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Large-scale robust regression with truncated loss via majorization-minimization algorithm

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第2期319卷 494-504页

作者： Huang, Ling-Wei Shao, Yuan-Hai Lv, Xiao-Jing Li, Chun-Na Hainan Univ Int Business Sch Haikou 570228 Peoples R China Hainan Univ Sch Math & Stat Haikou 570228 Peoples R China

The utilization of regression methods employing truncated loss functions is widely praised for its robustness in handling outliers and representing the solution in the sparse form of the samples. However, due to the non-convexity of the truncated loss, the commonly used algorithms such as difference of convex algorithm (DCA) fail to maintain sparsity when dealing with non-convex loss functions, and adapting DCA for efficient optimization also incurs additional development costs. To address these challenges, we propose a novel approach called truncated loss regression via majorization-minimization algorithm (TLRM). TLRM employs a surrogate function to approximate the original truncated loss regression and offers several desirable properties: (i) Eliminating outliers before the training process and encapsulating general convex loss regression within its structure as iterative subproblems, (ii) Solving the convex loss problem iteratively thereby facilitating the use of a well-established toolbox for convex optimization. (iii) Converging to a truncated loss regression and providing a solution with sample sparsity. Extensive experiments demonstrate that TLRM achieves superior sparsity without sacrificing robustness, and it can be several tens of thousands of times faster than traditional DCA on large-scale problems. Moreover, TLRM is also applicable to datasets with millions of samples, making it a practical choice for real-world scenarios. The codebase for methods with truncated loss functions is accessible at https://***/***/Resources/Code/***.

关键词： Robust regression Truncated loss function Sparsity and scalability majorization-minimization algorithm Huber regression and support vector regression

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Fuzzy serial-parallel stochastic configuration networks based on nonconvex dynamic membership function optimization

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INFORMATION SCIENCES 2025年 690卷

作者： Qiao, Jinghui Qiao, Jiayu Gao, Peng Bai, Zhe Xiong, Ningkang Shenyang Univ Technol Sch Mech Engn Shenyang 110870 Peoples R China Northeastern Univ Sch Resources & Civil Engn Shenyang 110819 Peoples R China Natl Local Joint Engn Res Ctr High Efficient Expl Shenyang 110819 Peoples R China

A fuzzy series-parallel stochastic configuration networks (F-SPSCN) is proposed based on the application of nonconvex optimization in fuzzy systems. Firstly, the kernel density estimation method is used to fit the distribution of original input data to generate dynamic nonconvex membership functions, which enhances the fuzzy system ability to handle uncertain industrial data. Then the parameters of the nonconvex membership functions are optimized based on majorization-minimization algorithm and Generalized Projective Gradient Descent algorithm. The optimized membership matrices and fuzzy outputs are used as inputs of the serial-parallel stochastic configuration networks to improve the overall prediction accuracy of the model. Finally, the prediction accuracy of the F-SPSCN model has been verified by performing prediction experiments with two different functions and four benchmark datasets. The F-SPSCN model demonstrates superior performance compared to other models in predicting the magnetic separation recovery ratio (MSRR) of hydrogen-based mineral phase transformation (HMPT) process for refractory iron ore.

关键词： Stochastic configuration networks (SCN) Nonconvex optimization majorization-minimization algorithm Generalized projective gradient descent algorithm Fuzzy systems Magnetic separation recovery ratio (MSRR) Hydrogen-based mineral phase transformation (HMPT)

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Parsimony and parameter estimation for mixtures of multivariate leptokurtic-normal distributions

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2024年第3期18卷 597-625页

作者： Browne, Ryan P. Bagnato, Luca Punzo, Antonio Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON Canada Univ Cattolica Sacro Cuore Dept Econ & Social Sci Milan Italy Univ Catania Dept Econ & Business Catania Italy

Mixtures of multivariate leptokurtic-normal distributions have been recently introduced in the clustering literature based on mixtures of elliptical heavy-tailed distributions. They have the advantage of having parameters directly related to the moments of practical interest. We derive two estimation procedures for these mixtures. The first one is based on the majorization-minimization algorithm, while the second is based on a fixed point approximation. Moreover, we introduce parsimonious forms of the considered mixtures and we use the illustrated estimation procedures to fit them. We use simulated and real data sets to investigate various aspects of the proposed models and algorithms.

