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coordinate descent algorithm for generalized group fused Lasso

Behaviormetrika 2025年第1期52卷 105-137页

作者： Ohishi, Mineaki Okamura, Kensuke Itoh, Yoshimichi Wakaki, Hirofumi Yanagihara, Hirokazu Center for Data-driven Science and Artificial Intelligence Tohoku University Sendai Japan Tokyo Kantei Co. Ltd. Shinagawa Japan Graduate School of Advanced Science and Engineering Hiroshima University Higashi-Hiroshima Japan

We deal with a model with discrete varying coefficients to consider modeling for heterogeneity and clustering for homogeneity, and estimate the varying coefficients by generalized group fused Lasso (GGFL). GGFL allows homogeneous groups to be joined together based on one-to-many relationships among groups. This makes GGFL a powerful technique, but to date there has been no effective algorithm for obtaining the solutions. Here we propose an algorithm for obtaining a GGFL solution based on the coordinate descent method, and show that a solution for each coordinate direction converges to the optimal solution. In a simulation, we show our algorithm is superior to ADMM, which is one of the popular algorithms. We also present an application to a spatial data analysis. © The Author(s) 2024.

关键词： Clustering coordinate descent algorithm Fused Lasso Spatial analysis

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coordinate descent algorithm for Ramp Loss Linear Programming Support Vector Machines

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NEURAL PROCESSING LETTERS 2016年第3期43卷 887-903页

作者： Xi, Xiangming Huang, Xiaolin Suykens, Johan A. K. Wang, Shuning Tsinghua Univ Tsinghua Natl Lab Informat Sci & Technol Dept Automat Beijing 100084 Peoples R China Katholieke Univ Leuven ESAT STADIUS Dept Elect Engn Kasteelpk Arenberg 10 B-3001 Leuven Belgium

In order to control the effects of outliers in training data and get sparse results, Huang et al. (J Mach Learn Res 15:2185-2211, 2014) proposed the ramp loss linear programming support vector machine. This combination of regularization and ramp loss does not only lead to the sparsity of parameters in decision functions, but also limits the effects of outliers with a maximal penalty. However, due to its non-convexity, the computational cost to achieve a satisfying solution is often expensive. In this paper, we propose a modified coordinate descent algorithm, which deals with a series of one-variable piecewise linear subproblems. Considering that the obtained subproblems are DC programming problems, we linearize the concave part of the objective functions and solve the obtained convex problems. To test the performances of the proposed algorithm, numerical experiments have been carried out and analysed on benchmark data sets. To enhance the sparsity and robustness, the experiments are initialized from C-SVM solutions. The results confirm its excellent performances in classification accuracy, robustness and efficiency in computation.

关键词： Support vector machines Ramp loss l(1) Regularization coordinate descent algorithm

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coordinate descent algorithm of generalized fused Lasso logistic regression for multivariate trend filtering

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JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE 2022年第2期5卷 535-551页

作者： Ohishi, Mineaki Yamamura, Mariko Yanagihara, Hirokazu Hiroshima Univ Educ & Res Ctr Artificial Intelligence & Data Inn Hiroshima Japan Radiat Effects Res Fdn Dept Stat Hiroshima Japan Hiroshima Univ Grad Sch Adv Sci & Engn Higashihiroshima Japan

Generalized fused Lasso (GFL) is an extension of fused Lasso and performs multivariate trend filtering based on adjacent information among parameters. This paper deals with an optimization problem for GFL logistic regression. Model parameters for the generalized linear model including the logistic regression model are usually optimized by minimizing a linear approximation of an objective function because the minimizer of the objective function cannot be obtained in closed form. In this paper, we propose an algorithm for solving the optimization problem for GFL logistic regression without approximating the objective function, for the purpose of optimizing fast and accurately. Specifically, we derive update equations of a coordinate descent algorithm for solving the optimization problem in closed form. Moreover, we show an example for spatio-temporal data analysis.

