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A Tutorial on Libra: R package for the Linearized Bregman Algorithm in High Dimensional Statistics

The R package, Libra, stands for the LInearized BRegman Al- gorithm in high dimensional statistics. The Linearized Bregman Algorithm is a simple iterative procedure to generate sparse regularization paths of model estimation, which are rstly discovered in applied mathematics for image restoration and particularly suitable for parallel implementation in large scale problems. The limit of such an algorithm is a sparsity-restricted gradient descent ow, called the Inverse Scale Space, evolving along a par- simonious path of sparse models from the null model to over tting ones. In sparse linear regression, the dynamics with early stopping regularization can provably meet the unbiased Oracle estimator under nearly the same condition as LASSO, while the latter is biased. Despite their successful applications, statistical consistency theory of such dynamical algorithms remains largely open except for some recent progress on linear regression. In this tutorial, algorithmic implementations in the package are discussed for several widely used sparse models in statistics, including linear regression, logistic regres- sion, and several graphical models (Gaussian, Ising, and Potts). Besides the simulation examples, various application cases are demonstrated, with real world datasets from diabetes, publications of COPSS award winners, as well as social networks of two Chinese classic novels, Journey to the West and Dream of the Red Chamber.