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1 code implementation • 28 May 2021 • Heng Yang, Ling Liang, Kim-Chuan Toh, Luca Carlone

STRIDE dominates a diverse set of five existing SDP solvers and is the only solver that can solve degenerate rank-one SDPs to high accuracy (e. g., KKT residuals below 1e-9), even in the presence of millions of equality constraints.

no code implementations • 22 Oct 2020 • Yangjing Zhang, Kim-Chuan Toh, Defeng Sun

Motivated by the observation that the ability of the $\ell_1$ norm in promoting sparsity in graphical models with Laplacian constraints is much weakened, this paper proposes to learn graph Laplacian with a non-convex penalty: minimax concave penalty (MCP).

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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 24 Sep 2016 • Ethan X. Fang, Han Liu, Kim-Chuan Toh, Wen-Xin Zhou

This paper studies the matrix completion problem under arbitrary sampling schemes.

no code implementations • CVPR 2016 • Zhuwen Li, Shuoguang Yang, Loong-Fah Cheong, Kim-Chuan Toh

Estimating the number of clusters remains a difficult model selection problem.

no code implementations • 6 Sep 2013 • Yu-Xiang Wang, Choon Meng Lee, Loong-Fah Cheong, Kim-Chuan Toh

Low-rank matrix completion is a problem of immense practical importance.

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