关键词： coordinate descent algorithm Generalized fused Lasso Logistic regression Spatio-temporal analysis Trend filtering

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Robust coordinate descent algorithm Robust Solution Path for High-dimensional Sparse Regression Modeling

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2016年第1期45卷 115-129页

作者： Park, H. Konishi, S. Univ Tokyo Inst Med Sci Ctr Human Genome Minato Ku Tokyo 1128551 Japan Chuo Univ Dept Math Fac Sci & Engn Bunkyo Ku Tokyo Japan

The L-1-type regularization provides a useful tool for variable selection in high-dimensional regression modeling. Various algorithms have been proposed to solve optimization problems for L-1-type regularization. Especially the coordinate descent algorithm has been shown to be effective in sparse regression modeling. Although the algorithm shows a remarkable performance to solve optimization problems for L-1-type regularization, it suffers from outliers, since the procedure is based on the inner product of predictor variables and partial residuals obtained from a non-robust manner. To overcome this drawback, we propose a robust coordinate descent algorithm, especially focusing on the high-dimensional regression modeling based on the principal components space. We show that the proposed robust algorithm converges to the minimum value of its objective function. Monte Carlo experiments and real data analysis are conducted to examine the efficiency of the proposed robust algorithm. We observe that our robust coordinate descent algorithm effectively performs for the high-dimensional regression modeling even in the presence of outliers.

关键词： coordinate descent algorithm Dimension reduction High-dimensional data L-1-type regularization Robust regression modeling

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Natural coordinate descent algorithm for L1-penalised regression in generalised linear models

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2016年 97卷 60-70页

作者： Michoel, Tom Univ Edinburgh Roslin Inst Easter Bush EH25 9RG Midlothian Scotland

The problem of finding the maximum likelihood estimates for the regression coefficients in generalised linear models with an l(1) sparsity penalty is shown to be equivalent to minimising the unpenalised maximum log-likelihood function over a box with boundary defined by the l(1)-penalty parameter. In one-parameter models or when a single coefficient is estimated at a time, this result implies a generic soft-thresholding mechanism which leads to a novel coordinate descent algorithm for generalised linear models that is entirely described in terms of the natural formulation of the model and is guaranteed to converge to the true optimum. A prototype implementation for logistic regression tested on two large-scale cancer gene expression datasets shows that this algorithm is efficient, particularly so when a solution is computed at set values of the l(1)-penalty parameter as opposed to along a regularisation path. Source code and test data are available from http://***/glmnat/. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Penalised regression Generalised linear model coordinate descent algorithm Logistic regression

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A coordinate descent algorithm for computing penalized smooth quantile regression

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STATISTICS AND COMPUTING 2017年第4期27卷 865-883页

作者： Mkhadri, Abdallah Ouhourane, Mohamed Oualkacha, Karim Cadi Ayyad Univ Dept Math Marrakech Morocco Univ Quebec Dept Math Montreal PQ H2X 3Y7 Canada

The computation of penalized quantile regression estimates is often computationally intensive in high dimensions. In this paper we propose a coordinate descent algorithm for computing the penalized smooth quantile regression (cdaSQR) with convex and nonconvex penalties. The cdaSQR approach is based on the approximation of the objective check function, which is not differentiable at zero, by a modified check function which is differentiable at zero. Then, using the maximization-minimization trick of the gcdnet algorithm (Yang and Zou in, J Comput Graph Stat 22(2):396-415, 2013), we update each coefficient simply and efficiently. In our implementation, we consider the convex penalties and the nonconvex penalties SCAD (or MCP) . We establishe the convergence property of the csdSQR with penalty. The numerical results show that our implementation is an order of magnitude faster than its competitors. Using simulations we compare the speed of our algorithm to its competitors. Finally, the performance of our algorithm is illustrated on three real data sets from diabetes, leukemia and Bardet-Bidel syndrome gene expression studies.

关键词： Variable selection Quantile regression Smooth check function coordinate descent algorithm

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A Fast coordinate descent algorithm Improving both Coverage and Capacity in Cellular Networks 10

A Fast Coordinate Descent Algorithm Improving both Coverage ...

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10th IEEE International Conference on Electronics Information and Emergency Communication (IEEE ICEIEC)

作者： Wei An Liu, Yaxi Wei Huangfu Univ Sci & Technol Beijing USTB Beijing Engn & Technol Ctr Convergence Networks & Beijing Peoples R China Univ Sci & Technol Beijing Shunde Grad Sch Foshan Peoples R China

ISBN: (数字)9781728163130

ISBN: (纸本)9781728163130;9781728163123

It is an essential task for mobile operators to extend the coverage and improve the capacity by adjusting the radio parameters in cellular networks, especially in self-organizing networks. In the existing algorithm, the decoration of target local performance is neglected, which severely deteriorates the algorithm efficiency. In this paper, we propose a hierarchy induced coordinate descent algorithm, which focuses on the local decoration of the target function to solve the coverage and capacity optimization problems by obtaining the optimal antenna tilt and azimuth settings in cellular networks. Such algorithm alternatively executes the optimization step decision where the original complex constrained optimization problem is converted into a non-constrained simple one with the penalty term and the optimization variable selection that balances the influences of the hierarchy and the distance according to different system parameter settings. Besides, in the optimization step decision mentioned above, we adopt the non-linear interpolation to obtain the optimal optimization direction and its corresponding length.

