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Automatic structure discovery for varying-coefficient partially linear models

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2017年第15期46卷 7703-7716页

作者： Yang, Guangren Sun, Yanqing Cui, Xia Jinan Univ Sch Econ Dept Stat Guangzhou Guangdong Peoples R China Univ N Carolina Dept Math & Stat Charlotte NC USA Guangzhou Univ Sch Econ & Stat Guangzhou 510006 Guangdong Peoples R China

Varying-coefficient partially linear models provide a useful tools for modeling of covariate effects on the response variable in regression. One key question in varying-coefficient partially linear models is the choice of model structure, that is, how to decide which covariates have linear effect and which have non linear effect. In this article, we propose a profile method for identifying the covariates with linear effect or non linear effect. Our proposed method is a penalized regression approach based on group minimax concave penalty. Under suitable conditions, we show that the proposed method can correctly determine which covariates have a linear effect and which do not with high probability. The convergence rate of the linear estimator is established as well as the asymptotical normality. The performance of the proposed method is evaluated through a simulation study which supports our theoretical results.

关键词： B-spline coordinate descent algorithm group MCP varying-coefficient partially linear models

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Penalized B-spline estimator for regression functions using total variation penalty

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2017年 184卷 77-93页

作者： Jhong, Jae-Hwan Koo, Ja-Yong Lee, Seong-Whan Korea Univ Dept Stat Seoul 136701 South Korea Korea Univ Dept Brain & Cognit Engn Seoul 136701 South Korea

We carry out a study on a penalized regression spline estimator with total variation penalty. In order to provide a spatially adaptive method, we consider total variation penalty for the estimating regression function. This paper adopts B-splines for both numerical implementation and asymptotic analysis because they have small supports, so the information matrices are sparse and banded. Once we express the estimator with a linear combination of B-splines, the coefficients are estimated by minimizing a penalized residual sum of squares. A new coordinate descent algorithm is introduced to handle total variation penalty determined by the B-spline coefficients. For large-sample inference, a nonasymptotic oracle inequality for penalized B-spline estimators is obtained. The oracle inequality is then used to show that the estimator is an optimal adaptive for the estimation of the regression function up to a logarithm factor. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Adaptive estimation coordinate descent algorithm LASSO Oracle inequalities Penalized least squares

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Bayesian Estimation of Smooth Altimetric Parameters: Application to Conventional and Delay/Doppler Altimetry

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2016年第4期54卷 2207-2219页

作者： Halimi, Abderrahim Mailhes, Corinne Tourneret, Jean-Yves Snoussi, Hichem Univ Technol Troyes Inst Charles Delaunay CNRS F-10010 Troyes France Univ Toulouse IRIT INPENSEEIHT TeSA F-31071 Toulouse France

This paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non -identically Gaussian distribution. We introduce a prior enforcing a smooth temporal evolution of the altimetric parameters which improves their physical interpretation. The posterior distribution of the resulting model is optimized using a gradient descent algorithm which allows us to compute the maximum a posteriori estimator of the unknown model parameters. This algorithm has a low computational cost that is suitable for real-time applications. The proposed Bayesian strategy and the corresponding estimation algorithm are evaluated using both synthetic and real data associated with conventional and delay/Doppler altimetry. The analysis of real Jason -2 and CryoSat-2 waveforms shows an improvement in parameter estimation when compared to state-of-the-art estimation algorithms.

关键词： Altimetry Bayesian algorithm coordinate descent algorithm delay/Doppler altimetry (DDA) natural gradient simultaneous autoregression (SAR) altimetry smooth estimation

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Reinforced Angle-Based Multicategory Support Vector Machines

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2016年第3期25卷 806-825页

作者： Zhang, Chong Liu, Yufeng Wang, Junhui Zhu, Hongtu Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON N2L 3G1 Canada Univ North Carolina Chapel Hill Dept Stat & Operat Res Dept Genet Chapel Hill NC 28223 USA Univ North Carolina Chapel Hill Dept Biostat Chapel Hill NC 28223 USA City Univ Hong Kong Dept Math Hong Kong Hong Kong Peoples R China Univ North Carolina Chapel Hill Dept Biostat Chapel Hill NC 28223 USA

The support vector machine (SVM) is a very popular classification tool with many successful applications. It was originally designed for binary problems with desirable theoretical properties. Although there exist various multicategory SVM (MSVM) extensions in the literature, some challenges remain. In particular, most existing MSVMs make use of k classification functions for a k-class problem, and the corresponding optimization problems are typically handled by existing quadratic programming solvers. In this article, we propose a new group of MSVMs, namely, the reinforced angle-based MSVMs (RAMSVMs), using an angle-based prediction rule with k - 1 functions directly. We prove that RAMSVMs can enjoy Fisher consistency. Moreover, we show that the RAMSVM can be implemented using the very efficient coordinate descent algorithm on its dual problem. Numerical experiments demonstrate that our method is. highly competitive in terms of computational speed, as well as classification prediction performance. Supplemental materials for the article are available online.

