no code implementations • 13 Oct 2012 • Weimin Miao, Shaohua Pan, Defeng Sun
To seek a solution of high recovery quality beyond the reach of the nuclear norm, in this paper, we propose a rank-corrected procedure using a nuclear semi-norm to generate a new estimator.
no code implementations • ICML 2018 • Yancheng Yuan, Defeng Sun, Kim-Chuan Toh
Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications.
no code implementations • 22 Aug 2018 • Meixia Lin, Yong-Jin Liu, Defeng Sun, Kim-Chuan Toh
Based on the new formulation, we derive an efficient procedure for its computation.
no code implementations • 12 Sep 2018 • Lei Yang, Jia Li, Defeng Sun, Kim-Chuan Toh
When the support points of the barycenter are pre-specified, this problem can be modeled as a linear programming (LP) problem whose size can be extremely large.
no code implementations • 4 Oct 2018 • Defeng Sun, Kim-Chuan Toh, Yancheng Yuan
The perfect recovery properties of the convex clustering model with uniformly weighted all pairwise-differences regularization have been proved by Zhu et al. (2014) and Panahi et al. (2017).
no code implementations • 1 Feb 2019 • Meixia Lin, Defeng Sun, Kim-Chuan Toh, Yancheng Yuan
In addition, we derive the corresponding HS-Jacobian to the proximal mapping and analyze its structure --- which plays an essential role in the efficient computation of the PPA subproblem via applying a semismooth Newton method on its dual.
no code implementations • 27 Mar 2019 • Peipei Tang, Chengjing Wang, Defeng Sun, Kim-Chuan Toh
In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems.
no code implementations • 26 Feb 2020 • Meixia Lin, Defeng Sun, Kim-Chuan Toh
We prove that the least squares estimator is computable via solving a constrained convex quadratic programming (QP) problem with $(n+1)d$ variables and at least $n(n-1)$ linear inequality constraints, where $n$ is the number of data points.
no code implementations • 17 Apr 2020 • Meixia Lin, Defeng Sun, Kim-Chuan Toh, Chengjing Wang
The sparsity and clustering structure of the concentration matrix is enforced to reduce model complexity and describe inherent regularities.
no code implementations • 22 Oct 2020 • Yangjing Zhang, Kim-Chuan Toh, Defeng Sun
We consider the problem of learning a graph under the Laplacian constraint with a non-convex penalty: minimax concave penalty (MCP).
no code implementations • 3 Dec 2022 • Shuai Wang, Yanqing Xu, Zhiguo Wang, Tsung-Hui Chang, Tony Q. S. Quek, Defeng Sun
In this paper, we firstly reveal the fact that the federated ADMM is essentially a client-variance-reduced algorithm.
no code implementations • 29 Mar 2023 • Ziwen Wang, Yancheng Yuan, Jiaming Ma, Tieyong Zeng, Defeng Sun
In this paper, we propose a randomly projected convex clustering model for clustering a collection of $n$ high dimensional data points in $\mathbb{R}^d$ with $K$ hidden clusters.
no code implementations • 11 Jan 2024 • Xijun Li, Fangzhou Zhu, Hui-Ling Zhen, Weilin Luo, Meng Lu, Yimin Huang, Zhenan Fan, Zirui Zhou, Yufei Kuang, Zhihai Wang, Zijie Geng, Yang Li, Haoyang Liu, Zhiwu An, Muming Yang, Jianshu Li, Jie Wang, Junchi Yan, Defeng Sun, Tao Zhong, Yong Zhang, Jia Zeng, Mingxuan Yuan, Jianye Hao, Jun Yao, Kun Mao
To this end, we present a comprehensive study on the integration of machine learning (ML) techniques into Huawei Cloud's OptVerse AI Solver, which aims to mitigate the scarcity of real-world mathematical programming instances, and to surpass the capabilities of traditional optimization techniques.