camel.tiger: Tuning Insensitive Graph Estimation and Regression
In camel: Calibrated Machine Learning

Description Usage Arguments Details Value Author(s) References See Also Examples

The function "camel.cmr" implements TIGER and Calibrated CLIME using L1 norm regularization

camel.tiger(data, lambda = NULL, nlambda = NULL, lambda.min.ratio = NULL, 
      method = "slasso", sym = "or", shrink=NULL, prec = 1e-4, mu = 0.01,
      max.ite = 1e4, standardize = FALSE, correlation = FALSE,
      perturb = TRUE, verbose = TRUE)

`data`	There are 2 options for `"clime"`: (1) `data` is an `n` by `d` data matrix (2) a `d` by `d` sample covariance matrix. The program automatically identifies the input matrix by checking the symmetry. (`n` is the sample size and `d` is the dimension). For `"slasso"`, covariance input is not supported.
`lambda`	A sequence of decresing positive numbers to control the regularization. Typical usage is to leave the input `lambda = NULL` and have the program compute its own `lambda` sequence based on `nlambda` and `lambda.min.ratio`. Users can also specify a sequence to override this. Default value is from lambda.max to `lambda.min.ratiolambda.max`. For TIGER, the default value of lambda.max* is π√{\log(d)/n}. For CLIME , the default value of lambda.max is the minimum regularization parameter, which yields an all-zero off-diagonal estiamtes.
`nlambda`	The number of values used in `lambda`. Default value is 10.
`lambda.min.ratio`	The smallest value for `lambda`, as a fraction of the uppperbound (`MAX`) of the regularization parameter. The program can automatically generate `lambda` as a sequence of length = `nlambda` starting from `MAX` to `lambda.min.ratio*MAX` in log scale. The default value is `0.25` for TIGER and `0.5` for CLIME.
`method`	TIGER is applied if `method = "slasso"`, CLIME is applied if `method="clime"`. Default value is `"slasso"`.
`sym`	Symmetrization of output graphs. If `sym = "and"`, the edge between node `i` and node `j` is selected ONLY when both node `i` and node `j` are selected as neighbors for each other. If `sym = "or"`, the edge is selected when either node `i` or node `j` is selected as the neighbor for each other. The default value is `"or"`.
`shrink`	Shrinkage of regularization parameter based on precision of estimation. The default value is 1.5 if `method = "clime"` and the default value is 0 if `method="slasso"` or `method = "aclime"`.
`prec`	Stopping criterion. The default value is 1e-4.
`mu`	The smoothing parameter. The default value is 0.01.
`max.ite`	The iteration limit. The default value is 1e4.
`standardize`	All varaibles are standardized to have mean zero and standard deviation one if `standardize = TRUE`. The default value is `FALSE`.
`correlation`	Correlation matrix is used as the input of `Sigma` for `method = "clime"` if `correlation = TRUE`. The default value is `FALSE`.
`perturb`	The diagonal of `Sigma` is added by a positive value to guarantee that `Sigma` is positive definite if `perturb = TRUE`. User can specify a numeric value for `perturbe`. The default value is TRUE.
`verbose`	Tracing information is disabled if `verbose = FALSE`. The default value is `TRUE`.

TIGER and Calibrated CLIME adjust the regularization with respect to each column of the sparse precision matrix. Thus it achieves both improved finite sample performance and tuning insensitiveness.

An object with S3 class "tiger" is returned:

`data`	The `n` by `d` data matrix or `d` by `d` sample covariance matrix from the input.
`cov.input`	An indicator of the sample covariance.
`lambda`	The sequence of regularization parameters `lambda` used in the program.
`nlambda`	The number of values used in `lambda`.
`icov`	A list of `d` by `d` precision matrices corresponding to regularization parameters.
`sym`	The `sym` from the input.
`method`	The `method` from the input.
`path`	A list of `d` by `d` adjacency matrices of estimated graphs as a graph path corresponding to `lambda`.
`sparsity`	The sparsity levels of the graph path.
`ite`	If `method = "clime"`, it is a list of two matrices where ite[[1]] is the number of external iterations and ite[[2]] is the number of internal iterations with the entry of (i,j) as the number of iteration of i-th column and j-th lambda. If `method="slasso"`, it is a matrix of iteration with the entry of (i,j) as the number of iteration of i-th column and j-th lambda.
`df`	It is a `d` by `nlambda` matrix. Each row contains the number of nonzero coefficients along the lasso solution path.
`standardize`	The `standardize` from the input.
`correlation`	The `correlation` from the input.
`perturb`	The `perturb` from the input.
`verbose`	The `verbose` from the input.

Xingguo Li, Tuo Zhao, and Han Liu
Maintainer: Xingguo Li <xingguo.leo@gmail.com>

1. T. Cai, W. Liu and X. Luo. A constrained L1 minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association, 2011.
2. H. Liu and L. Wang. TIGER: A tuning-insensitive approach for optimally estimating large undirected graphs. Technical Report, 2012.

camel-package, camel.tiger.generator, camel.tiger.select, camel.plot, camel.tiger.roc, plot.tiger, plot.select, plot.roc, plot.sim, print.tiger, print.select, print.roc and print.sim.

## generating data
n = 100
d = 100
D = camel.tiger.generator(n=n,d=d,graph="hub",g=10)
plot(D)

## sparse precision matrix estimation with method "clime"
out1 = camel.tiger(D$data, method = "clime")
plot(out1)
camel.plot(out1$path[[7]])

## sparse precision matrix estimation with method "slasso"
out2 = camel.tiger(D$data, method = "slasso")
plot(out2)
camel.plot(out2$path[[4]])