  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.