关键词： Cellular networks coordinate descent algorithm coverage and capacity antenna tilt and azimuth hierarchy-induced

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A coordinate descent MM algorithm for fast computation of sparse logistic PCA

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2013年 62卷 26-38页

作者： Lee, Seokho Huang, Jianhua Z. Hankuk Univ Foreign Studies Dept Stat Seoul South Korea Texas A&M Univ Dept Stat College Stn TX 77843 USA

Sparse logistic principal component analysis was proposed in Lee et al. (2010) for exploratory analysis of binary data. Relying on the joint estimation of multiple principal components, the algorithm therein is computationally too demanding to be useful when the data dimension is high. We develop a computationally fast algorithm using a combination of coordinate descent and majorization-minimization (MM) auxiliary optimization. Our new algorithm decouples the joint estimation of multiple components into separate estimations and consists of closed-form elementwise updating formulas for each sparse principal component. The performance of the proposed algorithm is tested using simulation and high-dimensional real-world datasets. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Binary data coordinate descent algorithm MM algorithm Penalized maximum likelihood Principal component analysis

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Cloud-hosting of agricultural crop simulator and optimizer for model calibration and farm input recommendations

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COMPUTERS AND ELECTRONICS IN AGRICULTURE 2025年 236卷

作者： Pokuri, Balaji Sesha Srikanth Bhar, Anupam Kumar, Ratnesh Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA

Agricultural models have traditionally been designed for Windows desktop computers, limiting their accessibility and usability across different operating systems and devices. In contrast, cloud-based tools have the potential to improve accessibility, lower individual computational requirements, and enable transparency of results and ease of collaboration. In this paper, we report the first cloud-hosting of a widely used agricultural crop model, Root Zone Water Quality Model (RZWQM2), along with our own-developed optimizer for model calibration and farm decision recommendation, on the MyGeoHub cyber-infrastructure for the benefit of the agricultural research and farming community, and other stakeholders. The optimization is implemented based on a randomized block coordinated descent (rbCD) search that is shown to outperform the previous RBFOptbased optimizer utilized within the MISSION (Model-predictive In-Season Scheduling of Irrigation Or/and Nitrogen) framework for farm input management. The paper also presents a new equivalent formulation of the optimization function introduced in MISSION that renders its MINLP (Mixed-Integer Non-Linear Program) to a simpler NLP (Non-Linear Program), removing the integer variables, reducing the number of decision variables to half and improving the optimization result as well as speed. To demonstrate the effectiveness of the cloud-hosted RZWQM2 model and the new optimizer, we also conducted a case study using a test dataset of maize growth in Greeley, CO. MISSION ' predicts higher crop yield and profit than both the expert recommendation (25.8% yield, 39.8% profit) as well as the published RBFOpt-based optimizer (2% yield, 3% profit) in 2008. We also report up to 26% higher yield and 40% higher profit of MISSION ' over expert recommendations for 4 different seasons over 2008-2011 The NLP reformulation of MISSION ' combined with the rbCD algorithm provided speedup that allows searching for input applications on all days of the sea

关键词： Real-time agriculture management Irrigation and fertilizer scheduling GFS weather integration RZWQM2 MyGeoHub coordinate descent algorithm

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Simultaneous estimation of quantile regression functions using B-splines and total variation penalty

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2019年 133卷 228-244页

作者： Jhong, Jae-Hwan Koo, Ja-Yong Korea Univ Dept Stat Seoul 02841 South Korea

We consider the problem of simultaneously estimating a finite number of quantile functions with B-splines and the total variation penalty. For the implementation of simultaneous quantile function estimators, we develop a new coordinate descent algorithm taking into account a special structure of the total variation penalty determined by B-spline coefficients. The entire paths of solution paths for several quantile function estimators and tuning parameters can be efficiently computed using the coordinate descent algorithm. We also consider non-crossing quantile function estimators having additional constraints at the knots of spline functions. Numerical studies using both simulated and real data sets are provided to illustrate the performance of the proposed method. For a theoretical result, we prove that the proposed the quantile regression function estimators achieve the minimax rate under regularity conditions. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Binary method coordinate descent algorithm Minimax rate Non-crossing Total variation Weighted quantile

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