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Optimal design measures under asymmetric errors, with application to binary design points

JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2015年 159卷 28-36页

作者： Bose, Mausumi Mukerjee, Rahul Indian Stat Inst Appl Stat Div Kolkata 700108 India Indian Inst Management Calcutta Kolkata 700104 India

We study the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed, taking due cognizance of the nonlinearity of the underlying information matrix in the design measure. This yields necessary and sufficient conditions that a D- or A-optimal design measure must satisfy. The results are then applied to find optimal design measures when the design points are binary. The issue of reducing the support size of the optimal design measure is also addressed. (C) 2014 Elsevier B.V. All rights reserved.

关键词： A-criterion D-criterion Directional derivative multiplicative algorithm Second-order least squares Support size Weighing design

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Optimal designs subject to cost constraints in simultaneous equations models

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TEST 2015年第4期24卷 701-713页

作者： Casero-Alonso, Victor Lopez-Fidalgo, Jesus Univ Castilla La Mancha Inst Math Appl Sci & Engn Dept Math E-13071 Ciudad Real Spain

A procedure based on a multiplicative algorithm for computing optimal experimental designs subject to cost constraints in simultaneous equations models is presented. A convex criterion function based on a usual criterion function and an appropriate cost function is considered. A specific L-optimal design problem and a numerical example are taken from Conlisk (J Econ 11:63-76, 1979) to compare the procedure. The problem would need integer nonlinear programming to obtain exact designs. To avoid this, he solves a continuous nonlinear programming problem and then he rounds off the number of replicates of each experiment. The procedure provided in this paper reduces dramatically the computational efforts in computing optimal approximate designs. It is based on a specific formulation of the asymptotic covariance matrix of the full-information maximum likelihood estimators, which simplifies the calculations. The design obtained for estimating the structural parameters of the numerical example by this procedure is not only easier to compute, but also more efficient than the design provided by Conlisk.

关键词： Approximate design Cost constraints Exact design L-optimal design multiplicative algorithm Simultaneous equations Structural equations

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multiplicative methods for computing D-optimal stratified designs of experiments

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2014年 146卷 82-94页

作者： Harman, Radoslav Comenius Univ Dept Appl Math & Stat Fac Math Phys & Informat Bratislava 84248 Slovakia

Consider a linear regression experiment with uncorrelated real-valued observations and a finite design space. An approximate experimental design is stratified if it allocates given proportions of trials to selected non-overlapping partitions of the design space. To calculate an approximate D-optimal stratified design, we propose two multiplicative methods: a re-normalisation heuristic and a barycentric algorithm, both of which are very simple to implement. The re-normalisation heuristic is generally more rapid, but for the barycentric algorithm, we can prove monotonic convergence to the optimum. We also develop rules for the removal of design points that cannot support any D-optimal stratified design, which significantly improves the speed of both proposed multiplicative methods. (C) 2013 Elsevier B.V. All rights reserved.

关键词： D-optimal design Stratified design Marginal constraints multiplicative algorithm Barycentric algorithm

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A multiplicative algorithm for Convolutive Non-Negative Matrix Factorization Based on Squared Euclidean Distance

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2009年第7期57卷 2858-2864页

作者： Wang, Wenwu Cichocki, Andrzej Chambers, Jonathon A. Univ Surrey Dept Elect Engn Ctr Vis Speech & Signal Proc Guildford GU2 7XH Surrey England RIKEN Brain Sci Inst Lab Adv Brain Signal Proc Wako Saitama 3510198 Japan Univ Loughborough Adv Signal Proc Grp Dept Elect & Elect Engn Loughborough LE11 3TU Leics England

Using the convolutive nonnegative matrix factorization (NMF) model due to Smaragdis, we develop a novel algorithm for matrix decomposition based on the squared Euclidean distance criterion. The algorithm features new formally derived learning rules and an efficient update for the reconstructed nonnegative matrix. Performance comparisons in terms of computational load and audio onset detection accuracy indicate the advantage of the Euclidean distance criterion over the Kullback-Leibler divergence criterion.

关键词： Audio object separation convolutive nonnegative matrix factorization multiplicative algorithm squared Euclidean distance

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multiplicative algorithms for Constrained Non-negative Matrix Factorization

Multiplicative Algorithms for Constrained Non-negative Matri...

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12th IEEE International Conference on Data Mining (ICDM)

作者： Peng, Chengbin Wong, Ka-Chun Rockwood, Alyn Zhang, Xiangliang Jiang, Jinling Keyes, David King Abdullah Univ Sci & Technol Comp Elect & Math Sci & Engn Thuwal Saudi Arabia Univ Toronto Dept Comp Sci Toronto ON Canada Aalborg Univ Dept Comp Sci Aalborg Denmark

ISBN: (纸本)9781467346498;9780769549057

Non-negative matrix factorization (NMF) provides the advantage of parts-based data representation through additive only combinations. It has been widely adopted in areas like item recommending, text mining, data clustering, speech denoising, etc. In this paper, we provide an algorithm that allows the factorization to have linear or approximatly linear constraints with respect to each factor. We prove that if the constraint function is linear, algorithms within our multiplicative framework will converge. This theory supports a large variety of equality and inequality constraints, and can facilitate application of NMF to a much larger domain. Taking the recommender system as an example, we demonstrate how a specialized weighted and constrained NMF algorithm can be developed to fit exactly for the problem, and the tests justify that our constraints improve the performance for both weighted and unweighted NMF algorithms under several different metrics. In particular, on the Movielens data with 94% of items, the Constrained NMF improves recall rate 3% compared to SVD50 and 45% compared to SVD150, which were reported as the best two in the top-N metric.

