Sparse regression at scale: branch-and-bound rooted in first-order optimization

[1]  T. Rutherford,et al.  Nonlinear Programming , 2021, Mathematical Programming Methods for Geographers and Planners.

[2]  Rahul Mazumder,et al.  Discussion of “Best Subset, Forward Stepwise or Lasso? Analysis and Recommendations Based on Extensive Comparisons” , 2020 .

[3]  Alper Atamtürk,et al.  Safe Screening Rules for $\ell_0$-Regression. , 2020, 2004.08773.

[4]  R. Mazumder,et al.  Learning Sparse Classifiers: Continuous and Mixed Integer Optimization Perspectives , 2020, J. Mach. Learn. Res..

[5]  Cees G. M. Snoek,et al.  Variable Selection , 2019, Model-Based Clustering and Classification for Data Science.

[6]  Dimitris Bertsimas,et al.  Sparse Regression: Scalable Algorithms and Empirical Performance , 2019, Statistical Science.

[7]  Rahul Mazumder,et al.  Learning Hierarchical Interactions at Scale: A Convex Optimization Approach , 2019, AISTATS.

[8]  Alper Atamtürk,et al.  Rank-one Convexification for Sparse Regression , 2019, ArXiv.

[9]  Weijun Xie,et al.  Scalable Algorithms for the Sparse Ridge Regression , 2018, SIAM J. Optim..

[10]  Hussein Hazimeh,et al.  Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms , 2018, Oper. Res..

[11]  Dimitris Bertsimas,et al.  Sparse classification: a scalable discrete optimization perspective , 2017, Machine Learning.

[12]  Bart P. G. Van Parys,et al.  Sparse high-dimensional regression: Exact scalable algorithms and phase transitions , 2017, The Annals of Statistics.

[13]  P. Radchenko,et al.  Subset Selection with Shrinkage: Sparse Linear Modeling When the SNR Is Low , 2017, Oper. Res..

[14]  R. Tibshirani,et al.  Extended Comparisons of Best Subset Selection, Forward Stepwise Selection, and the Lasso , 2017, 1707.08692.

[15]  David Gamarnik,et al.  High Dimensional Regression with Binary Coefficients. Estimating Squared Error and a Phase Transtition , 2017, COLT.

[16]  Russell Bent,et al.  Extended Formulations in Mixed-Integer Convex Programming , 2015, IPCO.

[17]  Siu Kwan Lam,et al.  Numba: a LLVM-based Python JIT compiler , 2015, LLVM '15.

[18]  Jeff T. Linderoth,et al.  Regularization vs. Relaxation: A conic optimization perspective of statistical variable selection , 2015, ArXiv.

[19]  D. Bertsimas,et al.  Best Subset Selection via a Modern Optimization Lens , 2015, 1507.03133.

[20]  Iain Dunning,et al.  Extended formulations in mixed integer conic quadratic programming , 2015, Mathematical Programming Computation.

[21]  Martin J. Wainwright,et al.  Sparse learning via Boolean relaxations , 2015, Mathematical Programming.

[22]  Ryuhei Miyashiro,et al.  Subset selection by Mallows' Cp: A mixed integer programming approach , 2015, Expert Syst. Appl..

[23]  David C. Miller,et al.  Learning surrogate models for simulation‐based optimization , 2014 .

[24]  Martin J. Wainwright,et al.  Lower bounds on the performance of polynomial-time algorithms for sparse linear regression , 2014, COLT.

[25]  Peter Bühlmann,et al.  High-Dimensional Statistics with a View Toward Applications in Biology , 2014 .

[26]  Zhi-Quan Luo,et al.  Iteration complexity analysis of block coordinate descent methods , 2013, Mathematical Programming.

[27]  Amir Beck,et al.  On the Convergence of Block Coordinate Descent Type Methods , 2013, SIAM J. Optim..

[28]  Christian Kirches,et al.  Mixed-integer nonlinear optimization*† , 2013, Acta Numerica.

