  Regularization is a popular technique in machine learning for model
estimation and avoiding overfitting. Prior studies have found that modern
ordered regularization can be more effective in handling highly correlated,
high-dimensional data than traditional regularization. The reason stems from
the fact that the ordered regularization can reject irrelevant variables and
yield an accurate estimation of the parameters. How to scale up the ordered
regularization problems when facing the large-scale training data remains an
unanswered question. This paper explores the problem of parameter estimation
with the ordered $\ell_{2}$-regularization via Alternating Direction Method of
Multipliers (ADMM), called ADMM-O$\ell_{2}$. The advantages of ADMM-O$\ell_{2}$
include (i) scaling up the ordered $\ell_{2}$ to a large-scale dataset, (ii)
predicting parameters correctly by excluding irrelevant variables
automatically, and (iii) having a fast convergence rate. Experiment results on
both synthetic data and real data indicate that ADMM-O$\ell_{2}$ can perform
better than or comparable to several state-of-the-art baselines.
