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Found 10 papers, 0 papers with code
Learning Graph Laplacian with MCP
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).
Estimation of sparse Gaussian graphical models with hidden clustering structure
The sparsity and clustering structure of the concentration matrix is enforced to reduce model complexity and describe inherent regularities.
Efficient algorithms for multivariate shape-constrained convex regression problems
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.
A sparse semismooth Newton based proximal majorization-minimization algorithm for nonconvex square-root-loss regression problems
In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems.
A dual Newton based preconditioned proximal point algorithm for exclusive lasso models
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.
Convex Clustering: Model, Theoretical Guarantee and Efficient Algorithm
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).
A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters
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.
Efficient sparse semismooth Newton methods for the clustered lasso problem
Based on the new formulation, we derive an efficient procedure for its computation.
An Efficient Semismooth Newton Based Algorithm for Convex Clustering
Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications.
A Rank-Corrected Procedure for Matrix Completion with Fixed Basis Coefficients
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.
