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Non-negative Constrained Penalty for High-Dimensional Correlated Data

COMMUNICATIONS IN MATHEMATICS AND STATISTICS 2025年 1-20页

作者： Ming, Hao Chen, Yinjun Yang, Hu Chongqing Univ Coll Math & Stat Chongqing 401331 Peoples R China

In this paper, we investigate five estimators for high-dimensional correlated data with the non-negative constraints on the coefficients, which are nnMnet, nnSnet, nnSace, nnGsace and nnSsace estimators. Specifically, three commonly used penalties: Mnet, smooth adjustment for correlated effects (Sace), and generalized smooth adjustment for correlated effects (Gsace), under which three non-negative penalty estimators, nnMnet, nnSace and nnGsace are proposed, accordingly. Similar to the nnMnet and nnGsace estimators, we further combine the Scad penalty function with Liu estimator and Ridge estimator to propose non-negative Snet (nnSnet) and non-negative Ssace (nnSsace), respectively. For non-negative variable selection, we give two algorithms, fast active set block coordinate descent algorithm and one-step estimator with coordinate descent algorithm. Furthermore, we demonstrate the consistency of variable selection and estimation error bounds for the nnSace estimator, and the oracle non-negative biased estimator property for nnMnet, nnSnet, nnGsace and nnSsace estimators, respectively. Finally, we show the advantages of the proposed method through some simulations and apply our method on stock data.

关键词： Correlated effects Non-negative penalized estimator Active set block coordinate descent algorithm

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block coordinate descent energy minimization for dynamic cohesive fracture

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2019年 354卷 663-688页

作者： Hirmand, M. Reza Papoulia, Katerina D. Univ Waterloo Dept Mech & Mechatron Engn Waterloo ON N2L 3G1 Canada Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada

A block coordinate descent algorithm within a discontinuous Galerkin finite element formulation is proposed for both explicit and implicit energy minimization in solid bodies in which rigid-cohesive fractures initiate and propagate. The crack opening dependent Barenblatt type surface cohesive energy function is non-differentiable at the origin. In each iteration or each explicit update, the algorithm minimizes the potential with respect to each crack opening displacement unknown and with respect to the block of deformation unknowns, sequentially. This decomposes minimization of the full non-differentiable problem into a number of "small" non-differentiable sub-problems that must be solved locally at the inter-element boundaries of the finite element mesh and an "easy" differentiable sub-problem that characterizes global equilibrium. As a result, non-differentiability is effectively treated locally and the algorithm can be easily incorporated into standard finite element codes. On the basis of a convexity analysis of the proposed non-differentiable energy functional, we obtain a minimum cohesive process zone resolution criterion, known empirically in the previous literature as a requirement for capturing the amount of dissipated fracture energy correctly. The method is free of any regularization parameters and preserves the discrete nature of fracture without introducing a stress discontinuity at initiation of decohesion. Robustness of the method is shown through several numerical examples of fragmentation and branching and through comparisons with existing numerical and experimental results. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Cohesive fracture Non-differentiable energy minimization Generalized differential calculus block coordinate descent algorithm

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Multiple Tensor-on-Tensor Regression: An Approach for Modeling Processes With Heterogeneous Sources of Data

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TECHNOMETRICS 2021年第2期63卷 147-159页

作者： Gahrooei, Mostafa Reisi Yan, Hao Paynabar, Kamran Shi, Jianjun Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA Arizona State Univ Sch Comp Informat & Decis Syst Engn Tempe AZ USA Georgia Inst Technol H Milton Stewart Sch Ind & Syst 436 Groseclose Bld765 Ferst Dr Atlanta GA 30332 USA

In recent years, measurement or collection of heterogeneous sets of data such as those containing scalars, waveform signals, images, and even structured point clouds, has become more common. Statistical models based on such heterogeneous sets of data that represent the behavior of an underlying system can be used in the monitoring, control, and optimization of the system. Unfortunately, available methods mainly focus on the scalars and profiles and do not provide a general framework for integrating different sources of data to construct a model. This article addresses the problem of estimating a process output, measured by a scalar, curve, image, or structured point cloud by a set of heterogeneous process variables such as scalar process setting, profile sensor readings, and images. We introduce a general multiple tensor-on-tensor regression approach in which each set of input data (predictor) and output measurements are represented by tensors. We formulate a linear regression model between the input and output tensors and estimate the parameters by minimizing a least square loss function. To avoid overfitting and reduce the number of parameters to be estimated, we decompose the model parameters using several basis matrices that span the input and output spaces, and provide efficient optimization algorithms for learning the basis and coefficients. Through several simulation and case studies, we evaluate the performance of the proposed method. The results reveal the advantage of the proposed method over some benchmarks in the literature in terms of the mean square prediction error. for this article are available online.