关键词： Leptokurtic-normal distribution majorization-minimization algorithm Mixture models Parsimony 62Hxx Multivariate analysis

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A majorization-minimization scheme for L₂ support vector regression

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2021年第15期91卷 3087-3107页

作者： Zheng, Songfeng Missouri State Univ Dept Math Springfield MO 65897 USA

In a support vector regression (SVR) model, using the squared epsilon-insensitive loss function makes the optimization problem strictly convex and yields a more concise solution. However, the formulation of L-2-SVR leads to a quadratic programming which is expensive to solve. This paper reformulates the optimization problem of L-2-SVR by absorbing the constraints in the objective function, which can be solved efficiently by a majorization-minimization approach, in which an upper bound for the objective function is derived in each iteration which is easier to be minimized. The proposed approach is easy to implement, without requiring any additional computing package other than basic linear algebra operations. Numerical studies on real-world datasets show that, compared to the alternatives, the proposed approach can achieve similar prediction accuracy with substantially higher time efficiency in training.

关键词： Support vector regression squared epsilon-insensitive loss function quadratic programming majorization-minimization algorithm

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A dimension reduction assisted credit scoring method for big data with categorical features

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FINANCIAL INNOVATION 2025年第1期11卷 1-30页

作者： Miljkovic, Tatjana Wang, Pei Miami Univ Dept Stat 100 Bishop Circle 334E Upham Hall Oxford OH 45056 USA Bowling Green State Univ Dept Appl Stat & Operat Res 819 E Wooster St Bowling Green OH 43403 USA

In the past decade, financial institutions have invested significant efforts in the development of accurate analytical credit scoring models. The evidence suggests that even small improvements in the accuracy of existing credit-scoring models may optimize profits while effectively managing risk exposure. Despite continuing efforts, the majority of existing credit scoring models still include some judgment-based assumptions that are sometimes supported by the significant findings of previous studies but are not validated using the institution's internal data. We argue that current studies related to the development of credit scoring models have largely ignored recent developments in statistical methods for sufficient dimension reduction. To contribute to the field of financial innovation, this study proposes a Dimension Reduction Assisted Credit Scoring (DRA-CS) method via distance covariance-based sufficient dimension reduction (DCOV-SDR) in majorization-minimization (MM) algorithm. First, in the presence of a large number of variables, the DRA-CS method results in greater dimension reduction and better prediction accuracy than the other methods used for dimension reduction. Second, when the DRA-CS method is employed with logistic regression, it outperforms existing methods based on different variable selection techniques. This study argues that the DRA-CS method should be used by financial institutions as a financial innovation tool to analyze high-dimensional customer datasets and improve the accuracy of existing credit scoring methods.

关键词： Credit scoring Dimension reduction Logistic regression majorization-minimization algorithm C40 D91 E41 G21 G41

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A nonconvex sparse recovery method for DOA estimation based on the trimmed lasso

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DIGITAL SIGNAL PROCESSING 2024年 153卷

作者： Bai, Longxin Zhang, Jingchao Qiao, Liyan Harbin Inst Technol Dept Automatic Test & Control Harbin 150001 Peoples R China

Sparse direction -of -arrival (DOA) estimation methods can be formulated as a group -sparse optimization problem. Meanwhile, sparse recovery methods based on nonconvex penalty terms have been a hot topic in recent years due to their several appealing properties. Herein, this paper studies a new nonconvex regularized approach called the trimmed lasso for DOA estimation. We define the penalty term of the trimmed lasso in the multiple measurement vector model by l(2,1)-norm. First, we use the smooth approximation function to change the nonconvex objective function to the convex weighted problem. Next, we derive sparse recovery guarantees based on the extended Restricted Isometry Property and regularization parameter for the trimmed lasso in the multiple measurement vector problem. Our proposed method can control the desired level of sparsity of estimators exactly and give a more precise solution to the DOA estimation problem. Numerical simulations show that our proposed method overperforms traditional approaches, which is more close to the Cramer -Rao bound.

关键词： Direction-of-arrival estimation The trimmed LASSO majorization-minimization algorithm Recovery guarantee Nonconvex penalty

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Acoustic object canceller: removing a known signal from monaural recording using blind synchronization

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EURASIP JOURNAL ON AUDIO SPEECH AND MUSIC PROCESSING 2023年第1期2023卷 35页

作者： Kawamura, Takao Yamaoka, Kouei Wakabayashi, Yukoh Ono, Nobutaka Miyazaki, Ryoichi Tokyo Metropolitan Univ Dept Comp Sci Tokyo Japan Toyohashi Univ Technol Dept Comp Sci & Engn Toyohashi Aichi Japan Tokuyama Coll Natl Inst Technol Dept Comp Sci & Elect Engn Yamaguchi Japan

In this paper, we propose a technique for removing a specific type of interference from a monaural recording. Nonstationary interferences are generally challenging to eliminate from such recordings. However, if the interference is a known sound like a cell phone ringtone, music from a CD or streaming service, or a radio or TV broadcast, its source signal can be easily obtained. In our method, we define such interference as an acoustic object. Even if the sampling frequencies of the recording and the acoustic object do not match, we compensate for the mismatch and use the maximum likelihood estimation technique with the auxiliary function to remove the interference from the recording. We compare several probabilistic models for representing the object-canceled signal. Experimental evaluations confirm the effectiveness of our proposed method.