[29]  Yurii Nesterov,et al.  Gradient methods for minimizing composite functions , 2012, Mathematical Programming.

[30]  Yurii Nesterov,et al.  Efficiency of Coordinate Descent Methods on Huge-Scale Optimization Problems , 2012, SIAM J. Optim..

[31]  Yonina C. Eldar,et al.  Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms , 2012, SIAM J. Optim..

[32]  Sven Leyffer,et al.  Mixed Integer Nonlinear Programming , 2011 .

[33]  T. Hastie,et al.  SparseNet: Coordinate Descent With Nonconvex Penalties , 2011, Journal of the American Statistical Association.

[34]  David L. Woodruff,et al.  Pyomo: modeling and solving mathematical programs in Python , 2011, Math. Program. Comput..

[35]  Oktay Günlük,et al.  Perspective reformulations of mixed integer nonlinear programs with indicator variables , 2010, Math. Program..

[36]  Trevor Hastie,et al.  Regularization Paths for Generalized Linear Models via Coordinate Descent. , 2010, Journal of statistical software.

[37]  Bin Yu,et al.  Minimax Rates of Estimation for High-Dimensional Linear Regression Over q -Balls , 2009, IEEE Trans. Inf. Theory.

[38]  Sinan Gürel,et al.  A strong conic quadratic reformulation for machine-job assignment with controllable processing times , 2009, Oper. Res. Lett..

[39]  Sven Hammarling,et al.  Updating the QR factorization and the least squares problem , 2008 .

[40]  George L. Nemhauser,et al.  A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs , 2008, INFORMS J. Comput..

[41]  Mike E. Davies,et al.  Iterative Hard Thresholding for Compressed Sensing , 2008, ArXiv.

[42]  Vivek K Goyal,et al.  Necessary and Sufficient Conditions on Sparsity Pattern Recovery , 2008, ArXiv.

[43]  Martin J. Wainwright,et al.  Information-Theoretic Limits on Sparsity Recovery in the High-Dimensional and Noisy Setting , 2007, IEEE Transactions on Information Theory.

[44]  Peng Zhao,et al.  On Model Selection Consistency of Lasso , 2006, J. Mach. Learn. Res..

[45]  E. Greenshtein Best subset selection, persistence in high-dimensional statistical learning and optimization under l1 constraint , 2006, math/0702684.

[46]  C. Gentile,et al.  Perspective cuts for a class of convex 0–1 mixed integer programs , 2006, Math. Program..

[47]  Nikolaos V. Sahinidis,et al.  A polyhedral branch-and-cut approach to global optimization , 2005, Math. Program..

[48]  Erling D. Andersen,et al.  On implementing a primal-dual interior-point method for conic quadratic optimization , 2003, Math. Program..

[49]  P. Tseng Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization , 2001 .

[50]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

[51]  Ignacio E. Grossmann,et al.  An outer-approximation algorithm for a class of mixed-integer nonlinear programs , 1986, Math. Program..

[52]  Dimitris Bertsimas,et al.  Rejoiner-Sparse regression: Scalable algorithms and empirical performance , 2020 .

[53]  Noname manuscript No. (will be inserted by the editor) More Branch-and-Bound Experiments in Convex Nonlinear Integer Programming , 2011 .

[54]  Garvesh Raskutti,et al.  Minimax rates of estimation for high-dimensional linear regression over l q-balls , 2011 .

[55]  A. Owen A robust hybrid of lasso and ridge regression , 2006 .

[56]  R. Bixby,et al.  On the Solution of Traveling Salesman Problems , 1998 .

[57]  R. Tibshirani Regression Shrinkage and Selection via the Lasso , 1996 .

[58]  R. J. Dakin,et al.  A tree-search algorithm for mixed integer programming problems , 1965, Comput. J..

[59]  T. Koch,et al.  Branching rules revisited , 2005, Oper. Res. Lett..