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The MLE algorithm for the matrix normal distribution

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 1999年第2期64卷 105-123页

作者： Dutilleul, P McGill Univ Dept Plant Sci Lab Appl Stat Ste Anne De Bellevue PQ H9X 3V9 Canada

The maximum likelihood estimation (MLE) of the parameters of the matrix normal distribution is considered, In the absence of analytical solutions of the system of likelihood equations for the among-row and among-column covariance matrices, a two-stage algorithm must be solved to obtain their maximum likelihood estimators. A necessary and sufficient condition for the existence of maximum likelihood estimators is given and the question of their stability as solutions of the system of likelihood equations is addressed. In particular, the covariance matrix parameters and their maximum likelihood estimators are defined up to a positive multiplicative constant;only their direct product is uniquely defined. Using simulated data under two variance-covariance structures that, otherwise, are indistinguishable by semivariance analysis, further specific aspects of the procedure are studied: (1) the convergence of the MLE algorithm is assessed;(2) the empirical bias of the direct product of covariance matrix estimators is calculated for various sample sizes;and (3) the consistency of the estimator is evaluated by its mean Euclidean distance from the parameter, as a function of the sample size. The adequacy of the matrix normal model, including the separability of the variance-covariance structure, is tested on multiple time series of dental medicine data;other applications to real doubly multivariate data are outlined.

关键词： matrix normal distribution separability of variance-covariance structure maximum likelihood estimation two-stage algorithm existence and stability of estimators test of model adequacy

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A Fast Solution to the Lasso Problem with Equality Constraints

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2024年第3期33卷 804-813页

作者： Tran, Lam Li, Gen Luo, Lan Jiang, Hui Univ Michigan Dept Biostat Ann Arbor MI 48109 USA Rutgers State Univ Dept Biostat & Epidemiol New Brunswick NJ USA

The equality-constrained lasso problem augments the standard lasso by imposing additional structure on regression coefficients. Despite the broad utilities of the equality-constrained lasso, existing algorithms are typically computationally inefficient and only applicable to linear and logistic models. In this article, we devise a fast solution to the equality-constrained lasso problem with a two-stage algorithm: first obtaining candidate covariate subsets of increasing size from unconstrained lasso problems and then leveraging an efficient combined alternating direction method of multipliers/Newton-Raphson algorithm. Our proposed algorithm leads to substantial speedups in getting the solution path of the constrained lasso and can be easily adapted to generalized linear models and Cox proportional hazards models. We conduct extensive simulation studies to demonstrate the computational advantage of the proposed method over existing solvers. To further show the unique utility of our method, we consider two real-world data examples: a microbiome regression analysis and a myeloma survival analysis;neither example could be solved by naively fitting the constrained lasso problem on the full predictor set. Supplementary materials for this article are available online.

关键词： Candidate subset approach Compositional microbiome data Constrained lasso two-stage algorithm

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Data center supply chain configuration design: A two-stage decision approach

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SOCIO-ECONOMIC PLANNING SCIENCES 2019年 66卷 119-135页

作者： Ibn Faiz, Tasnim Noor-E-Alam, Md Northeastern Univ Dept Mech & Ind Engn 360 Huntington Ave Boston MA 02115 USA

Data centers are special-purpose facilities that enable customers to perform cloud based real-time online transactions and rigorous computing operations. Service levels of data center facilities are characterized by response time between query and action, which to a large extent depends on data center location and data travel distance. Another aspect of service level is resource up-time availability, which is determined by data center configuration. Data center location and configuration decisions are, therefore, of great significance to ensure uninterrupted operations in customers of manufacturing and service industries relying on cloud-based computing resources. In this study, following a grid-based location approach, we present two mixed integer linear programming models for capacitated single-source data center location-allocation problems. The first model provides optimal locations, capacities and configurations of data centers, and allocation of demands to open facilities when there is no existing facilities in the region. Our second model considers the decision problem of meeting new demand when the existing demand is met by the already opened facilities. We term these newly arrived demand as replication demand, which results either from emergence of new users of existing customers at distant locations in the future, or as a means of increasing data resilience by creating data replication as a backup. To solve the decision problem for meeting primary and replication demand optimally, we propose a two-stage decision algorithm. The algorithm provides optimal locations, capacities and configurations for new data centers, capacity addition decisions to the existing facilities and subsequent allocation of demands. Both models and solution algorithm are implemented using AMPL programming language and solved with CPLEX solver. The models are found to be scalable and capable to provide high quality solutions in reasonable time.

