This paper describes an R package named flare, which implements a family of
new high dimensional regression methods (LAD Lasso, SQRT Lasso, $\ell_q$ Lasso,
and Dantzig selector) and their extensions to sparse precision matrix
estimation (TIGER and CLIME). These methods exploit different nonsmooth loss
functions to gain modeling flexibility, estimation robustness, and tuning
insensitiveness. The developed solver is based on the alternating direction
method of multipliers (ADMM). The package flare is coded in double precision C,
and called from R by a user-friendly interface. The memory usage is optimized
by using the sparse matrix output. The experiments show that flare is efficient
and can scale up to large problems.

本文介绍了一个名为 flare 的 R 包，它实现了一系列新的高维回归方法和它们对稀疏精度矩阵估计的扩展。这些方法利用不同的非平滑损失函数来获得建模灵活性，估计稳健性和调优不敏感性。开发的求解器基于交替方向乘子法（ADMM）。包 flare 采用双精度 C 编写，并通过用户友好的界面从 R 中调用。使用稀疏矩阵输出来优化内存使用。实验表明，flare 高效且能够扩展到大规模问题。

R 中高维线性回归和精度矩阵估计的 flare 包

The flare Package for High Dimensional Linear Regression and Precision  Matrix Estimation in R

Many machine learning techniques sacrifice convenient computational
structures to gain estimation robustness and modeling flexibility. However, by
exploring the modeling structures, we find these "sacrifices" do not always
require more computational efforts. To shed light on such a "free-lunch"
phenomenon, we study the square-root-Lasso (SQRT-Lasso) type regression
problem. Specifically, we show that the nonsmooth loss functions of SQRT-Lasso
type regression ease tuning effort and gain adaptivity to inhomogeneous noise,
but is not necessarily more challenging than Lasso in computation. We can
directly apply proximal algorithms (e.g. proximal gradient descent, proximal
Newton, and proximal Quasi-Newton algorithms) without worrying the
nonsmoothness of the loss function. Theoretically, we prove that the proximal
algorithms combined with the pathwise optimization scheme enjoy fast
convergence guarantees with high probability. Numerical results are provided to
support our theory.

本研究针对机器学习中使用的 Square-root-Lasso（SQRT-Lasso）回归问题，发现通过研究建模结构，这种方法可以同时获得效率和准确性，同时提出使用 proximal 算法（如 proximal gradient descent，proximal Newton 和 proximal quasi-Newton）进一步地提高效率。