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【2021.08.08-08.10 北京&騰訊會議】矩陣優化及機器學習前沿論壇
2021-08-05 | 编辑:

Workshop on Matrix Optimization and Machine Learning

88日 - 10, 2021年

 

中國科學院數學與系統科學研究院南樓204

主辦單位:中國科學院數學與系統科學研究院

北京工業大學

清華大學

 

中國科學院大學

矩陣優化及機器學習前沿論壇

    爲包含矩陣優化和機器學習在內的的相關領域的專家學者提供交流與討論的平台,促進運籌優化同仁間的學術合作,分享最新研究進展,探討相關研究領域未來發展方向,于202188-10日在北京舉辦矩陣優化及機器學習前沿論壇學術研討會。本次研討會特邀國內外知名優化專家做學術報告,並進行相關領域的前沿進展研討,旨在推動國內外運籌優化領域學者之間的交流。

組織委員會

丁超  (中國科學院數學與系統科學研究院)

趙欣苑 (北京工業大學)

包承龍(清華大學)

 

騰訊會議號

809騰訊會議ID454 342 500 密碼:2021

810騰訊會議ID917 739 463 密碼:2021


程安排

地點: 中國科學院數學與系統科學研究院南樓204

報告摘要

 

時間

標題

報告人

主持人

8.8

18:00-20:00

報到

騰訊會議ID454 342 500 密碼:2021

8.9

8:30-9:00

開幕式

9:00-9:45

機器學習中的0/1損失優化

修乃華

 

9:45-10:00

茶歇

10:00-10:45

Intuitionistic Fuzzy Laplacian Twin Support Vector Machine for Semi-supervised Classification

白延琴

 

10:45-11:30

Global Optimization for Nonconvex Programs via Proximal Point Methods

邢文訓

11:30-13:00

午餐

13:00-13:45

Yuan's lemma: from matrix to fourth order tensor

楊慶之

 

13:45-14:30

DOMP Algorithms for Optimization Problems with Sparsity Constraints

趙雲彬

14:30-15:00

茶歇

15:00-15:45

基于三角級數的不確定性分析

朱文興

 

15:45-16:30

An eigenvalue-based method for the unbalanced Procrustes problem

楊衛紅

17:00-20:00

晚餐

騰訊會議ID917 739 463 密碼:2021

8.10

8:30-9:15

Robust Tensor Completion: Equivalent Surrogates, Error Bounds and Algorithms

白敏茹

 

9:15-10:00

Distibutionally robust optimization (DRO) with decision-dependent ambiguity set and its approximation

童小嬌

10:00-10:15

茶歇

10:15-11:00

Link-road based internet network traffic recovery problem

張立平

 

11:00-11:45

Approximate first-order primal-dual algorithms for saddle point problems

韓德仁

 

11:45-12:00

閉幕式

12:00-13:30

午餐

报告標題: 機器學習中的0/1損失優化

報告人: 修乃華 (北京交通大學)

摘要: 最優化是機器學習的關鍵技術,而損失函數是其優化模型的核心組成部分。統計學理論分析表明,0/1損失機器學習優化模型是最爲理想的,然而,0/1損失是數學上很難處理的非凸非連續函數,一直以來人們回避它而采用近似松弛方法。近兩年來,我們北京交大優化團隊成員經初步研究發現,0/1損失函數可以利用變分分析技術進行有效處理,建立最優性理論,設計具有低計算複雜度的高性能求解器。

 

 

报告標題: Intuitionistic Fuzzy Laplacian Twin Support Vector Machine for Semi-supervised Classification

報告人: 白延琴 (上海大學)

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.

 

 

 

 

报告標題: Global Optimization for Nonconvex Programs via Proximal Point Methods

報告人: 邢文訓 (清華大學)

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.

 

 

 

 

報告題目: Yuan's lemma: from matrix to fourth order tensor

報告人: 楊慶之 (南开大學)

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.

 

 

 

 

报告標題: DOMP Algorithms for Optimization Problems with Sparsity Constraints

報告人: 趙雲彬 (深圳市大數據研究院)

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.

 

 

报告標題: 基于三角級數的不確定性分析

報告人: 朱文興 (中國科學院數學與系統科學研究院)

摘要: 隨著芯片制造進入納米時代,工藝偏差對芯片性能的影響變得愈加明顯,很小的隨機誤差也會導致芯片性能的退化,甚至失效,因而快速准確地在設計制造階段對芯片的性能進行不確定性分析是重要的問題。現有的技術利用廣義混沌多項式做基函數構建代理模型,也有研究將多元多項式按字典排序後構造正交多項式做基函數,當真實響應面波動性較大或者呈現一定周期性時,逼近效果會變差,且當多項式階數過高時容易在響應面邊界造成龍格現象,導致代理模型的精度下降。本研究選取三角函數,通過施密特正交化構造基函數,利用求解一個優化問題確定基函數的系數以及所需要的樣本點。理論和數值實驗表明所提出方法可以在少量計算成本的情況下得到高精度的結果,克服了現有技術在真實響應面波動性較大或存在一定周期性情況下的計算效率、精確性降低的問題。

 

 

 

 

报告標題: An eigenvalue-based method for the unbalanced Procrustes problem

報告人: 楊衛紅 (复旦大學)

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.

 

 

报告標題: Approximate first-order primal-dual algorithms for saddle point problems

報告人: 韓德仁 (北京航空航天大學)

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.

 

 

报告標題: Robust Tensor Completion: Equivalent Surrogates, Error Bounds and Algorithms

報告人: 白敏茹 (湖南大學)

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.

 

 

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

報告人: 童小嬌 (湖南第一師範學院)

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.

 

 

报告標題: Link-road based internet network traffic recovery problem

報告人: 張立平 (清華大學)

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.

 

 

注意事項

本次會議不收取注冊費,交通及住宿費用自理。

 

 

 

聯系人

丁超      電話:18518604995    郵箱:dingchao@amss.ac.cn

包承龍    電話:15711160698    郵箱:clbao@mail.tsinghua.edu.cn

趙欣苑    電話:18618161356    郵箱:xyzhao@bjut.edu.cn