Tuning Insensitive Graph Estimation and Regression
R (>= 2.14), glmnet, lattice, igraph, MASS, Matrix
The package "bigmatrix" solves for the precision matrix
estimations with two different methods. The first is the tuning
insensitive graph estimation and regression implemented with
scaled Lasso. Another method is by estimating at a grid of
values for the constrained lambda and the augmented Lagrangian
multiplier rho based on constrained L1 minimization for sparse
precision matrix estimation, which guarantees positive definite
output by projected augmented Lagrangian method and further
accelerates the algorithm via coordinate descent and active set
methods.

Xingguo Li, Tuo Zhao, Lie Wang and Han Liu

The package "bigmatrix" targets at high dimensional
precision matrix estimation problem. We adopt two estimation
procedures based column by column scheme: (1) Tuning
Insensitive Graph Estimation and Regression (TIGER). (2) The
Constrained L1 minimization for sparse precision Matrix
Estimation (CLIME). Both TIGER and CLIME have better
performance than graphical lasso in parameter estimation under
the spectral norm. Moreover, TIGER is less sensitive to tuning
parameter than graphical lasso. The algorithm is implemented
based on Alternative Direction Method combined with coordinate
descent, which scales up to large problems. The computation is
memory-optimized using the sparse matrix output.

The package "bigmatrix" estimates high dimensional
precision matrices for Gaussian graphical models. We adopt two
estimation procedures based column by column regression: (1)
Tuning-Insensitive Graph Estimation and Regression (TIGER). (2)
The Constrained L1 Minimization for Sparse Precision Matrix
Estimation (CLIME). (3) Adaptive Lasso for Sparse Precision
Matrix Estimation (ADP). The optimization algorithm for CLIME
and ADP are based on alternative direction method combined with
coordinate decent. The computation is memory-optimized using
the sparse matrix output.

The package "bigmatrix" estimates high dimensional
precision matrices for Gaussian graphical models. We adopt
three estimation procedures based on column by column
regression: (1) Tuning-Insensitive Graph Estimation and
Regression (TIGER); (2) The Constrained L1 Minimization for
Sparse Precision Matrix Estimation (CLIME); (3) Adaptive CLIME
for Sparse Precision Matrix Estimation (ADP). The optimization
algorithms for all three methods are based on alternative
direction method combined with coordinate decent. The
computation is memory-optimized using the sparse matrix output.