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A hybrid algorithm for the search of long binary sequences with low aperiodic autocorrelations

SOFT COMPUTING 2021年第20期25卷 12725-12744页

作者： Zhang, Mingxing Zhou, Zhengchun Yang, Meng Liu, Zilong Yang, Yang Southwest Jiaotong Univ Sch Informat Sci & Technol Chengdu Peoples R China Southwest Jiaotong Univ Sch Math Chengdu Peoples R China Univ Essex Sch Comp Sci & Elect Engn Colchester Essex England

Binary sequences with low aperiodic autocorrelation play an important role in communication and radar. The search of long low autocorrelation binary sequences (LABS) is a classical but challenging research problem. Exhaustive sequence search is infeasible for large lengths due to its prohibitively high complexity. Albeit many algorithms on LABS search in the literature, they are effective for lengths up to a few hundred only. In this paper, we propose an efficient hybrid algorithm which combines the strength of coordinate descent algorithm and the simulated annealing algorithm. Our proposed hybrid algorithm can efficiently generate long LABS of lengths up to several thousand and outperforms existing approaches in most cases.

关键词： Aperiodic autocorrelation Binary sequence Hybrid algorithm coordinate descent algorithm Simulated annealing algorithm

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Penalized I-spline monotone regression estimation

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2021年第11期50卷 3714-3732页

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

We propose a penalized regression spline estimator for monotone regression. To construct the estimator, we adopt the I-splines with the total variation penalty. The I-splines lend themselves to the monotonicity because of the simpler form of restrictions, and the total variation penalty induces a data-driven knot selection scheme. A coordinate descent algorithm is developed for the estimator. If the number of complexity parameter candidates sufficiently increases, the algorithm considers all possible monotone linear spline fits to the given data. The pruning process of the algorithm not only provides numerical stability, but also implements the data-driven knot selection. We also compute the maximum candidate of the complexity parameter to facilitate complexity parameter selection. Extensive numerical studies show that the proposed estimator captures spatially inhomogeneous behaviors of data, such as sudden jumps.

关键词： coordinate descent algorithm I-splines Knot selection Maximum complexity parameter Monotone regression Total variation penalty

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coordinate optimization for generalized fused Lasso

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第24期50卷 5955-5973页

作者： Ohishi, M. Fukui, K. Okamura, K. Itoh, Y. Yanagihara, H. Hiroshima Univ Grad Sch Sci Higashihiroshima Japan Osaka Med Coll Res & Dev Ctr Takatsuki Osaka Japan Tokyo Kantei Co Ltd Shinagawa Japan Hiroshima Univ Educ & Res Ctr Artificial Intelligence & Data Inn Hiroshima Japan Hiroshima Univ Grad Sch Adv Sci & Engn Higashihiroshima Japan

Fused Lasso is one of extensions of Lasso to shrink differences of parameters. We focus on a general form of it called generalized fused Lasso (GFL). The optimization problem for GFL can be came down to that for generalized Lasso and can be solved via a path algorithm for generalized Lasso. Moreover, the path algorithm is implemented via the genlasso package in R. However, the genlasso package has some computational problems. Then, we apply a coordinate descent algorithm (CDA) to solve the optimization problem for GFL. We give update equations of the CDA in closed forms, without considering the Karush-Kuhn-Tucker conditions. Furthermore, we show an application of the CDA to a real data analysis.

关键词： coordinate descent algorithm generalized fused Lasso generalized Lasso

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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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Large scale multi-class classification with truncated nuclear norm regularization

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NEUROCOMPUTING 2015年 148卷 310-317页

作者： Hu, Yao Jin, Zhongming Shi, Yi Zhang, Debing Cai, Deng He, Xiaofei Zhejiang Univ State Key Lab CAD&CG Hangzhou 310058 Zhejiang Peoples R China

In this paper, we consider the problem of multi-class image classification when the classes behaviour has a low rank structure. That is, classes can be embedded into a low dimensional space. Traditional multi-class classification algorithms usually use nuclear norm to approximate the rank of the weight matrix. Considering the limited ability of the nuclear norm for the accurate approximation, we propose a new scalable large scale multi-class classification algorithm by using the recently proposed truncated nuclear norm as a better surrogate of the rank operator of matrices along with multinomial logisitic loss. To solve the non-convex and non-smooth optimization problem, we further develop an efficient iterative procedure. In each iteration, by lifting the non-smooth convex subproblem into an infinite dimensional l(1) norm regularized problem, a simple and efficient accelerated coordinate descent algorithm is applied to find the optimal solution;We conduct a series of evaluations on several public large scale image datasets, where the experimental results show the encouraging improvement of classification accuracy of the proposed algorithm in comparison with the state-of-the-art multi-class classification algorithms. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Truncated nuclear norm coordinate descent algorithm Multi-class classification

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Penalized logistic regressions with technical indicators predict up and down trends

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SOFT COMPUTING 2023年第18期27卷 13677-13688页

作者： Jiang, Huifeng Hu, Xuemei Jia, Hong Chongqing Technol & Business Univ Res Ctr Econ Upper Reaches Yangtse River 19 Xuefu Ave Chongqing 400067 Peoples R China Chongqing Technol & Business Univ Sch Math & Stat Chongqing Key Lab Social Econ & Appl Stat 19 Xuefu Ave Chongqing 400067 Peoples R China

