trans_precision {TransGraph}

Transfer learning for vector-valued precision matrix (graphical model).

Description

The transfer learning for vector-valued precision matrix via D-trace loss method.

Usage

trans_precision(t.data=NULL, A.data=NULL, precision.method="CLIME",
                       cov.method="opt", cn.lam2=seq(1,2.5,length.out=10),
                       theta.algm="cd", adjust.BIC=FALSE, symmetry=TRUE,
                       preselect.aux=0, sel.type="L2", input.A.cov=FALSE,
                       A.cov=NULL, nA.vec=NULL, t.Theta.hat0=NULL,
                       t.n=NULL, correlation=FALSE)

Arguments

t.data

The target data, a n * p matrix, where n is the sample size and p is data dimension.

A.data

The auxiliary data in K auxiliary domains, a list with K elements, each of which is a nk * p matrix, where nk is the sample size of the k-th auxiliary domain.

precision.method

The initial method of estimating the target precision matrix, which can be selected as "CLIME" or "glasso".

cov.method

The method of aggregating K auxiliary covariance matrices, which can be selected as "size" (the sum weighted by the sample sizes), "weight" (the sum weighted by the differences) or "opt" (select the optimal one).

cn.lam2

A vector or a float value: the coefficients set in tuning parameters used to solve the target precision matrix, default is cn.lam2*sqrt( log(p) / n ).

theta.algm

The optimization algorithm used to solve the precision, which can be selected as "admm" (ADMM algorithm) or "cd" (coordinate descent).

adjust.BIC

Whether to use the adjusted BIC to select lambda2, the default setting is FALSE.

symmetry

Whether to symmetrize the final estimated precision matrices, and the default is True.

preselect.aux

Whether to pre-select informative auxiliary domains based on the distance between initially estimated auxiliary and target parameters. The default is 0, which means that pre-selection will not be performed. If "preselect.aux" is specified as a real number greater than zero, then the threshold value is forpreselect.auxssqrt( log(p) / n ).

sel.type

If pre-selection should be performed, "sel.type" is the type of distance. The default is L2 norm, and can be specified as "L1" to use L1 norm.

input.A.cov

Whether to input the covariance matrices of the auxiliary domains. The default setting is FALSE, which means that the raw data of the auxiliary domain is input, and the covariance will be calculated within this function. If input.A.cov=T, then the calculated covariance matrices must be input through parameter "A.cov", and parameter "A.data" can be defaulted at this time. This setting is suitable for situations where raw data cannot be obtained but the covariance matrix can be obtained.

A.cov

If input.A.cov=T, the "A.cov" must be auxiliary covariance matrices in K auxiliary domains, a list with K elements, each of which is a p * p matrix.

nA.vec

If input.A.cov=T, the "nA.vec" must be a vector consisting of sample sizes of K auxiliary domains.

t.Theta.hat0

Whether to input the estimated target precision matrix based on the target domain only, and the default setting is NULL. If "t.Theta.hat0" is specified as an estimated precision matrix, it will not be recalculated in the initialization phase. This parameter mainly plays a role in transfer learning of GGMMs.

t.n

Whether to input the target sample size, and the default setting is NULL. This parameter mainly plays a role in transfer learning of GGMMs.

correlation

Whether to use correlation matrix for initial parameters in both target and auxiliary domains. The default setting is F.

Value

A result list including:

Theta.hat

The target precision matrix via transfer learning.

Theta.hat0

The initial target precision matrix.

k.check

The number of the optimal auxiliary domain.

N

The minimum sample size for auxiliary domain.

Author(s)

Mingyang Ren [e-mail].

References

Ren, M., Zhen Y., and Wang J. (2022). Transfer learning for tensor graphical models. Ren, M., He X., and Wang J. (2023). Structural transfer learning of non-Gaussian DAG.

Examples

library(TransGraph)
# load example data from github repository
# Please refer to https://github.com/Ren-Mingyang/example_data_TransGraph
# for detailed data information
githublink = "https://github.com/Ren-Mingyang/example_data_TransGraph/"
load(url(paste0(githublink,"raw/main/example.data.GGM.RData")))
t.data = example.data.GGM$target.list$t.data
t.precision = example.data.GGM$target.list$t.precision
A.data = example.data.GGM$A.data
A.data.infor = example.data.GGM$A.data.infor

# using all auxiliary domains
res.trans.weight = trans_precision(t.data, A.data, cov.method="weight")
res.trans.opt = trans_precision(t.data, A.data, cov.method="opt")
res.trans.size = trans_precision(t.data, A.data, cov.method="size")
Theta.trans.weight = res.trans.weight$Theta.hat
Theta.trans.opt = res.trans.opt$Theta.hat
Theta.trans.size = res.trans.size$Theta.hat
Theta.single = res.trans.weight$Theta.hat0  # initial rough estimation via the target domain
Theta.single[abs(Theta.single)<0.0001] = 0

Evaluation.GGM(Theta.single, t.precision)
Evaluation.GGM(Theta.trans.weight, t.precision)
Evaluation.GGM(Theta.trans.opt, t.precision)
Evaluation.GGM(Theta.trans.size, t.precision)

# using informative auxiliary domains
res.trans.size.oracle = trans_precision(t.data, A.data.infor, cov.method="size")
Evaluation.GGM(res.trans.size.oracle$Theta.hat, t.precision)