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Poisson reduced-rank models with sparse loadings

JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2021年第4期50卷 1079-1097页

作者： Lee, Eun Ryung Park, Seyoung Sungkyunkwan Univ Dept Stat Seoul South Korea

High-dimensional Poisson reduced-rank models have been considered for statistical inference on low-dimensional locations of the individuals based on the observations of high-dimensional count vectors. In this study, we assume sparsity on a so-called loading matrix to enhance its interpretability. The sparsity assumption leads to the use of L-1 penalty, for the estimation of the loading. We provide novel computational and theoretical analyses for the corresponding penalized Poisson maximum likelihood estimation. We establish theoretical convergence rates for the parameters under weak-dependence conditions;this implies consistency even in large-dimensional problems. To implement the proposed method involving several computational issues, including nonconvex log-likelihoods, L-1 penalty, and orthogonal constraints, we developed an iterative algorithm. Further, we propose a Bayesian-Information-Criteria-based penalty parameter selection, which works well in the implementation. Some numerical evidence is provided by conducting real-data-based simulation analyses and the proposed method is illustrated with the analysis of German party manifesto data.

关键词： Poisson reduced-rank models Interpretation Sparsity Rotation LASSO L-1 Orthogonal constraint iterative algorithm

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A Heuristic algorithm for Arbitrary-criterion Optimization of Quantization Scales

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OPTICAL MEMORY AND NEURAL NETWORKS 2021年第2期30卷 140-145页

作者： Gashnikov, M., V Samara Natl Res Univ Samara 443086 Russia RAS IPSI RAS Branch FSRC Crystallog & Photon Samara 443001 Russia

The paper considers the generation of effective quantization scales which meet any quality criteria under any constrains. The analysis of work of available methods allows a concept of a heuristic iterative algorithm for generating near-optimal quantization scales. The concept uses a uniform scale as an initial approach followed by an iterative target-criterion-optimizing recalculation of quantization interval boundaries with adhering to the constrains at each iteration. The formal description of the algorithm is presented. The software implementation of the algorithm is incorporated into the hierarchical image-compression method. The numerical experiments are carried out to test the efficiency of the algorithm and substantiate the convergence of the algorithm to the best solution.

关键词： quantization optimization iterative algorithm uniform scale error

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A Sparse Learning Approach to Relative-Volatility-Managed Portfolio Selection

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SIAM JOURNAL ON FINANCIAL MATHEMATICS 2021年第1期12卷 410-445页

作者： Pun, Chi Seng Nanyang Technol Univ Sch Phys & Math Sci Singapore 637371 Singapore

This paper proposes a self-calibrated sparse learning approach for estimating a sparse target vector, which is a product of a precision matrix and a vector, and investigates its application to finance to provide an innovative construction of a relative-volatility-managed portfolio. The proposed iterative algorithm, called DECODE, jointly estimates a performance measure of the market and the effective parameter vector in the optimal portfolio solution, where the relative-volatility timing is introduced into the risk exposure of an efficient portfolio via the control of its sparsity. The portfolio's risk exposure level, which is linked to its sparsity in the proposed framework, is automatically tuned with the latest market condition without using cross validation. The algorithm is efficient as it costs only a few computations of quadratic programming. We prove that the iterative algorithm converges and show the oracle inequalities of the DECODE, which provide sufficient conditions for a consistent estimate of an optimal portfolio. The algorithm can also handle the curse of dimensionality in that the number of training samples is less than the number of assets. Our empirical studies of over-12-year backtest illustrate the relative-volatility timing feature of the DECODE and the superior out-of-sample performance of the DECODE portfolio, which beats the equally weighted portfolio and improves over the shrinkage portfolio.

关键词： direct estimation iterative algorithm self-calibrated regularization oracle inequality relative-volatility timing market-sensitive asset selection

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Hierarchical Principle-Based iterative Parameter Estimation algorithm for Dual-Frequency Signals

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2019年第7期38卷 3251-3268页

作者： Liu, Siyu Ding, Feng Xu, Ling Hayat, Tasawar Jiangnan Univ Sch Internet Things Engn Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Jiangsu Peoples R China Hubei Univ Technol Sch Elect & Elect Engn Wuhan 430068 Hubei Peoples R China King Abdulaziz Univ Dept Math Fac Sci Jeddah 21589 Saudi Arabia

In this paper, we consider the parameter estimation problem of dual-frequency signals disturbed by stochastic noise. The signal model is a highly nonlinear function with respect to the frequencies and phases, and the gradient method cannot obtain the accurate parameter estimates. Based on the Newton search, we derive an iterative algorithm for estimating all parameters, including the unknown amplitudes, frequencies, and phases. Furthermore, by using the parameter decomposition, a hierarchical least squares and gradient-based iterative algorithm is proposed for improving the computational efficiency. A gradient-based iterative algorithm is given for comparisons. The numerical examples are provided to demonstrate the validity of the proposed algorithms.

