TY - JOUR
T1 - ADMM for least square problems with pairwise-difference penalties for coefficient grouping
AU - Park, Soohee
AU - Shin, Seung Jun
N1 - Funding Information:
This work is partially funded by the National Research Foundation of Korea (NRF) grants 2018R1D1A1B07043034 and 2019R1A4A1028134. 1Corresponding author: Department of Statistics, Korea University, 145 Anam-Ro, Sungbuk-Gu, Seoul 02841, Korea. E-mail: sjshin@korea.ac.kr
Publisher Copyright:
© 2022. The Korean Statistical Society, and Korean International Statistical Society. All rights reserved.
PY - 2022
Y1 - 2022
N2 - In the era of bigdata, scalability is a crucial issue in learning models. Among many others, the Alternating Direction of Multipliers (ADMM, Boyd et al., 2011) algorithm has gained great popularity in solving large-scale problems efficiently. In this article, we propose applying the ADMM algorithm to solve the least square problem penalized by the pairwise-difference penalty, frequently used to identify group structures among coefficients. ADMM algorithm enables us to solve the high-dimensional problem efficiently in a unified fashion and thus allows us to employ several different types of penalty functions such as LASSO, Elastic Net, SCAD, and MCP for the penalized problem. Additionally, the ADMM algorithm naturally extends the algorithm to distributed computation and real-time updates, both desirable when dealing with large amounts of data.
AB - In the era of bigdata, scalability is a crucial issue in learning models. Among many others, the Alternating Direction of Multipliers (ADMM, Boyd et al., 2011) algorithm has gained great popularity in solving large-scale problems efficiently. In this article, we propose applying the ADMM algorithm to solve the least square problem penalized by the pairwise-difference penalty, frequently used to identify group structures among coefficients. ADMM algorithm enables us to solve the high-dimensional problem efficiently in a unified fashion and thus allows us to employ several different types of penalty functions such as LASSO, Elastic Net, SCAD, and MCP for the penalized problem. Additionally, the ADMM algorithm naturally extends the algorithm to distributed computation and real-time updates, both desirable when dealing with large amounts of data.
KW - Alternating direction of multipliers
KW - Grouping coefficients
KW - High-dimensional data
KW - Real-time update
UR - http://www.scopus.com/inward/record.url?scp=85135815973&partnerID=8YFLogxK
U2 - 10.29220/CSAM.2022.29.4.441
DO - 10.29220/CSAM.2022.29.4.441
M3 - Article
AN - SCOPUS:85135815973
SN - 2287-7843
VL - 29
SP - 441
EP - 451
JO - Communications for Statistical Applications and Methods
JF - Communications for Statistical Applications and Methods
IS - 4
ER -