mlsanityData to 7 Oct 2026

Dynamic Incremental Optimization for Best Subset Selection

arXiv 2402.02322 ↗First posted 4 Feb 2024cs.LG stat.MLcited by 0

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Abstract (arXiv)

Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of a family of ℓ0-regularized problems. An efficient primal-dual algorithm is developed based on the primal and dual problem structures. By leveraging the dual range estimation along with the incremental strategy, our algorithm potentially reduces redundant computation and improves the solutions of best subset selection. Theoretical analysis and experiments on synthetic and real-world datasets validate the efficiency and statistical properties of the proposed solutions.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 20 of its 41 references that are in the map. First posted on arXiv 4 Feb 2024.

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20 of 41 references.

References · 20

  1. 2015Best Subset Selection via a Modern Optimization Lenscited by 99
  2. 2014On Iterative Hard Thresholding Methods for High-dimensional M-Estimationcited by 53
  3. 2018Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithmscited by 52
  4. 2020Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimizationcited by 45
  5. 2017Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitionscited by 43
  6. 2016Gap Safe screening rules for sparsity enforcing penaltiescited by 38
  7. 2015Mind the duality gap: safer rules for the Lassocited by 31
  8. 2018Celer: a Fast Solver for the Lasso with Dual Extrapolationcited by 31
  9. 2020Learning Sparse Classifiers: Continuous and Mixed Integer Optimization Perspectivescited by 26
  10. 2014Support recovery without incoherence: A case for nonconvex regularizationcited by 25
  11. 2017Subset Selection with Shrinkage: Sparse Linear Modeling when the SNR is lowcited by 17
  12. 2015GAP Safe screening rules for sparse multi-task and multi-class modelscited by 16
8 more
  1. 2016A Tight Bound of Hard Thresholdingcited by 16
  2. 2017Extended Comparisons of Best Subset Selection, Forward Stepwise Selection, and the Lassocited by 16
  3. 2013Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimizationcited by 13
  4. 2015Regularization vs. Relaxation: A conic optimization perspective of statistical variable selectioncited by 12
  5. 2017High-Dimensional Regression with Binary Coefficients. Estimating Squared Error and a Phase Transitioncited by 12
  6. 2016Structured Sparse Regression via Greedy Hard-Thresholdingcited by 6
  7. 2015The Discrete Dantzig Selector: Estimating Sparse Linear Models via Mixed Integer Linear Optimizationcited by 5
  8. 2017Dual Iterative Hard Thresholding: From Non-convex Sparse Minimization to Non-smooth Concave Maximizationcited by 3

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