Package 'fssemR' reference manual

Title:	Fused Sparse Structural Equation Models to Jointly Infer Gene Regulatory Network
Description:	An optimizer of Fused-Sparse Structural Equation Models, which is the state of the art jointly fused sparse maximum likelihood function for structural equation models proposed by Xin Zhou and Xiaodong Cai (2018 <doi:10.1101/466623>).
Authors:	Xin Zhou, Xiaodong Cai
Maintainer:	Xin Zhou <[email protected]>
License:	GPL (>=3)
Version:	0.1.8
Built:	2025-01-23 05:57:09 UTC
Source:	https://github.com/ivis4ml/fssemr

cv.multiFSSEMiPALM

Description

cv.multiFSSEMiPALM

Usage

cv.multiFSSEMiPALM(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  nfold = 5,
  p,
  q,
  wt = TRUE,
  plot = FALSE
)
cv.multiFSSEMiPALM(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  nfold = 5,
  p,
  q,
  wt = TRUE,
  plot = FALSE
)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`nlambda`	number of hyper-parameter of lasso term in CV
`nrho`	number of hyper-parameter of fused-lasso term in CV
`nfold`	CVfold number. Default 5/10
`p`	number of genes
`q`	number of eQTLs
`wt`	use adaptive lasso or not. Default TRUE.
`plot`	plot contour of cvmean or not. Default FALSE.

Value

list of cross-validation result

cv.multiFSSEMiPALM2

Description

cv.multiFSSEMiPALM2

Usage

cv.multiFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  nfold = 5,
  p,
  q,
  wt = TRUE,
  plot = FALSE
)
cv.multiFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  nfold = 5,
  p,
  q,
  wt = TRUE,
  plot = FALSE
)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`nlambda`	number of hyper-parameter of lasso term in CV
`nrho`	number of hyper-parameter of fused-lasso term in CV
`nfold`	CVfold number. Default 5/10
`p`	number of genes
`q`	number of eQTLs
`wt`	use adaptive lasso or not. Default TRUE.
`plot`	plot contour of cvmean or not. Default FALSE.

Value

list of cross-validation result

cv.multiNFSSEMiPALM2

Description

cv.multiNFSSEMiPALM2

Usage

cv.multiNFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  nfold = 5,
  p,
  q,
  wt = TRUE,
  plot = FALSE
)
cv.multiNFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  nfold = 5,
  p,
  q,
  wt = TRUE,
  plot = FALSE
)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`nlambda`	number of hyper-parameter of lasso term in CV
`nrho`	number of hyper-parameter of fused-lasso term in CV
`nfold`	CVfold number. Default 5/10
`p`	number of genes
`q`	number of eQTLs
`wt`	use adaptive lasso or not. Default TRUE.
`plot`	plot contour of cvmean or not. Default FALSE.

Value

list of cross-validation result for NFSSEM

cv.multiRegression

Description

cv.multiRegression

Usage

cv.multiRegression(Xs, Ys, Sk, ngamma = 20, nfold = 5, n, p, k)
cv.multiRegression(Xs, Ys, Sk, ngamma = 20, nfold = 5, n, p, k)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Sk`	eQTL index of genes
`ngamma`	number of hyper-parameter in CV
`nfold`	CVfold number. Default 5/10
`n`	number of observations
`p`	number of genes
`k`	number of eQTLs

Value

gamma_min optimal gamma to minimize cross-validation error

cwiseGradient4FSSEM

Description

function generator function

Usage

cwiseGradient4FSSEM(n, c, Y, R, Y2norm, sigma2)
cwiseGradient4FSSEM(n, c, Y, R, Y2norm, sigma2)

Arguments

`n`	number of observations
`c`	cofactor vector
`Y`	Matrix of gene expression
`R`	Residual matrix
`Y2norm`	Column of YtY
`sigma2`	noise variance

Value

function whose argument is column vector bi

FDR

Description

False discovery rate for network prediction

Usage

FDR(X, B, PREC = 0)
FDR(X, B, PREC = 0)

Arguments

`X`	list of predicted network matrices
`B`	list of true network matrices
`PREC`	precision threshold for FDR test. Default 0.

flinvB

Description

inversed difference of two B matrices. For adaptive fused lasso penalty

Usage

flinvB(Bs)
flinvB(Bs)

Arguments

`Bs`	list of network matrices

Value

inversed difference matrices

floneB

Description

if you do not want adaptive fused lasso penalty, floneB replace flinvB

Usage

floneB(Bs)
floneB(Bs)

Arguments

`Bs`	list of network matrices

Value

matrix whose entries are all 1

Solving Sparse Structural Equation Model

Description

Solving Sparse Structural Equation Model

Author(s)

Xin Zhou <[email protected]>

Examples

seed = as.numeric(Sys.time())
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
library(fssemR)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
                           N, Ng, Nk)
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
Xs    = data$Data$X
Ys    = data$Data$Y
Sk    = data$Data$Sk

## cross-validation
## cvfitc <- cv.multiFSSEMiPALM(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
##                              sigma2 = fit$sigma2, nlambda = 10, nrho = 10,
##                              nfold = 5, p = Ng, q = Nk, wt = TRUE)

fitm <- opt.multiFSSEMiPALM(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                           sigma2 = fit$sigma2, nlambda = 10, nrho = 10,
                           p = Ng, q = Nk, wt = TRUE)

fitc0 <- fitm$fit

(TPR(fitc0$Bs[[1]], data$Vars$B[[1]]) + TPR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
(FDR(fitc0$Bs[[1]], data$Vars$B[[1]]) + FDR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
TPR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
FDR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
seed = as.numeric(Sys.time())
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
library(fssemR)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
                           N, Ng, Nk)
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
Xs    = data$Data$X
Ys    = data$Data$Y
Sk    = data$Data$Sk