关键词： Alternating least square algorithm Blessing of dimensionality block coordinate descent algorithm High-dimensional process modeling Tucker decomposition

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Functional Graphical Models

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2019年第525期114卷 211-222页

作者： Qiao, Xinghao Guo, Shaojun James, Gareth M. London Sch Econ Dept Stat London England Renmin Univ China Inst Stat & Big Data Beijing Peoples R China Univ Southern Calif Dept Data Sci & Operat Los Angeles CA USA

Graphical models have attracted increasing attention in recent years, especially in settings involving high-dimensional data. In particular, Gaussian graphical models are used to model the conditional dependence structure among multiple Gaussian random variables. As a result of its computational efficiency, the graphical lasso (glasso) has become one of the most popular approaches for fitting high-dimensional graphical models. In this paper, we extend the graphical models concept to model the conditional dependence structure among p random functions. In this setting, not only is p large, but each function is itself a high-dimensional object, posing an additional level of statistical and computational complexity. We develop an extension of the glasso criterion (fglasso), which estimates the functional graphical model by imposing a block sparsity constraint on the precision matrix, via a group lasso penalty. The fglasso criterion can be optimized using an efficient block coordinate descent algorithm. We establish the concentration inequalities of the estimates, which guarantee the desirable graph support recovery property, that is, with probability tending to one, the fglasso will correctly identify the true conditional dependence structure. Finally, we show that the fglasso significantly outperforms possible competing methods through both simulations and an analysis of a real-world electroencephalography dataset comparing alcoholic and nonalcoholic patients.

关键词： block coordinate descent algorithm block sparse precision matrix Functional data Functional principal component analysis Graphical models

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A New Phase Linking algorithm for Multi-temporal InSAR based on the Maximum Likelihood Estimator

A New Phase Linking Algorithm for Multi-temporal InSAR based...

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IEEE International Geoscience and Remote Sensing Symposium (IGARSS)

作者： Vu, Phan Viet Hoa Brigui, Frederic Breloy, Arnaud Yan, Yajing Ginolhac, Guillaume Off Natl Etud & Rech Aerosp F-91120 Palaiseau France Paris Nanterre Univ LEME EA 4416 F-92410 Ville Davray France Univ Savoie Mt Blanc LISTIC F-74000 Annecy France

ISBN: (数字)9781665427920

ISBN: (纸本)9781665427920

This paper presents a new algorithm for improving the estimation of interferometric SAR (InSAR) phases in the context of time series and phase linking approach. Based on maximum likelihood estimator of a multivariate Gaussian model, the estimation of the InSAR phases is solved using a block coordinate descent algorithm. Compared to the state-of-the-art approaches, the main improvement lies on the joint estimation of the covariance matrix and the InSAR phases instead of using a plug-in coherence estimate obtained from the sample covariance of the data or the modeling of the temporal decorrelation of the target under observation. Results of synthetic simulations confirm the improvement brought by the proposed estimator.

关键词： Multi-temporal InSAR Surface Displacement Monitoring Phase Linking Maximum Likelihood Estimator block coordinate descent algorithm

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OPTIMAL ASYNCHRONOUS MULTI-SENSOR REGISTRATION IN 3 DIMENSIONS

OPTIMAL ASYNCHRONOUS MULTI-SENSOR REGISTRATION IN 3 DIMENSIO...