关键词： coordinate descent algorithm Fisher consistency Multicategory classification Quadratic programming Reproducing kernel Hilbert space

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The shooting S-estimator for robust regression

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COMPUTATIONAL STATISTICS 2016年第3期31卷 829-844页

作者： Ollerer, Viktoria Alfons, Andreas Croux, Christophe Katholieke Univ Leuven Fac Econ & Business Naamsestr 69 B-3000 Louvain Belgium Erasmus Univ Erasmus Sch Econ POB 1738 NL-3000 DR Rotterdam Netherlands

To perform multiple regression, the least squares estimator is commonly used. However, this estimator is not robust to outliers. Therefore, robust methods such as S-estimation have been proposed. These estimators flag any observation with a large residual as an outlier and downweight it in the further procedure. However, a large residual may be caused by an outlier in only one single predictor variable, and downweighting the complete observation results in a loss of information. Therefore, we propose the shooting S-estimator, a regression estimator that is especially designed for situations where a large number of observations suffer from contamination in a small number of predictor variables. The shooting S-estimator combines the ideas of the coordinate descent algorithm with simple S-regression, which makes it robust against componentwise contamination, at the cost of failing the regression equivariance property.

关键词： Cellwise outliers Componentwise contamination Shooting algorithm coordinate descent algorithm Regression S-estimation

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Customized algorithms for growing connected resistive networks

Customized algorithms for growing connected resistive networ...

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10th IFAC Symposium on Nonlinear Control Systems (NOLCOS)

作者： Moghaddam, Sepideh Hassan Juvanovic, Mihailo R. Univ Minnesota Dept Elect & Comp Engn Minneapolis MN 55455 USA

We consider the problem of adding edges to connected resistive networks in order to optimally enhance their performance. The performance is captured by the H-2 norm of the closed-loop network and the l(1) regularization is introduced as a means to promote sparsity of the controller graph Laplacian. The resulting optimal control problem can be used to officiently compute the optimal solution for small and medium size networks. In the paper, we develop two efficient customized algorithms for large-scale problems. Our customized algorthms are based on the proximal gradient method and the sequential quadratic approximation method. In the latter, the Newton direction is obtained using coordinate descent algorthm over the set of active varibles. We provide compricon of these methods and show that both of them can be effectively employed to solve topology identification and optimal design problem for large scale networks. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Convex optimization coordinate descent algorithm resistive networks proximal gradient method semidefinite programming sequential quadratic approximation

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FILTERING SMOOTH ALTIMETRIC SIGNALS USING A BAYESIAN algorithm 24

FILTERING SMOOTH ALTIMETRIC SIGNALS USING A BAYESIAN ALGORIT...

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24th European Signal Processing Conference (EUSIPCO)

作者： Halimi, Abderrahim Buller, Gerald McLaughlin, Steve Honeine, Paul Heriot Watt Univ Sch Engn & Phys Sci Edinburgh Midlothian Scotland Normandie Univ UNIROUEN UNIHAVRE INSA RouenLITIS Rouen France

ISBN: (纸本)9780992862657

This paper presents a new Bayesian strategy for the estimation of smooth signals corrupted by Gaussian noise. The method assumes a smooth evolution of a succession of continuous signals that can have a numerical or an analytical expression with respect to some parameters. The Bayesian model proposed takes into account the Gaussian properties of the noise and the smooth evolution of the successive signals. In addition, a gamma Markov random field prior is assigned to the signal energies and to the noise variances to account for their known properties. The resulting posterior distribution is maximized using a fast coordinate descent algorithm whose parameters are updated by analytical expressions. The proposed algorithm is tested on satellite altimetric data demonstrating good denoising results on both synthetic and real signals. The proposed algorithm is also shown to improve the quality of the altimetric parameters when combined with a parameter estimation strategy.

