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A majorized-generalized alternating direction method of multipliers for convex composite programming

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arXiv 2021年

作者： Qin, Congying Xiao, Yunhai Li, Peili School of Mathematics and Statistics Henan University Kaifeng475000 China Henan Engineering Research Center for Artificial Intelligence Theory and Algorithms Henan University Kaifeng475000 China School of Statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal University Shanghai200062 China

The linearly constrained convex composite programming problems whose objective function contains two blocks with each block being the form of nonsmooth+smooth arises frequently in multiple fields of applications. If both of the smooth terms are quadratic, this problem can be solved efficiently by using the symmetric Gaussian-Seidel (sGS) technique based proximal alternating direction method of multipliers (ADMM). However, in the non-quadratic case, the sGS technique can not be used any more, which leads to the separable structure of nonsmooth+smooth had to be ignored. In this paper, we present a generalized ADMM and particularly use a majorization technique to make the corresponding subproblems more amenable to efficient computations. Under some appropriate conditions, we prove its global convergence for the relaxation factor in (0, 2). We apply the algorithm to solve a kind of simulated convex composite optimization problems and a type of sparse inverse covariance matrix estimation problems which illustrates that the effectiveness of the algorithm are obvious. Copyright © 2021, The Authors. All rights reserved.

关键词： Covariance matrix

Cross Attention Based Style Distribution for Controllable Person Image Synthesis

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arXiv 2022年

作者： Zhou, Xinyue Yin, Mingyu Chen, Xinyuan Sun, Li Gao, Changxin Li, Qingli Shanghai Key Laboratory of Multidimensional Information Processing East China Normal University Shanghai China Key Laboratory of Advanced Theory and Application in Statistics and Data Science East China Normal University Shanghai China Shanghai AI Laboratory Shanghai China Huazhong University of Science and Technology Wuhan China

Controllable person image synthesis task enables a wide range of applications through explicit control over body pose and appearance. In this paper, we propose a cross attention based style distribution module that computes between the source semantic styles and target pose for pose transfer. The module intentionally selects the style represented by each semantic and distributes them according to the target pose. The attention matrix in cross attention expresses the dynamic similarities between the target pose and the source styles for all semantics. Therefore, it can be utilized to route the color and texture from the source image, and is further constrained by the target parsing map to achieve a clearer objective. At the same time, to encode the source appearance accurately, the self attention among different semantic styles is also added. The effectiveness of our model is validated quantitatively and qualitatively on pose transfer and virtual try-on tasks. Codes are available at https://***/xyzhouo/CASD. Copyright © 2022, The Authors. All rights reserved.

关键词： Semantics

NOVEL ENSEMBLE ALGORITHMS FOR RANDOM TWO-DOMAIN PARABOLIC PROBLEMS

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arXiv 2023年

作者： Sun, Yizhong Wang, Jiangshan Zheng, Haibiao School of Mathematical Sciences East China Normal University Shanghai China School of Mathematical Sciences East China Normal University Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Key Laboratory of Advanced Theory and Application in Statistics and Data Science Shanghai China

In this paper, three efficient ensemble algorithms are proposed for fast-solving the random fluid-fluid interaction model. Such a model can be simplified as coupling two heat equations with random diffusion coefficients and a friction parameter due to its complexity and uncertainty. We utilize the Monte Carlo method for the coupled model with random inputs to derive some deterministic fluid-fluid numerical models and use the ensemble idea to realize the fast computation of multiple problems. Our remarkable feature of these algorithms is employing the same coefficient matrix for multiple linear systems, significantly reducing the computational cost. By data-passing partitioned techniques, we can decouple the numerical models into two smaller sub-domain problems and achieve parallel computation. Theoretically, we derive that both algorithms are unconditionally stable and convergent. Finally, numerical experiments are conducted not only to support the theoretical results but also to validate the exclusive feature of the proposed algorithms. © 2023, CC BY-NC-SA.

关键词： Numerical models

Time-Consistent Portfolio Selection for Rank-Dependent Utilities in an Incomplete Market

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arXiv 2024年

作者： Wei, Jiaqin Xia, Jianming Zhao, Qian Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai200062 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Statistics and Information Shanghai University of International Business and Economics Shanghai201620 China

We investigate the portfolio selection problem for an agent with rank-dependent utility in an incomplete financial market. For a constant-coefficient market and CRRA utilities, we characterize the deterministic strict equilibrium strategies. In the case of time-invariant probability weighting function, we provide a comprehensive characterization of the deterministic strict equilibrium strategy. The unique non-zero equilibrium, if exists, can be determined by solving an autonomous ODE. In the case of time-variant probability weighting functions, we observe that there may be infinitely many non-zero deterministic strict equilibrium strategies, which are derived from the positive solutions to a nonlinear singular ODE. By specifying the maximal solution to the singular ODE, we are able to identify all the positive solutions. In addition, we address the issue of selecting an optimal strategy from the numerous equilibrium strategies available. © 2024, CC BY-NC-ND.

