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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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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 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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High-Dimensional Fused Lasso Regression Using majorization-minimization and Parallel Processing

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2015年第1期24卷 121-153页

作者： Yu, Donghyeon Won, Joong-Ho Lee, Taehoon Lim, Johan Yoon, Sungroh Keimyung Univ Dept Stat Taegu South Korea Seoul Natl Univ Dept Stat Seoul South Korea Seoul Natl Univ Dept Elect & Comp Engn Seoul South Korea

In this article, we propose a majorization-minimization (MM) algorithm for high-dimensional fused lasso regression (FLR) suitable for parallelization using graphics processing units (GPUs). The MM algorithm is stable and flexible as it can solve the FLR problems with various types of design matrices and penalty structures within a few tens of iterations. We also show that the convergence of the proposed algorithm is guaranteed. We conduct numerical studies to compare our algorithm with other existing algorithms, demonstrating that the proposed MM algorithm is competitive in many settings including the two-dimensional FLR with arbitrary design matrices. The merit of GPU parallelization is also exhibited. Supplementary materials are available online.

关键词： majorization-minimization algorithm Graphics processing unit Parallel computation

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majorization-minimization generalized Krylov subspace methods for - optimization applied to image restoration

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BIT NUMERICAL MATHEMATICS 2017年第2期57卷 351-378页

作者： Huang, G. Lanza, A. Morigi, S. Reichel, L. Sgallari, F. Chengdu Univ Technol Coll Management Sci Geomath Key Lab Sichuan Chengdu 610059 Peoples R China Univ Bologna Dept Math Bologna Italy Kent State Univ Dept Math Sci Kent OH 44242 USA

A new majorization-minimization framework for - image restoration is presented. The solution is sought in a generalized Krylov subspace that is build up during the solution process. Proof of convergence to a stationary point of the minimized - functional is provided for both convex and nonconvex problems. Computed examples illustrate that high-quality restorations can be determined with a modest number of iterations and that the storage requirement of the method is not very large. A comparison with related methods shows the competitiveness of the method proposed.

关键词： l(p)-l(q) minimization Generalized Krylov subspace majorization-minimization algorithm Image restoration

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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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Nonnegative Matrix Factorization With Basis Clustering Using Cepstral Distance Regularization

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IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2018年第6期26卷 1025-1036页

作者： Kameoka, Hirokazu Higuchi, Takuya Tanaka, Mikihiro Li, Li NTT Corp NTT Commun Sci Labs Tokyo 2430198 Japan Univ Tokyo Tokyo 1138656 Japan Univ Tsukuba Tsukuba Ibaraki 3058577 Japan

One successful approach for audio source separation involves applying nonnegative matrix factorization (NMF) to a magnitude spectrogram regarded as a nonnegative matrix. This can be interpreted as approximating the observed spectra at each time frame as the linear sum of the basis spectra scaled by time-varying amplitudes. This paper deals with the problem of the unsupervised instrument-wise source separation of polyphonic signals based on an extension of the NMF approach. We focus on the fact that each piece of music is typically played on a handful of musical instruments, which allows us to assume that the spectra of the underlying audio events in a polyphonic signal can be grouped into a reasonably small number of clusters in the mel-frequency cepstral coefficient (MFCC) domain. Based on this assumption, we propose formulating factorization of amagnitude spectrogram and clustering of the basis spectra in the MFCC domain as a joint optimization problem and derive a novel optimization algorithm based on the majorization-minimization principle. Experimental results revealed that our method was superior to a two-stage algorithm that consists of performing factorization followed by clustering the basis spectra, thus showing the advantage of the joint optimization approach.

关键词： Audio source separation nonnegative matrix factorization (NMF) basis clustering mel-frequency cepstral coefficient (MFCC) majorization-minimization algorithm

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Accelerated image reconstruction in fluorescence molecular tomography using a nonuniform updating scheme with momentum and ordered subsets methods

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JOURNAL OF BIOMEDICAL OPTICS 2016年第1期21卷 1-10页

作者： Zhu, Dianwen Li, Changqing Univ Calif Merced Sch Engn 5200 N Lake Rd Merced CA 95343 USA

Fluorescence molecular tomography (FMT) is a significant preclinical imaging modality that has been actively studied in the past two decades. It remains a challenging task to obtain fast and accurate reconstruction of fluorescent probe distribution in small animals due to the large computational burden and the ill-posed nature of the inverse problem. We have recently studied a nonuniform multiplicative updating algorithm that combines with the ordered subsets (OS) method for fast convergence. However, increasing the number of OS leads to greater approximation errors and the speed gain from larger number of OS is limited. We propose to further enhance the convergence speed by incorporating a first-order momentum method that uses previous iterations to achieve optimal convergence rate. Using numerical simulations and a cubic phantom experiment, we have systematically compared the effects of the momentum technique, the OS method, and the nonuniform updating scheme in accelerating the FMT reconstruction. We found that the proposed combined method can produce a high-quality image using an order of magnitude less time. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： fluorescence molecular tomography iterative image reconstruction ordered subsets momentum nonuniform update majorization-minimization algorithm

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Reweighted Nuclear Norm Approach for Interference Alignment

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第9期61卷 3754-3765页

作者： Du, Huiqin Ratnarajah, Tharmalingam Sellathurai, Mathini Papadias, Constantinos B. Univ Edinburgh Sch Engn Inst Digital Commun Edinburgh EH9 3JL Midlothian Scotland Heriot Watt Univ Sch Engn & Phys Sci Edinburgh EH14 4AS Midlothian Scotland Athens Informat Technol Athens 19002 Greece

Managing uncoordinated interference becomes a substantial problem for heterogeneous networks, since the unplanned interferences from the femtos cannot be coordinately aligned with that from the macro/pico base stations (BSs). Due to the uncoordinated interference, perfect interference alignment (IA) may be not attained. In order to achieve linear capacity scaling by IA, we follow the rank-constrained rank minimization (RCRM) framework which minimizes the rank of the interference subspace with full rank constraint on the direct signal space. Considering that the sum of log function can obtain low-rank solutions to linear matrix inequality (LMI) problems for positive semidefinite matrices, we introduce sum of log function as an approximation surrogate of the rank function. To minimize the concave function, we implement a majorization-minimization (MM) algorithm and develop a reweighted nuclear norm minimization algorithm with a weight matrix introduced. Moreover, considering the practical available signal-to-noise ratio (SNR), a mixed approach is developed to further improve the achievable sum rate in low-to-moderate SNR region. Simulation results show that the proposed algorithm considerably improves the sum rate performance and achieves the highest multiplexing gain than the recently developed IA approaches for various interference channels.

关键词： Interference alignment rank-constrained rank minimization majorization-minimization algorithm reweighted nuclear norm minimization

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