关键词： Data center location Supply chain configuration design Mixed integer linear program Grid-based location problem two-stage algorithm

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Minimum cost-compression risk in principal component analysis

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AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 2022年第4期64卷 422-441页

作者： Chattopadhyay, Bhargab Banerjee, Swarnali Indian Inst Technol Jodhpur Sch Management & Entrepreneurship Jodhpur 342030 Rajasthan India Loyola Univ Chicago Dept Math & Stat Chicago IL 60660 USA

Principal Component Analysis (PCA) is a popular multivariate analytic tool which can be used for dimension reduction without losing much information. Data vectors containing a large number of features arriving sequentially may be correlated with each other. An effective algorithm for such situations is online PCA. Existing Online PCA research works revolve around proposing efficient scalable updating algorithms focusing on compression loss only. They do not take into account the size of the dataset at which further arrival of data vectors can be terminated and dimension reduction can be applied. It is well known that the dataset size contributes to reducing the compression loss - the smaller the dataset size, the larger the compression loss while larger the dataset size, the lesser the compression loss. However, the reduction in compression loss by increasing dataset size will increase the total data collection cost. In this paper, we move beyond the scalability and updation problems related to Online PCA and focus on optimising a cost-compression loss which considers the compression loss and data collection cost. We minimise the corresponding risk using a two-stage PCA algorithm. The resulting two-stage algorithm is a fast and an efficient alternative to Online PCA and is shown to exhibit attractive convergence properties with no assumption on specific data distributions. Experimental studies demonstrate similar results and further illustrations are provided using real data. As an extension, a multi-stage PCA algorithm is discussed as well. Given the time complexity, the two-stage PCA algorithm is emphasised over the multi-stage PCA algorithm for online data.

关键词： compression loss covariance matrix estimation dimension reduction principal component analysis two-stage algorithm

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NEW algorithm FOR SOLVING CERTAIN VARIATIONAL PROBLEMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1977年第3期22卷 389-397页

作者： NG, KYK SANCHO, NGF CANADA DEPT NATL DEF OPERAT RES & ANAL ESTABOTTAWAONTARIOCANADA MCGILL UNIV DEPT MATHMONTREAL H3C 3G1QUEBECCANADA

A technique for finding the solution of discrete, multistate dynamic programming problems is applied to solve certain variational problems. The algorithm is a method of successive approximations using a general two-stage solution. The advantage of the method is that it provides a means of reducing Bellman's “curse of dimensionality.” An example on the Plateau problem or the minimal surface area problem is considered, and the algorithm is found to be computationally efficient.

关键词： Calculus of variations dynamic programming reduction of dimensionality two-stage algorithm

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Heterogeneous-IRS: A Green IRS Structure With Dynamically and Statically Tunable Elements

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IEEE WIRELESS COMMUNICATIONS LETTERS 2024年第12期13卷 3464-3468页

作者： Zhao, Weibiao Wu, Qiucen Yu, Guanghua Li, Ping Zhu, Yu Fudan Univ Sch Informat Sci & Technol Key Lab Informat Sci Electromagnet Waves MoE Shanghai 200433 Peoples R China ZTE Corp Wireless & Comp Prod R&D Inst Algorithm Dept Shanghai 201203 Peoples R China

Recently, intelligent reflecting surface (IRS) has received significant attention due to its ability to smartly reconfigure the wireless environment. However, in practical implementation, the power consumption of the conventional IRS could be prohibitive with the large number of reflecting elements and control circuits employed. To tackle this problem, in this letter, we propose a green heterogeneous-IRS (HE-IRS) structure consisting of both dynamically tunable elements (DTEs) and statically tunable elements (STEs). Compared to the conventional IRS comprising only DTEs, the HE-IRS provides a better trade-off between performance and power consumption by integrating power-free STEs. To show the efficiency of the proposed HE-IRS, we apply it in a multi-input multi-output system and formulate a joint base station precoding, HE-IRS beamforming and user equipment (UE) decoding optimization problem. Furthermore, we propose a two-stage algorithm to solve it. Simulation results show that with the prior information of the UE location area, the HE-IRS can achieve a competitive spectral efficiency as that of the conventional IRS but with much lower power consumption.

关键词： Power demand Vectors Optimization Circuits Wireless communication Tuning Millimeter wave communication MIMO communication Green products Array signal processing Heterogeneous intelligent reflecting surface statically tunable elements two-stage algorithm

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Mode-based energy storage control approach for residential photovoltaic systems

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IET SMART GRID 2019年第1期2卷 69-76页

作者： Henri, Gonzague Lu, Ning Carrejo, Carlos North Carolina State Univ Dept Elect & Comp Engn Raleigh NC 27695 USA Total Energy Management Syst Dept Paris France

This study presents a novel mode-based energy storage control approach. Assuming that an energy storage device (ESD) is equipped with a set of predetermined real-time control modes, the dispatch objective is to select an optimal mode instead of a continuous charging or discharging power value. A two-stage algorithm is developed for mode selection. In the first stage, a sliding 24h economic model predictive control algorithm is used to determine the power outputs of the ESD for the next 24h. In the second stage, the output sign for the next time step determines the class of modes to be elected (charging or discharging). The information from the first stage is used to compute the total cost for each selected mode. The mode with the lowest day-ahead cost is chosen. The residential electricity consumption data collected in the PECAN Street Project is used in the simulation to validate the performance of the proposed algorithm. Simulation results show that using a mode-based approach reduces the sensitivity to forecasting errors along with load and solar variability. The algorithm performance is consistent across different load patterns.