Correctly predicting up and down trends for stock prices is of immense important in the financial market. To further improve the prediction performance, in this paper we introduce five penalties: ridge, least absolute shrinkage and selection operator, elastic net, smoothly clipped absolute deviation and minimax concave penalty to logistic regressions with 19 technical indicators, and propose the five penalized logistic regressions to predict up and down trends for stock prices. Firstly, we translate the five penalized logistic log-likelihood functions into the five penalized weighted least squares functions and combine them with the tenfold cross-validation method to calculate the solution path to parameter estimators. Secondly, we combine the binomial deviation with cross-validation error as a risk measure to choose an appropriate tuning parameter for the penalty functions and apply the training set and the coordinate descent algorithm to obtain parameter estimators and probability estimators. Thirdly, we employ the testing set and the chosen optimal thresholds to construct two-class confusion matrices and receiver operating characteristic curves to assess the prediction performances to the five regressions. Finally, we compare the proposed five penalized logistic regressions with logistic regression, support vector machine and artificial neural network and found that the minimax concave penalty logistic regression performs the best in terms of the prediction performance to up and down trends for Google's stock prices. Therefore, in this paper we propose the five new prediction methods to improve the prediction accuracy of stock returns and bring economic benefits for investors.

关键词： Penalized logistic regressions Up and down trends coordinate descent algorithm Support vector machine Artificial neural network

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Penalized log-density estimation using Legendre polynomials

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2020年第11期49卷 2844-2860页

作者： Lee, JungJun Jhong, Jae-Hwan Cho, Young-Rae Kim, SungHwan Koo, Ja-Yong Korea Univ Dept Stat Seoul South Korea ETUDE Corp Seoul South Korea Konkuk Univ Dept Appl Stat Seoul South Korea

In this article, we present a penalized log-density estimation method using Legendre polynomials with l(1) penalty to adjust estimate's smoothness. Re-expressing the logarithm of the density estimator via a linear combination of Legendre polynomials, we can estimate parameters by maximizing the penalized log-likelihood function. Besides, we proposed an implementation strategy that builds on the coordinate decent algorithm, together with the Bayesian information criterion (BIC). In particular, we derive a numerical solution to the maximum tuning parameter lambda(max) which leads to all zero coefficients and practically facilitates searching the optimal tuning parameter. Extensive simulation studies clearly show that our proposed estimator is computationally competitive with other existing nonparametric density estimators (e.g., kernel, kernel smooth and logspline estimators) benchmarked by the mean integrated squared errors (MISE) and the mean integrated absolute error (MIAE) under the experiment scenario of separated bimodal models in regard to the true density function. With an application to Old Faithful geyser data, our proposed method is found to effectively perform density estimation.

关键词： Penalized log-density estimation nonparametric density estimation Legendre polynomial basis coordinate descent algorithm l(1) penalty maximum tuning parameter

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Visual search difficulty prediction with image ROI information

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NEURAL COMPUTING & APPLICATIONS 2022年第9期34卷 6799-6809页

作者： Xiao, Bo Liu, Xuelian Wang, Chunyang Xian Technol Univ Sch Optoelect Engn Xian 710021 Peoples R China Xian Technol Univ Informat Percept & Intelligent Control Lab Xian 710021 Peoples R China

Target recognition difficulty quantification and prediction using the search time for the human visual system to target an object is a challenging task, which can effectively guide the training of machine learning models such as target recognition and target location. Our work focuses on how to use region-of-interest (ROI) information to improve the accuracy of the visual search difficulty prediction model. First, the influence of ROI information on visual search difficulty is explored in this paper. Then, based on the learning using privileged information paradigm, we build a support vector regression model using privileged information (SVR +), which uses the deep features of ROIs in the training stage. Next, a coordinate descent algorithm is developed to solve the dual optimization problem in SVR + training. Comprehensive experiments validate the improvement in the accuracy of the proposed model in predicting the difficulty of visual search and the efficiency of our coordinate descent algorithm in model training.

关键词： Visual search difficulty prediction Region of interest Learning using privileged information coordinate descent algorithm

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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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Locally penalized single-index model using B-splines and spherical coordinates

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年第1期53卷 273-287页

作者： Jhong, Jae-Hwan Kim, Jae-Young Lee, Jae-Deok Koo, Ja-Yong Chungbuk Natl Univ Dept Informat Stat Cheongju South Korea NAVER Corp Seongnam Si South Korea Korea Univ Dept Stat Seoul South Korea

In this study, we focus on the estimation of the regression function in the single-index model based on B-splines using penalization techniques. We adopt a spherical coordinates reparameterization of an index vector to deal with an identification problem of the single-index model. To provide a spatially adaptive method, two types of penalties are applied to the estimation of the index vector and the regression function. A special penalty called the localized penalty is introduced to handle the sparsity of the index vector using the spherical coordinates, and the total variation penalty is considered to deal with the smoothing function. Using a coordinate descent algorithm with a grid search of the two tuning parameters, the entire solution paths of the index coefficients and the regression functions for tuning parameters can be obtained efficiently. The performance of the proposed estimator is studied through both numerical simulations and real data sets. An R software package pbssim is available.

关键词： coordinate descent algorithm localized penalty total variation

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