关键词： Noise suppression Acoustic object Blind synchronization Sampling frequency mismatch Maximum likelihood estimation majorization-minimization algorithm

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Adaptively robust geographically weighted regression

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SPATIAL STATISTICS 2022年 48卷 100623-100623页

作者： Sugasawa, Shonosuke Murakami, Daisuke Univ Tokyo Ctr Spatial Informat Sci Tokyo Japan Inst Stat Math Dept Stat Data Sci Tokyo Japan 5-1-5 Kashiwanoha Kashiwa Chiba 2778568 Japan

We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on gamma-divergence. A novel feature of the proposed approach is that two tuning parameters that control robustness and spatial smoothness are automatically tuned in a data-dependent manner. Further, the proposed method can produce robust standard error estimates and give us a reasonable quantity for local outlier detection. We demonstrate that the proposed method is superior to the existing robust geographically weighted regression through simulation and data analysis. (C)& nbsp;2022 Elsevier B.V. All rights reserved.

关键词： majorization-minimization algorithm Robust divergence Outliers

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L1 model-driven recursive multi-scale denoising network for image super-resolution

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KNOWLEDGE-BASED SYSTEMS 2021年 225卷 107115-107115页

作者： Sun, Zhongfan Zhao, Jianwei Zhou, Zhenghua Gao, Qingqing China Jiliang Univ Coll Sci Dept Informat Sci & Math Hangzhou 310018 Peoples R China Nanjing Univ State Key Lab Novel Software Technol Nanjing 210093 Peoples R China

Most existing deep learning based single-image super-resolution (SISR) methods mainly improve the reconstruction performances from the perspective of data-driven, i.e., widening or deepening the networks according to the huge scale of the training data. However, it will bring a huge amount of weights and biases, and cost the expensive computations. Recently, some people have proposed a new frame for designing the deep networks according to the algorithms deduced from the l(2)-optimization problem. But they did not consider the case with outliers. Since l(1)-norm can describe the sparsity of the outliers better than l(2)-norm, we propose an effective deep network designed according to the new algorithm deduced from the l(1)-optimization problem. In our proposed method, an effective iterative algorithm for the l(1) reconstructed optimization problem is deduced based on the split Bregman algorithm, majorization-minimization algorithm, and soft thresholding operator. Then according to the deduced iterative algorithm, an effective deep network, named l(1) Model-Driven Recursive Multi-Scale Denoising Network (l(1)-MRMDN), is designed. Due to the iteration form of the deduced algorithm, the proposed l(1)-MRMDN contains an inner recursion and an outer recursion. Therefore, our proposed method can not only relieve its sensitiveness to the outliers because of the l(1) data fidelity term, but also avoid designing the deep network blindly via the guidance of prior knowledge. Extensive experimental results illustrate that our proposed method is superior to some related popular SISR methods. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Super-resolution Deep learning l(1) model-driven Iteration algorithm Denoising network majorization-minimization algorithm Soft thresholding operator

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A nonparametric Bayesian model for system identification based on a super-Gaussian distribution

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ELECTRONICS AND COMMUNICATIONS IN JAPAN 2019年第7期102卷 32-40页

作者： Tanji, Hiroki Murakami, Takahiro Kamata, Hiroyuki Meiji Univ Sch Sci & Technol Dept Elect & Bioinformat JSPS Res Fellowship Young Specialists DC2 Kawasaki Kanagawa Japan Meiji Univ Sch Sci & Technol Dept Elect & Bioinformat Kawasaki Kanagawa Japan

In the acoustic signal processing applications of finite impulse response (FIR) system identification, it is important to develop the identification method that is robust to super-Gaussian noises. Moreover, the identification method that estimates the FIR coefficients and the order of the unknown system is required, because the order of the unknown system is unavailable in advance. Therefore, in this paper, we propose a nonparametric Bayesian (NPB) model for FIR system identification using a super-Gaussian likelihood and the beta-Bernoulli process. In the proposed NPB model, we employ the hyperbolic secant distribution for the likelihood function. Then, we derive the inference algorithm to simultaneously estimate the FIR coefficients and the order of the unknown system. Our inference algorithm based on a hybrid inference approach combining the majorization-minimization (MM) algorithm and the Gibbs sampler. The simulation results suggest that the proposed method outperforms the conventional identification algorithms in a super-Gaussian noise environment.

关键词： beta-Bernoulli process Gibbs sampler majorization-minimization algorithm nonparametric Bayesian model super-Gaussian distribution system identification

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