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IEEE Global Conference on Signal and Information Processing (GlobalSIP)

作者： Jiang, Shunan Pu, Wenqiang Luo, Zhi-Quan Chinese Univ Hong Kong Shenzhen Res Inst Big Data Shenzhen Peoples R China Xidian Univ Natl Lab Radar Signal Proc Xian Shaanxi Peoples R China

ISBN: (纸本)9781728112954

The success of multi-sensor data fusion requires an important step called sensor registration, which involves estimating sensor biases from sensors 'asynchronous measurements. There are two difficulties in the bias estimation problem: one is the unknown target states which serve as the nuisance variables in the estimation problem, the other is the highly nonlinear coordinate transformation between sensors' local and common coordinate frames. In this work, we focus on the 3-dimensional scenario and propose a new nonlinear least squares (LS) formulation which avoids estimating target states. The proposed LS formulation eliminates the target states by exploiting the nearly-constant velocity property of the target motion. To address the intrinsic nonlinearity, we propose a block coordinate descent (BCD) scheme for solving the formulation which alternately updates various bias estimates. Specifically, semidefinite relaxation technique is introduced to handle the nonlinearity brought by angle biases. Furthermore, two BCD algorithms with different block picking rules are proposed. Finally, the effectiveness and the efficiency of the proposed BCD algorithms are demonstrated in the numerical simulation section.

关键词： Sensor registration problem nonlinear least squares block coordinate descent algorithm semidefinite relaxation

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Optimal Antenna Selection and Time Sharing in RF-Powered Cognitive Networks With Ambient Backscatter Communication 97

Optimal Antenna Selection and Time Sharing in RF-Powered Cog...

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97th IEEE Vehicular Technology Conference (VTC-Spring)

作者： Liu, Wenjing Shen, Shanpu Zhang, Chi Tsang, Danny H. K. Murch, Ross Hong Kong Univ Sci & Technol Dept ECE Hong Kong Peoples R China Hong Kong Univ Sci & Technol Guangzhou IoT Thrust Guangzhou Guangdong Peoples R China

ISBN: (纸本)9798350311143

In this paper, we propose a new solution to improve the achievable rate of radio frequency (RF) powered cognitive radio networks (CRNs) with ambient backscatter communication (AmBC). Assisted with AmBC, the secondary transmitter (ST) can harvest energy and backscatter ambient signals when the primary channel is busy, which enhances the achievable rate compared with conventional RF-powered CRNs adopting the harvest-then-transmit (HTT) protocol. Our work proposes an RF-powered CRN that uses a multi-antenna ST since implementing multiple antennas on ST can enhance energy harvesting and increase the data rate. We discuss the corresponding time sharing and antenna selection tradeoffs and propose a low-complexity and time-efficient block coordinate descent (BCD)-assisted exhaustive search algorithm to find the optimal tradeoff that maximizes the data rate of the system. Simulation results show that our proposed scheme outperforms both the HTT mode and the ambient backscatter technique, leading to improved overall system performance.

关键词： Ambient backscatter communication block coordinate descent algorithm cognitive radios multiple antennas

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Spatially multi-scale dynamic factor modeling via sparse estimation

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INTERNATIONAL JOURNAL OF MATHEMATICS FOR INDUSTRY 2019年第1期11卷

作者： Araki, Takamitsu Akaho, Shotaro Natl Inst Adv Ind Sci & Technol Human Informat Res Inst 1-1-1 Umezono Tsukuba Ibaraki 3058568 Japan

In many spatio-temporal data, their spatial variations have inherent global and local structures. The spatially continuous dynamic factor model (SCDFM) decomposes the spatio-temporal data into a small number of spatial and temporal variations, where the spatial variations are represented by the factor loading (FL) functions. However, the FL functions estimated by the maximum likelihood or maximum L-2 penalized likelihood capture global structures but do not capture local structures. We propose a method for estimating the spatially multi-scale FL functions using a sparse penalty. To overcome the problems of existing sparse penalties, we propose the adaptive graph lasso (AGL) penalty. The method with the AGL penalty eliminates redundant basis functions contained in the FL functions, and leads to the FL functions having global and localized structures. We derive the EM algorithm with block coordinate descent that enables us to maximize the AGL penalized log-likelihood stably. Applications to synthetic and real data show that the proposed modeling procedure accurately extract not only the spatially global structures but also spatially local structures, which the L-2 penalized estimation do not extract.

关键词： Spatially multi-scale structure dynamic factor model adaptive graph lasso block coordinate descent algorithm EM algorithm

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