trans.local.DAG {TransGraph}

Structural transfer learning of non-Gaussian DAG.

Description

Structural transfer learning of non-Gaussian DAG.

Usage

trans.local.DAG(t.data, A.data, hardth=0.5, hardth.A=hardth, criti.val=0.01,
                       precision.method="glasso", precision.method.A = "CLIME",
                       cov.method="opt", cn.lam2=seq(1,2.5,length.out=10),
                       precision.refit=TRUE, ini.prec=TRUE, cut.off=TRUE,
                       preselect.aux=0, sel.type="L2")

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.

hardth

The hard threshold of regression in the target domain.

hardth.A

The hard threshold of regression in the auxiliary domains.

criti.val

The critical value of independence test based on distance covariance, and the default setting is 0.01.

precision.method

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

precision.method.A

The initial method of estimating the auxiliary precision matrices, 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 ).

precision.refit

Whether to perform regression for re-fitting the coefficients in the precision matrix to improve estimation accuracy, after determining the non-zero elements of the precision matrix. The default is True.

ini.prec

Whether to store the initial estimation of the precision matrix, and the default is True.

cut.off

Whether to truncate the finally estimated coefficients in the structural equation models at threshold "hardth", 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.

Value

A result list including:

A

The information of layer.

B

The coefficients in structural equation models.

prec.res0

The results about estimating the prscision matrix via transfer learning.

prec.res0$Theta.hat

The estimated prscision matrix via transfer learning.

prec.res0$Theta.hat0

The estimated prscision matrix based on the target domain only.

Author(s)

Mingyang Ren [e-mail], Xin He, and Junhui Wang

References

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.DAG.RData")))
t.data = example.data.DAG$target.DAG.data$X
true_adjace = example.data.DAG$target.DAG.data$true_adjace
A.data = example.data.DAG$auxiliary.DAG.data$X.list.A

# transfer method
res.trans = trans.local.DAG(t.data, A.data)
# Topological Layer method-based single-task learning (JLMR, 2022)
res.single = TLLiNGAM(t.data)

Evaluation.DAG(res.trans$B, true_adjace)$Eval_result
Evaluation.DAG(res.single$B, true_adjace)$Eval_result