关键词： iterative algorithm Signal modeling Hierarchical identification Least squares Newton search Gradient search

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Identification of MISO Wiener systems using the LMI algorithm

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2021年第3-4期37卷 285-291页

作者： Zhou, Lincheng Li, Xiangli Changshu Inst Technol Sch Elect Engn & Automat Changshu Jiangsu Peoples R China

This paper focuses on a new identification method for multiple-input single output (MISO) Wiener nonlinear systems, in which the static nonlinear block is assumed to be a polynomial. The basic idea is to establish a MISO Wiener nonlinear identification model with polynomial nonlinearities by means of the key term separation principle. Then, a new identification method based on Levenberg-Marquardt iterative (LMI) search techniques, which can make full use of all the measured input and output data, but also automatically change the search step-size according to the change values of the quadratic criterion function, is derived to obtain an accurate and fast parameter estimation of the model. Finally, the simulation results demonstrate the efficacy of this method.

关键词： LMI search parameter estimation iterative algorithm multiple-input single-output system Wiener nonlinear system

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Frequency-Limited Reduced Models for Linear and Bilinear Systems on the Riemannian Manifold

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第9期66卷 3938-3951页

作者： Jiang, Yao-Lin Xu, Kang-Li Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China

In this article, we propose two new iterative algorithms to solve the frequency-limited Riemannian optimization model order reduction problems of linear and bilinear systems. Different from the existing Riemannian optimization methods, we design a new Riemannian conjugate gradient scheme based on the Riemannian geometry notions on a product manifold, and then generate a new search direction. Theoretical analysis shows that the resulting search direction is always descent with depending neither on the line search used, nor on the convexity of the cost function. The proposed algorithms are also suitable for generating reduced systems over a frequency interval in bandpass form. Finally, two numerical examples are simulated to demonstrate the efficiency of our algorithms.

关键词： Manifolds Optimization Nonlinear systems Linear systems Frequency control Geometry Time-frequency analysis Finite frequency frequency-limited controllability and observability Gramians iterative algorithm model order reduction (MOR) product manifold Riemannian optimization

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Fast and Robust Unsupervised Dimensionality Reduction with Adaptive Bipartite Graphs

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KNOWLEDGE-BASED SYSTEMS 2023年第1期276卷

作者： Niu, Fan Zhao, Xiaowei Guo, Jun Shi, Mei Liu, Xiaoxia Liu, Baoying Northwest Univ Sch Informat Sci & Technol Xian 710127 Peoples R China Northwestern Polytech Univ Sch Comp Sci Xian 710072 Peoples R China Northwestern Polytech Univ Sch Artificial Intelligence Opt & Elect iOPEN Xian 710072 Peoples R China Shaanxi Int Joint Res Ctr Battery free Internet Th Xian 710127 Peoples R China

Recent unsupervised dimension reduction algorithms use similarity graphs between data point pairs to preserve local structure while reducing dimension. However, the time complexity of these methods is proportional to the square of the number of samples, which limits their application to large-scale datasets. Moreover, the square Euclidean calculation criterion between sample point pairs will magnify the bad influence of outliers on the graph. In addition, these methods only preserve the local structure while losing other important structural information. To this end, we propose a fast adaptive unsupervised projection model termed Fast and Robust Unsupervised Dimensionality Reduction with Adaptive Bipartite Graph (FRUDR-ABG), which uses a few anchor points and sample points to build a bipartite graph to preserve the local geometric structure of the data to reduce the running time and improve efficiency. We propose a criterion based on the l2,1 norm to calculate the distance between anchor points and data points to reduce the negative influence of outliers on graph construction. A practical strategy is also proposed to realize joint learning of global and local structures. According to the characteristics of graph construction and dimensionality reduction adaptive learning in the algorithm, we design an iterative reweighting method to solve the model. Experimental results on several benchmark datasets show that FRUDR-ABG has higher efficiency and recognition performance than existing unsupervised dimensionality reduction methods.& COPY;2023 Elsevier B.V. All rights reserved.

