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Separating variables to accelerate non-convex regularized optimization

Author

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  • Liu, Wenchen
  • Tang, Yincai
  • Wu, Xianyi

Abstract

In this paper, a novel variable separation algorithm stemmed from the idea of orthogonalization EM is proposed to find the minimization of general function with non-convex regularizer. The main idea of our algorithm is to construct a new function by adding an item that allows minimization to be solved separately on each component. Several attractive theoretical properties concerning the new algorithm are established. The new algorithm converges to one of the critical points with the condition that the objective function is coercive or the generated sequence is in a compact set. The convergence rate of the algorithm is also obtained. The Barzilai–Borwein (BB) rule and Nesterov’s method are also used to accelerate our algorithm. The new algorithm can also be used to solve the minimization of general function with group structure regularizer. The simulation and real data results show that these methods can accelerate our method obviously.

Suggested Citation

  • Liu, Wenchen & Tang, Yincai & Wu, Xianyi, 2020. "Separating variables to accelerate non-convex regularized optimization," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:csdana:v:147:y:2020:i:c:s0167947320300347
    DOI: 10.1016/j.csda.2020.106943
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    References listed on IDEAS

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    1. Dankmar Böhning & Bruce Lindsay, 1988. "Monotonicity of quadratic-approximation algorithms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 641-663, December.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    4. Mazumder, Rahul & Friedman, Jerome H. & Hastie, Trevor, 2011. "SparseNet: Coordinate Descent With Nonconvex Penalties," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1125-1138.
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