Parameter Estimation with the Ordered $\ell_{2}$ Regularization via an Alternating Direction Method of Multipliers
This addresses the challenge of handling high-dimensional, correlated data in machine learning, though it is incremental as it adapts an existing optimization method to a specific regularization technique.
The paper tackles scaling up ordered ℓ₂ regularization for parameter estimation on large datasets using an ADMM-based method, achieving performance comparable to or better than state-of-the-art baselines on synthetic and real data.
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.