关键词： Graph-based unsupervised dimension reduction Anchor points Subspace projection iterative algorithm

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Identification of Unknown Parameters of the Dynamic Model of Mass Transfer

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MATHEMATICAL MODELLING AND ANALYSIS 2023年第3期28卷 459-468页

作者： Zavialov, Volodymyr Lobok, Oleksii Mysiura, Taras Popova, Nataliia Chornyi, Valentyn Pohorilyi, Taras Natl Univ Food Technol Volodymyrska Str 68 UA-01033 Kiev Ukraine

An iterative algorithm for identifying unknown parameters of a mathematical model based on the Bayesian approach is proposed, which makes it possible to determine the most probable maximum informative estimates of these parameters. The example of the mathematical model of mass transfer dynamics shows the algorithm for finding the most probable and most informative estimate of the vector of unknown parameters, and also an analysis of the sequence of the corresponding steps is given. The results of computational experiments showed a significant dependence of the results of the calculations on the choice of the initial approximation point and slowing down the rate of convergence of the iterative process (and even its divergence) with an unsuccessful choice of the initial approximation. The validity of the obtained results is provided by analytical conclusions, the results of computational experiments, and statistical modeling. The results of computational experiments make it possible to assert that the proposed algorithm has a sufficiently high convergence for a given degree of accuracy and makes it possible to derive not only estimates of point values of mathematical model parameters based on a posteriori analysis, but also confidence intervals of these estimates. At the same time, it should be noted that the results of calculations depend significantly on the choice of the initial approximation point and the slowing of the convergence rate of the iterative process with an unsuccessful choice of the initial approximation. Analytical studies and results of calculations confirm the effectiveness of the proposed identification algorithm, which makes it possible, with the help of active, purposeful experiments, to build more accurate mathematical models. In accordance with the algorithm, a program was developed in the MatLab mathematics package and computational experiments were performed.

关键词： iterative algorithm mass transfer Bayesian approach mathematical modeling variance experiment

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Static-output-feedback robust HPo control for actively controlled systems considering uncertain input time delay

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EUROPEAN JOURNAL OF CONTROL 2025年 84卷

作者： Zheng, Yuanguang Shao, Yu Yu, Zhiqiang Nanchang Hangkong Univ Sch Math & Informat Sci Nanchang 330063 Jiangxi Peoples R China

This paper addresses the static output feedback control problem for systems with uncertain input time delay and proposes a robust control method that ensures HPo performance. Departing from traditional approaches based on Lyapunov-Krasovskii functionals, this work introduces a novel combination of time scale transformation, Chebyshev spectral continuous-time approximation, and cone complementarity linearization methods. Initially, the system with uncertain input time delay is reformulated into a delay-free system by introducing some specific augmented matrices, ensuring the solvability of the transformed system. Subsequently, robust HPo control is applied to this delay-free model, and a tailored iterative algorithm is developed to solve the bilinear matrix inequalities inherent in the control design, leading to the computation of the feedback gain matrix. The proposed method's effectiveness is demonstrated through numerical case studies.

关键词： HPoperformance Input time delay Bilinear matrix inequalities Output feedback control iterative algorithm

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Extension of nonnegative constraints to difference-map algorithm on both real and imaginary parts of real space in phase retrieval

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OPTICAL ENGINEERING 2023年第3期62卷 033108-033108页

作者： Liu, Mengxin Cao, Wenke Wang, Yongteng Yang, Wenjing Yu, Yiming Yue, Qing Sun, Chuanshuo Zhang, Jian Shandong Jianzhu Univ Sch Sci Jinan Shandong Peoples R China

The difference-map (DM) algorithm is an iterative method to retrieve the image of an object from its diffraction pattern. Our study proposes the use of nonnegative constraints, reducing the number of unknown variables by half, on both the real and imaginary parts of the object space to reconstruct the image of a complex-valued object in the iterative process of the DM algorithm. The feasibility of the algorithm in biological cell applications was demonstrated using both simulations and optical laser coherent diffraction experiments. The results show that a more accurate image of the object can be retrieved using a loose support by nonnegative constraints than by the same support alone. The comparison indicates that the DM algorithm is superior to the hybrid input-output algorithm in the presence of nonnegative constraints. Therefore, during the execution of a DM algorithm, a loose support allows for more accurate reconstruction than a tight support, which can hardly be found in most cases because of the noise blurring of the retrieved image, and considerable reduction in the reconstruction errors. (c) 2023 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： iterative algorithm coherent diffraction imaging nonnegative constraint difference map algorithm

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