关键词： Non-negative Matrix Factorization Linear Constraints multiplicative algorithm

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Nonnegative matrix factorization-based hyperspectral and panchromatic image fusion

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NEURAL COMPUTING & APPLICATIONS 2013年第3-4期23卷 895-905页

作者： Zhang, Zhou Shi, Zhenwei Beihang Univ Image Proc Ctr Sch Astronaut Beijing 100191 Peoples R China Beihang Univ Beijing Key Lab Digital Media Beijing 100191 Peoples R China Beihang Univ State Key Lab Virtual Real Technol & Syst Beijing 100191 Peoples R China

The fusion of hyperspectral image and panchromatic image is an effective process to obtain an image with both high spatial and spectral resolutions. However, the spectral property stored in the original hyperspectral image is often distorted when using the class of traditional fusion techniques. Therefore, in this paper, we show how explicitly incorporating the notion of "spectra preservation" to improve the spectral resolution of the fused image. First, a new fusion model, spectral preservation based on nonnegative matrix factorization (SPNMF), is developed. Additionally, a multiplicative algorithm aiming at get the numerical solution of the proposed model is presented. Finally, experiments using synthetic and real data demonstrate the SPNMF is a superior fusion technique for it could improve the spatial resolutions of hyperspectral images with their spectral properties reliably preserved.

关键词： Hyperspectral image fusion Spectra preservation Nonnegative matrix factorization (NMF) multiplicative algorithm

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multiplicative algorithms for computing optimum designs

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2009年第12期139卷 3947-3961页

作者： Torsney, B. Martin-Martin, R. Univ Castilla La Mancha Inst Appl Math Sci & Engn Dept Math Sch Comp Sci E-13071 Ciudad Real Spain Univ Glasgow Dept Stat Glasgow G12 8QW Lanark Scotland

We Study a new approach to determine optimal designs, exact or approximate, both for the uncorrelated case and when the responses may be correlated. A simple version of this method is based on transforming design points on a finite interval to proportions of the interval. Methods for determining optimal design weights can therefore be used to determine optimal values of these proportions. We explore the potential of this method in a range of examples encompassing linear and non-linear models, some assuming a correlation structure and some with more than one design variable. (C) 2009 Elsevier EIN. All rights reserved.

关键词： Exact design Approximate design multiplicative algorithm Covariance function

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Strict monotonicity and convergence rate of Titterington's algorithm for computing D-optimal designs

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2010年第6期54卷 1419-1425页

作者： Yu, Yaming Univ Calif Irvine Dept Stat Irvine CA 92697 USA

We study a class of multiplicative algorithms introduced by Silvey et al. (1978) for computing D-optimal designs. Strict monotonicity is established for a variant considered by Titterington (1978). A formula for the rate of convergence is also derived. This is used to explain why modifications considered by Titterington ( 1978) and Dette et al. (2008) usually converge faster. (C) 2010 Elsevier By. All rights reserved.

关键词： D-optimality Experimental design multiplicative algorithm

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MONOTONIC CONVERGENCE OF A GENERAL algorithm FOR COMPUTING OPTIMAL DESIGNS

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ANNALS OF STATISTICS 2010年第3期38卷 1593-1606页

作者： Yu, Yaming Univ Calif Irvine Dept Stat Irvine CA 92697 USA

Monotonic convergence is established for a general class of multiplicative algorithms introduced by Silvey, Titterington and Torsney [Comm. Statist. Theory Methods 14 (1978) 1379-1389] or computing optimal designs. A conjecture of Titterington [Appl. Stat. 27(1978) 227-234] is confirmed as a consequence. Optimal designs for logistic regression are used as an illustration.

关键词： A-optimality auxiliary variables c-optimality D-optimality experimental design generalized linear models multiplicative algorithm

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Approximate D-optimal designs of experiments on the convex hull of a finite set of information matrices

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MATHEMATICA SLOVACA 2009年第6期59卷 693-704页

作者： Harman, Radoslav Trnovska, Maria Comenius Univ Fac Math Phys & Informat Dept Appl Math & Stat SK-84248 Bratislava Slovakia

In the paper we solve the problem of D (a"<)-optimal design on a discrete experimental domain, which is formally equivalent to maximizing determinant on the convex hull of a finite set of positive semidefinite matrices. The problem of D (a"<)-optimality covers many special design settings, e.g., the D-optimal experimental design for multivariate regression models. For D (a"<)-optimal designs we prove several theorems generalizing known properties of standard D-optimality. Moreover, we show that D (a"<)-optimal designs can be numerically computed using a multiplicative algorithm, for which we give a proof of convergence. We illustrate the results on the problem of D-optimal augmentation of independent regression trials for the quadratic model on a rectangular grid of points in the plane.

关键词： D-optimal design multivariate regression multiplicative algorithm D-optimal augmentation of trials

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