Workshop on Matrix Optimization and Machine Learning

8月8日 - 10日, 2021年

 

中国科学院数学与系统科学研究院南楼204

主办单位：中国科学院数学与系统科学研究院

北京工业大学

清华大学

 

中国科学院大学

矩阵优化及机器学习前沿论坛

    为包含矩阵优化和机器学习在内的的相关领域的专家学者提供交流与讨论的平台，促进运筹优化同仁间的学术合作，分享最新研究进展，探讨相关研究领域未来发展方向，于2021年8月8-10日在北京举办“矩阵优化及机器学习前沿论坛”学术研讨会。本次研讨会特邀国内外知名优化专家做学术报告，并进行相关领域的前沿进展研讨，旨在推动国内外运筹优化领域学者之间的交流。

组织委员会

丁超  （中国科学院数学与系统科学研究院）

赵欣苑 (北京工业大学)

包承龙（清华大学）

 

腾讯会议号

8月09日 腾讯会议ID：454 342 500 密码：2021

8月10日 腾讯会议ID：917 739 463 密码：2021

日程安排

地点: 中国科学院数学与系统科学研究院南楼204

报告摘要

 

报告标题: 机器学习中的0/1损失优化

报告人: 修乃华 (北京交通大学)

摘要: 最优化是机器学习的关键技术，而损失函数是其优化模型的核心组成部分。统计学理论分析表明，0/1损失机器学习优化模型是最为理想的，然而，0/1损失是数学上很难处理的非凸非连续函数，一直以来人们回避它而采用近似松弛方法。近两年来，我们北京交大优化团队成员经初步研究发现，0/1损失函数可以利用变分分析技术进行有效处理，建立最优性理论，设计具有低计算复杂度的高性能求解器。

 

 

报告标题: Intuitionistic Fuzzy Laplacian Twin Support Vector Machine for Semi-supervised Classification

报告人: 白延琴 (上海大学)

摘要: In this talk, we introduce the ideas of fuzzy membership functions and the Laplacian twin support vector machine (Lap-TSVM). A formulation of the linear intuitionistic fuzzy Laplacian twin support vector machine (IFLap-TSVM) is presented. Experiments with constructed artificial datasets, several UCI benchmark datasets and MNIST dataset show that the IFLap-TSVM has better classification accuracy than other state-of-the-art twin support vector machine (TSVM), intuitionistic fuzzy twin support vector machine (IFTSVM) and Lap-TSVM.

 

 

 

 

报告标题: Global Optimization for Nonconvex Programs via Proximal Point Methods

报告人: 邢文训 (清华大学)

摘要: In this talk, a convex proximal point algorithm (CPPA) is considered for globally solving nonconvex optimization problems. Every accumulation point of CPPA is a stationary point of the nonconvex optimization problem. The initial point of CPPA is key to get a global minimizer. Serval sufficient conditions for the initial point selecting are provided for CPPA getting the global minimum. Motivated by these sufficient conditions, CPPA is applied for the convex quadratically constrained nonconvex quadratic programming problem with the initial point getting from its Lagrangian dual problem.  Numerical results show that the possibility to get the global minimum is higher than that of randomly selecting initial points.

 

 

 

 

报告题目: Yuan's lemma: from matrix to fourth order tensor

报告人: 杨庆之 (南开大学)

摘要: It is well-known that symmetric matrix is a class of simple and important matrix, while the positive semidefinite matrix is an important subclass of symmetric matrix. In this talk, I'll first introduce two interesting propositions related to positive semidefinite matrix, called Yuan's  lemma and Sturm-Zhang theorem respectively, then propose their extended versions in fourth order tensor situation.

 

 

 

 

报告标题: DOMP Algorithms for Optimization Problems with Sparsity Constraints

报告人: 赵云彬 (深圳市大数据研究院)

摘要: The orthogonal matching pursuit (OMP) plays a vital role in the development of heuristic algorithms for sparse optimization problems and signal reconstruction. In this paper, we propose an improved version of OMP called dynamic orthogonal matching pursuit (DOMP) which turns out to be numerically more efficient than the OMP for solving sparse optimization problems arising from signal reconstruction.  The theoretical analysis for the algorithm claims that the signal-reconstruction accuracy via the proposed algorithm can be controlled and   measured in terms of the number of iterations,  sparsity level of signals and the noise level of  signal measurements. Further improved versions of the DOMP are also proposed and the numerical performance of the proposed algorithms is also examined via simulations.

 

 

报告标题: 基于三角级数的不确定性分析

报告人: 朱文兴 (中国科学院数学与系统科学研究院)

摘要: 随着芯片制造进入纳米时代，工艺偏差对芯片性能的影响变得愈加明显，很小的随机误差也会导致芯片性能的退化，甚至失效，因而快速准确地在设计制造阶段对芯片的性能进行不确定性分析是重要的问题。现有的技术利用广义混沌多项式做基函数构建代理模型，也有研究将多元多项式按字典排序后构造正交多项式做基函数，当真实响应面波动性较大或者呈现一定周期性时，逼近效果会变差，且当多项式阶数过高时容易在响应面边界造成龙格现象，导致代理模型的精度下降。本研究选取三角函数，通过施密特正交化构造基函数，利用求解一个优化问题确定基函数的系数以及所需要的样本点。理论和数值实验表明所提出方法可以在少量计算成本的情况下得到高精度的结果，克服了现有技术在真实响应面波动性较大或存在一定周期性情况下的计算效率、精确性降低的问题。