关键词： Altimetry Bayesian algorithm coordinate descent algorithm gamma Markov random fields

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K-nearest neighbors and a kernel density estimator for GEFCom2014 probabilistic wind power forecasting

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INTERNATIONAL JOURNAL OF FORECASTING 2016年第3期32卷 1074-1080页

作者： Zhang, Yao Wang, Jianxue Xi An Jiao Tong Univ Sch Elect Engn Xian 710049 Peoples R China

Probabilistic forecasts provide quantitative information in relation to energy uncertainty, which is essential for making better decisions on the operation of power systems with an increasing penetration of wind power. On the basis of the k-nearest neighbors algorithm and a kernel density estimator method, this paper presents a general framework for the probabilistic forecasting of renewable energy generation, especially for wind power generation. It is a direct and non-parametric approach. Firstly, the k-nearest neighbors algorithm is used to find the k closest historical examples with characteristics similar to the future weather condition of wind power generation. Secondly, a novel kernel density estimator based on a logarithmic transformation and a boundary kernel is used to construct wind power predictive density based on the k closest historical examples. The effectiveness of this approach has been confirmed on the real data provided for GEFCom2014. The evaluation results show that the proposed approach can provide good quality, reliable probabilistic wind power forecasts. (C) 2015 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

关键词： Wind power Probabilistic forecasting Point forecasting k-nearest neighbors Kernel density estimator coordinate descent algorithm

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Hyperspectral Unmixing in Presence of Endmember Variability, Nonlinearity, or Mismodeling Effects

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2016年第10期25卷 4565-4579页

作者： Halimi, Abderrahim Honeine, Paul Bioucas-Dias, Jose M. Heriot Watt Univ Sch Engn & Phys Sci Edinburgh EH14 4AS Midlothian Scotland Univ Rouen Lab Informat Traitement Informat & Syst Normandie Univ F-76000 Rouen France Univ Lisbon Inst Telecomunicacoes P-1049001 Lisbon Portugal Univ Lisbon Inst Super Tecn P-1049001 Lisbon Portugal

This paper presents three hyperspectral mixture models jointly with Bayesian algorithms for supervised hyperspectral unmixing. Based on the residual component analysis model, the proposed general formulation assumes the linear model to be corrupted by an additive term whose expression can be adapted to account for nonlinearities (NLs), endmember variability (EV), or mismodeling effects (MEs). The NL effect is introduced by considering a polynomial expression that is related to bilinear models. The proposed new formulation of EV accounts for shape and scale endmember changes while enforcing a smooth spectral/ spatial variation. The ME formulation considers the effect of outliers and copes with some types of EV and NL. The known constraints on the parameter of each observation model are modeled via suitable priors. The posterior distribution associated with each Bayesian model is optimized using a coordinate descent algorithm, which allows the computation of the maximum a posteriori estimator of the unknown model parameters. The proposed mixture and Bayesian models and their estimation algorithms are validated on both synthetic and real images showing competitive results regarding the quality of the inferences and the computational complexity, when compared with the state-of-the-art algorithms.

关键词： Hyperspectral imagery endmember variability nonlinear spectral unmixing robust unmixing mismodelling effect Bayesian estimation coordinate descent algorithm Gaussian process Gamma Markov random field

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Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure

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BIOMETRICS 2015年第2期71卷 354-363页

作者： Li, Yanming Nan, Bin Zhu, Ji Univ Michigan Dept Biostat Ann Arbor MI 48109 USA Univ Michigan Dept Stat Ann Arbor MI 48109 USA

We propose a multivariate sparse group lasso variable selection and estimation method for data with high-dimensional predictors as well as high-dimensional response variables. The method is carried out through a penalized multivariate multiple linear regression model with an arbitrary group structure for the regression coefficient matrix. It suits many biology studies well in detecting associations between multiple traits and multiple predictors, with each trait and each predictor embedded in some biological functional groups such as genes, pathways or brain regions. The method is able to effectively remove unimportant groups as well as unimportant individual coefficients within important groups, particularly for large p small n problems, and is flexible in handling various complex group structures such as overlapping or nested or multilevel hierarchical structures. The method is evaluated through extensive simulations with comparisons to the conventional lasso and group lasso methods, and is applied to an eQTL association study.

关键词： coordinate descent algorithm EQTL Genetic association High-dimensional data Oracle inequalities Sparsity

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