simulated and real data experiments. • In Chapter 1, the motivation and underlying philosophies of single cell gene expression is reviewed. Methods for analysis of dose response experiments and gene co-expression networks are reviewed and novel statistical hypothesis to be investigated using single cell experiments are discussed. • In Chapter 2, I analyze a unique in vivo dose response hepatic scRNAseq dataset consisting of 9 dose groups with 3 biological replicates for 11 distinct liver cell types for greater than 100K cells. A Hurdle model for multiple group data is proposed, which models the bimodality of single cell gene expression within multiple groups. Based on the model assumptions, I derive a fit for purpose Bayesian test for simultaneously testing the differences in mean gene expression and zero proportions for multiple dose groups. For comparison the counterpart likelihood-ratio test for differential expression that incorporates testing for both components is also derived. This chapter was originally published in [1]. • In Chapter 3, dose response curve estimation for single cell experiments is studied. Current protocols for genomic dos

关键词： Differential gene expression Dose response curve estimation Graph signal processing mm algorithm Semiparametric regression Single cell gene expression

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Decode Phenome-Genome Interactions: A Data Science Approach

Decode Phenome-Genome Interactions: A Data Science Approach

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作者： Chattopadhyay, Abhijnan Michigan State University

学位级别：Ph.D., Doctor of Philosophy

The responses of plants to their environments are determined by multiple interacting genetic factors that themselves may operate through numerous biological mechanisms. Disentangling these complex genome-by-environment interactions is a significant challenge to understanding the underlying biology and developing more robust crops. This dissertation integrates high throughput phenotyping and genome sequencing and aims to harness these multidimensional interactions to test whether different genetic components affect biological processes through similar or distinct mechanisms. First, we present a comparison of different methods that can be practically used for genome-enabled prediction and selection purposes with the help of synthetic datasets with varying levels of difficulty and variability. Using such tools, we have found multiple traits are modulated by similar genomic regions, termed “co-localization.” But, the question remains, how can one test for co-segregation, or co-linkages, of multiple phenotypes to specific genetic polymorphisms? From domain knowledge, we can argue that there exist various physical modes of interactions among photosynthetic processes, which result in distinct patterns of interactions between measured parameters. We propose a Bayesian latent variable (LV) approach that tries to imitate such physical modes of interaction among photosynthetic processes by projecting the multivariate phenotypes into lower-dimensional latent factors. Estimation of the entries of the loading matrix (the connection between multidimensional phenotypes to LVs) is through the Automatic Relevance Determination (ARD) prior, which can automatically remove the irrelevant latent factors and add immediate interpretability. This means for a single genotype, the observed latent factors will likely reflect the effects of environmental or developmental effects on mechanistic interconnections. Also, these low-dimensional structure/ latent factors can be genetically mapped usin

关键词： Abiotic stress Correlation modeling mm algorithm Multi-omics Next generation sequencing Phenome-genome interaction

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Nonconvex regularization for convex image smoothing

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SIGNAL PROCESSING 2023年 205卷

作者： Zhu, Guoliang Lv, Xiaoguang Jiang, Le Sun, Xueman Fang, Biao Jiangsu Ocean Univ Sch Elect Engn Lianyungang 222005 Peoples R China Jiangsu Ocean Univ Sch Sci Lianyungang 222005 Peoples R China Jiangsu Ocean Univ Sch Comp Engn Lianyungang Peoples R China

Image smoothing is a fundamental part of many computer vision and graphics. In this paper, to improve the sparsity of the gradient norm of the smoothing image, we use nonconvex penalty functions as regu-larization terms. A condition on nonconvex regularizers is given to ensure that the objective functions are strictly convex. We apply the powerful majorization-minimization (mm) algorithm for solving the convex image smoothing models. Proof of global convergence for the mm algorithm is provided. The superiority of the proposed method in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and visual quality is verified through comprehensive experiments in a variety of applications such as image abstraction, artifact removal, detail enhancement, texture removal, image denoising and high dynamic range (HDR) tone mapping.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Nonconvex regularization mm algorithm Convergence Convex Image smoothing

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