 

 

 

 

报告标题: An eigenvalue-based method for the unbalanced Procrustes problem

报告人: 杨卫红 (复旦大学)

摘要: In this talk, we talk about a eigenvalue-based approach to solving the unbalanced orthogonal Procrustes problem. By making effective use of the necessary condition for the global minimizer and the orthogonal constraint, we show that the unbalanced Procrustes problem can be equivalently transformed into an eigenvalue minimization whose solution can be computed by solving a related eigenvector-dependent nonlinear eigenvalue problem. Theoretical convergence analysis of the SCF iteration is shown. The numerical experience indicates that the proposed eigenvalue-based SCF iteration is a promising method for the unbalanced orthogonal Procrustes problem.

 

 

报告标题: Approximate first-order primal-dual algorithms for saddle point problems

报告人: 韩德仁 (北京航空航天大学)

摘要: We propose two approximate versions of the first-order primal-dual algorithm (PDA) for solving a class of convex-concave saddle point problems. The introduced approximate criteria are easy to implement in the sense that they only involve the subgradient of a certain function at the current iterate. The first approximate PDA solves both subproblems inexactly and adopts absolute error criteria, which are based on nonnegative summable sequences. The second approximate PDA, assuming that one of the PDA subproblems can be solved exactly, solves the other subproblem approximately and adopts a relative error criterion. The relative error criterion only involves a single parameter ranging in [0, 1), which makes the method more applicable. For both versions, we establish the global convergence and O(1/N) rate of convergence measured by the iteration complexity, where N counts the number of iterations. Under further assumptions that partial of the underlying functions and the whole underlying functions are strongly convex, we show the accelerated 1 over N square and linear rate of convergence, respectively, for the inexact PDA with absolute error criteria. We then prove that these inexact criteria  can also be extended to solve a class of more general problems. Finally, we perform some numerical experiments on sparse recovery and image processing problems, and the results demonstrate the feasibility and superiority of the proposed methods.

 

 

报告标题: Robust Tensor Completion: Equivalent Surrogates, Error Bounds and Algorithms

报告人: 白敏茹 (湖南大学)

摘要: Robust Low-Rank Tensor Completion (RTC) problems have received considerable attention in recent years such as signal processing and computer vision. In this paper, we focus on the bound constrained RTC problem for third-order tensors which recovers a low-rank tensor from partial observations corrupted by impulse noise. A widely used convex relaxation of this problem is to minimize the tensor nuclear norm for low rank and the $\ell_1$-norm for sparsity. However, it may result in biased solutions. To handle this issue, we propose a nonconvex model with a novel nonconvex tensor rank surrogate function and a novel nonconvex sparsity measure for RTC problems under limited sample constraints and two bound constraints, where these two nonconvex terms have a difference of convex functions (DC) structure. Then, a proximal majorization-minimization (PMM) algorithm is developed to solve the proposed model and this algorithm consists of solving a series of convex subproblems with an initial estimator to generate a new estimator which is used for the next subproblem. Theoretically, for this new estimator, we establish a recovery error bound for its recoverability and give the theoretical guarantee that lower error bounds can be obtained when a reasonable initial estimator is available. Then, by using the Kurdyka-\L ojasiewicz property exhibited in the resulting problem, we show that the sequence generated by the PMM algorithm globally converges to a critical point of the problem. Extensive numerical experiments including color images and multispectral images show the high efficiency of the proposed model.

 

 

报告标题: Distibutionally robust optimization (DRO) with decision-dependent ambiguity set and its approximation

报告人: 童小娇 (湖南第一师范学院)

摘要: In this talk, we make the model analysis and discrete approximation for distributionally robust optimization (DRO) with decision-dependent ambiguity set. Under a general class of metrics called ζ-structure and Slater condition, we prove the local Lipschitz continuity for decision-dependent ambiguity set.  Moreover, we obtain the error between the original and approximated ambiguity set with Wasserstein metric. Finally, we study the stability of optimal value for addressed DRO problem.

 

 

报告标题: Link-road based internet network traffic recovery problem

报告人: 张立平 (清华大学)

摘要: It is challenging to recover the large-scale internet traffic data purely from the link-load measurements. With the rapid growth of the problem scale, it will be extremely difficult to sustain the recovery accuracy and the computational cost simultaneously. For the purpose of fast and accurate recovering the traffic data from link-load measurements, we establish a new Sparsity Low-Rank Recovery (SLRR) model based on the spatial low-rank property and  sparsity of traffic data and propose fast and accurate algorithms to solve the SLRR model. According to the numerical results on the classic datasets Abilene and GEANT, our methods achieve the higher accuracy with a low computational cost. Moreover, in our newly released large-scale real-life network traffic dataset HOD, our method perfectly reaches the seconds-level feedback, which meets the essential requirement for practical scenarios.

 

 

注意事项

本次会议不收取注册费，交通及住宿费用自理。

 

 

 

联系人

丁超      电话：18518604995    邮箱：dingchao@amss.ac.cn

包承龙    电话：15711160698    邮箱：clbao@mail.tsinghua.edu.cn

赵欣苑    电话：18618161356    邮箱：xyzhao@bjut.edu.cn