关键词： photovoltaic power systems energy storage power consumption predictive control load dispatching continuous charging two-stage algorithm mode selection economic model predictive control algorithm mode-based energy storage control approach energy storage device real-time control modes optimal mode residential electricity consumption data PECAN Street Project forecasting errors solar variability load patterns time 24 0 hour

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Trivial two-stage group testing for complexes using almost disjunct matrices

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DISCRETE APPLIED MATHEMATICS 2004年第1期137卷 97-107页

作者： Macula, AJ Rykov, VV Yekhanin, S SUNY Coll Geneseo Dept Math Geneseo NY 14454 USA Moscow MV Lomonosov State Univ Dept Cybernet & Comp Sci Moscow 119899 Russia

Let [t] represent a finite population with t elements. Suppose we have an unknown d-family of k-subsets Gamma of [t]. We refer to Gamma as the set of positive k-complexes. In the group testing for complexes problem, Gamma must be identified by performing 0, 1 tests on subsets or pools of [t]. A pool is said to be positive if it completely contains a complex;otherwise the pool is said to be negative. In classical group testing, each member of F is a singleton. In this paper, we exhibit and analyze a probabilistic trivial two-stage algorithm that identifies the positive complexes. (C) 2003 Elsevier B.V. All rights reserved.

关键词： group testing complexes disjunct martix two-stage algorithm hypergraphs

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Optimal spectrum assignment for cognitive radio sensor networks under coverage constraint

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IET COMMUNICATIONS 2014年第18期8卷 3318-3325页

作者： Eletreby, Rashad M. Elsayed, Hany M. Khairy, Mohamed M. Cairo Univ Fac Engn Dept Elect & Elect Commun Engn Cairo Egypt

Cognitive radios emerged as a solution to spectrum scarcity problem. The integration of cognitive radios and wireless sensor networks enables a new paradigm of communication, in which the sensor nodes can avoid heavily-crowded transmission bands by tuning their transmission parameters to less-crowded bands. The authors consider the problem of spectrum assignment for cognitive radio sensor network (CRSN) under coverage, interference, minimum data rate and power budget constraints. A mixed-integer non-linear programming problem formulation that addresses optimal power allocation, channel selection and node scheduling is presented. Following a practical assumption, that any CRSN node can only access one channel for its transmission with the CRSN base station, the problem is transformed to a binary linear programming (BLP) problem. Using the relaxation techniques, the problem is transformed to a linear programming problem that is solvable in polynomial time, and has the same optimal solution of the BLP problem. Hence, the minimum power algorithm that achieves the optimal solution of our problem is proposed. To further reduce the complexity of the solution, three heuristic lower-complexity algorithms are proposed to solve the problem: random, greedy and two-stage (decoupled) algorithms.

关键词： radio spectrum management cognitive radio radio networks wireless sensor networks radiofrequency interference nonlinear programming integer programming scheduling wireless channels linear programming polynomials greedy algorithms random processes optimal spectrum assignment cognitive radio sensor network spectrum scarcity problem wireless sensor network heavily-crowded transmission band avoidance CRSN interference power budget constraint minimum data rate constraint mixed-integer nonlinear programming problem optimal power allocation channel selection node scheduling base station binary linear programming problem BLP problem relaxation technique polynomial time minimum power algorithm heuristic lower-complexity algorithm random algorithm greedy algorithm two-stage algorithm decoupled algorithm

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Switching Time Optimization for Discontinuous Switched Systems

Switching Time Optimization for Discontinuous Switched Syste...

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European Control Conference (ECC)

作者： Schori, Markus Boehme, Thomas J. Jeinsch, Torsten Lampe, Bernhard IAV Automot Engn Dept Gasoline Engine Syst D-38518 Gifhorn Germany Univ Rostock Inst Automat D-18119 Rostock Germany

ISBN: (纸本)9783952426937

In this paper, an algorithm for switching time optimization for switched systems that exhibit discontinuities in the state trajectory on a switching is proposed. A derivative of the cost function with respect to the switching time is derived using a dynamic programming argumentation. Based on this derivative, a two-stage algorithm is described that alternates between solving an optimal control problem with fixed switching sequence and improving the switching times.

关键词： dynamic programming optimal control sampled data systems switching systems (control) cost function discontinuous switched systems dynamic programming argumentation fixed switching sequence optimal control problem state trajectory switching time optimization two-stage algorithm Cost function Optimal control Switched systems Switches Trajectory

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