关键词： Commerce

An asymptotic analysis of minibatch-based momentum methods for linear regression models

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arXiv 2021年

作者： Gao, Yuan Zhu, Xuening Qi, Haobo Li, Guodong Zhang, Riquan Wang, Hansheng School of Statistics East China Normal University Shanghai China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE East China Normal University Shanghai China School of Data Science Fudan University Shanghai China Guanghua School of Management Peking University Beijing China Department of Statistics and Actuarial Science University of Hong Kong Hong Kong

Momentum methods have been shown to accelerate the convergence of the standard gradient descent algorithm in practice and theory. In particular, the minibatch-based gradient descent methods with momentum (MGDM) are widely used to solve large-scale optimization problems with massive datasets. Despite the success of the MGDM methods in practice, their theoretical properties are still underexplored. To this end, we investigate the theoretical properties of MGDM methods based on the linear regression models. We first study the numerical convergence properties of the MGDM algorithm and further provide the theoretically optimal tuning parameters specification to achieve faster convergence rate. In addition, we explore the relationship between the statistical properties of the resulting MGDM estimator and the tuning parameters. Based on these theoretical findings, we give the conditions for the resulting estimator to achieve the optimal statistical efficiency. Finally, extensive numerical experiments are conducted to verify our theoretical results. © 2021, CC BY.

关键词： Gradient methods

An efficient semismooth Newton method for adaptive sparse signal recovery problems

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arXiv 2021年

作者： Ding, Yanyun Zhang, Haibin Li, Peili Xiao, Yunhai Department of Operations Research and Information Engineering Beijing University of Technology Beijing100124 China School of Statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal University Shanghai200062 China School of Mathematics and Statistics Henan University Kaifeng475000 China

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional methods might work not so well. Recently, it was shown that using the difference between l1- and l2-norm as a regularization always has superior performance. In this paper, we propose an adaptive lp-l1−2 model where the lp-norm with p ≥ 1 measures the data fidelity and the l1−2-term measures the sparsity. This proposed model has the ability to deal with different types of noises and extract the sparse property even under high coherent condition. We use a proximal majorization-minimization technique to handle the nonconvex regularization term and then employ a semismooth Newton method to solve the corresponding convex relaxation subproblem. We prove that the sequence generated by the semismooth Newton method admits fast local convergence rate to the subproblem under some technical assumptions. Finally, we do some numerical experiments to demonstrate the superiority of the proposed model and the progressiveness of the proposed algorithm. Copyright © 2021, The Authors. All rights reserved.

关键词： Compressed sensing

Variable screening in multivariate linear regression with high-dimensional covariates

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Statistical theory and Related Fields 2022年第3期6卷 241-253页

作者： Shiferaw B.Bizuayehu Lu Li Jin Xu School of Statistics East China Normal UniversityShanghaiPeople’s Republic of China School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghaiPeople’s Republic of China Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal UniversityShanghaiPeople’s Republic of China

We propose two variable selection methods in multivariate linear regression with highdimensional *** first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predictors to a moderate or low *** second method extends the univariate forward regression of Wang[(2009).Forward regression for ultra-high dimensional variable *** of the American Statistical Association,104(488),1512–***://***/10.1198/***08516]in a unified way such that the variable selection and model estimation can be obtained *** establish the sure screening property for both *** and real data applications are presented to show the finite sample performance of the proposed methods in comparison with some naive method.

关键词： Dimension reduction forward regression multiple correlation coefficient multivariate regression variable selection

A review of distributed statistical inference

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arXiv 2023年

作者： Gao, Yuan Liu, Weidong Wang, Hansheng Wang, Xiaozhou Yan, Yibo Zhang, Riquan School of Statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE East China Normal University Shanghai China School of Mathematical Sciences Key Lab of Artificial Intelligence - MOE Shanghai Jiao Tong University Shanghai China Guanghua School of Management Peking University Beijing China

The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of divide-and-conquer, various distributed frameworks for statistical estimation and inference have been proposed. They were developed to deal with large-scale statistical optimization problems. This paper aims to provide a comprehensive review for related literature. It includes parametric models, nonparametric models, and other frequently used models. Their key ideas and theoretical properties are summarized. The trade-off between communication cost and estimate precision together with other concerns are discussed. Copyright © 2023, The Authors. All rights reserved.

关键词： Principal component analysis

Derivatives of local times for some Gaussian fields

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arXiv 2019年

作者： Hong, Minhao Xu, Fangjun School of Statistics East China Normal University Shanghai200262 China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE School of Statistics East China Normal University Shanghai200062 China NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai 3663 Zhongshan Road North Shanghai200062 China

In this article, we consider derivatives of local time for a (2, d)-Gaussian field Z = {Z(t, s) = XtH1 − XeH2 , s, t ≥ 0}, s where XH1 and XeH2 are two independent processes from a class of d-dimensional centered Gaussian processes satisfying certain local nondeterminism property. We first give a condition for existence of derivatives of the local time. Then, under this condition, we show that derivatives of the local time are Hölder continuous in both time and space variables. Moreover, under some additional assumptions, we show that this condition is also necessary for existence of derivatives of the local time at the origin. Copyright © 2019, The Authors. All rights reserved.

关键词： Gaussian distribution