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A Subspace Acceleration Method for Minimization Involving a Group Sparsity-Inducing Regularizer

We consider the problem of minimizing an objective function that is the sum of a convex function and a group sparsity-inducing regularizer. Problems that integrate such regularizers arise in modern machine learning applications, often for the purpose of obtaining models that are easier to interpret and that have higher predictive accuracy. We present a new method for solving such problems that utilizes subspace acceleration, domain decomposition, and support identification. Our analysis provides the global iteration complexity of obtaining an ϵ-accurate solution and shows that, under common assumptions, the iterates locally converge superlinearly. Numerical results on regularized logistic and linear regression problems show that our approach is efficient and reliable and outperforms state-of-the-art methods on interesting classes of problems, especially when the number of data points is larger than the number of features. For solving problems when the number of data points is smaller than the number of features, algorithms that focus on solving a dual problem may be more efficient than our approach, which solves the primal problem.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.32 No.2 April-June 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 545-572

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

CONVEX OPTIMIZATION
SPARSITY
LINEAR REGRESSION
LOGISTIC REGRESSION
REGULARIZATION
NONLINEAR OPTIMIZATION
SUBSPACE ACCELERATION
WORST-CASE ITERATION COMPLEXITY
GROUP REGULARIZER

Info Detail Spesifik

https://doi.org/10.1137/21M1411111

Pernyataan Tanggungjawab

Frank E. Curtis, Yutong Dai, Daniel P. Robinson

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