## cross-validation
## cvfitc <- cv.multiFSSEMiPALM(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
##                              sigma2 = fit$sigma2, nlambda = 10, nrho = 10,
##                              nfold = 5, p = Ng, q = Nk, wt = TRUE)

fitm <- opt.multiFSSEMiPALM(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                           sigma2 = fit$sigma2, nlambda = 10, nrho = 10,
                           p = Ng, q = Nk, wt = TRUE)

fitc0 <- fitm$fit

(TPR(fitc0$Bs[[1]], data$Vars$B[[1]]) + TPR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
(FDR(fitc0$Bs[[1]], data$Vars$B[[1]]) + FDR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
TPR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
FDR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])

implFSSEM

Description

implementor function of FSSEM solver

Usage

implFSSEM(data = NULL, method = c("CV", "BIC"))
implFSSEM(data = NULL, method = c("CV", "BIC"))

Arguments

`data`	Data archive of experiment measurements, includeing eQTL matrices, Gene expression matrices of different conditions, marker of eQTLs and data generation SEM model
`method`	Use cross-validation (CV) or bayesian-information-criterion(BIC)

Value

List of TPR and FDR

initLambdaiPALM

Description

initLambdaiPALM

Usage

initLambdaiPALM(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, p, k)
initLambdaiPALM(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, p, k)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`Wl`	weight matrices for adaptive lasso terms
`Wf`	weight matrix for adaptive fused lasso term
`p`	number of genes
`k`	number of eQTL

Value

lambda_max

initLambdaiPALM2

Description

initLambdaiPALM2

Usage

initLambdaiPALM2(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, p, k)
initLambdaiPALM2(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, p, k)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`Wl`	weight matrices for adaptive lasso terms
`Wf`	weight matrix for adaptive fused lasso term
`p`	number of genes
`k`	number of eQTL

Value

lambda_max

initLambdaiPALM3

Description

initLambdaiPALM3

Usage

initLambdaiPALM3(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, p, k)
initLambdaiPALM3(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, p, k)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`Wl`	weight matrices for adaptive lasso terms
`Wf`	weight matrix for adaptive fused lasso term
`p`	number of genes
`k`	number of eQTL

Value

lambda_max

initRhoiPALM

Description

initRhoiPALM

Usage

initRhoiPALM(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, lambda, n, p)
initRhoiPALM(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, lambda, n, p)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`Wl`	weight matrices for adaptive lasso terms
`Wf`	weight matrix for adaptive fused lasso term
`lambda`	lambda w.r.t. rho_max
`n`	number of observations
`p`	number of genes

Value

rho_max

initRhoiPALM2

Description

initRhoiPALM2

Usage

initRhoiPALM2(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, lambda, n, p)
initRhoiPALM2(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, lambda, n, p)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`Wl`	weight matrices for adaptive lasso terms
`Wf`	weight matrix for adaptive fused lasso term
`lambda`	lambda w.r.t. rho_max
`n`	number of observations
`p`	number of genes

Value

rho_max

initRhoiPALM3

Description

initRhoiPALM3

Usage

initRhoiPALM3(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, lambda, n, p)
initRhoiPALM3(Xs, Ys, Bs, Fs, Sk, sigma2, Wl, Wf, lambda, n, p)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`Wl`	weight matrices for adaptive lasso terms
`Wf`	weight matrix for adaptive perturbation group lasso term
`lambda`	lambda w.r.t. rho_max
`n`	number of observations
`p`	number of genes

Value

rho_max

inverseB

Description

inverse matrices of B network for adaptive FSSEM

Usage

inverseB(Bs)
inverseB(Bs)

Arguments

`Bs`	list of network matrices

Value

list of inversed B matrices

invoneB

Description

if you do not want to get inversed B matrces, invoneB gives you a matrix with constant 1 instead in FSSEM

Usage

invoneB(Bs)
invoneB(Bs)

Arguments

`Bs`	list of network matrices

Value

list of invone B matrices

logLikFSSEM

Description

logLikFSSEM

Usage

logLikFSSEM(Bs, Wl, Wf, lambda, rho, sigma2, Dets, n, p)
logLikFSSEM(Bs, Wl, Wf, lambda, rho, sigma2, Dets, n, p)

Arguments

`Bs`	Network matrices
`Wl`	Weights for lasso term
`Wf`	Weights for fused term
`lambda`	Hyperparameter of lasso term
`rho`	Hyperparameter of fused lasso term
`sigma2`	noise variance
`Dets`	determinants of I-B matrices
`n`	number of observations
`p`	number of genes

Value

objective value of FSSEM with specified hyper-paramters

logLikNFSSEM

Description

logLikNFSSEM

Usage

logLikNFSSEM(Bs, Wl, Wf, lambda, rho, sigma2, Dets, n, p)
logLikNFSSEM(Bs, Wl, Wf, lambda, rho, sigma2, Dets, n, p)

Arguments

`Bs`	Network matrices
`Wl`	Weights for lasso term
`Wf`	Weights for group perturb lasso term
`lambda`	Hyperparameter of lasso term
`rho`	Hyperparameter of group fused lasso term
`sigma2`	noise variance
`Dets`	determinants of I-B matrices
`n`	number of observations
`p`	number of genes

Value

objective value of NFSSEM with specified hyper-paramters

multiFSSEMiPALM

Description

Implementing FSSELM algorithm for network inference. If Xs is identify for different conditions, multiFSSEMiPALM will be use, otherwise, please use multiFSSEMiPALM2 for general cases

Usage

multiFSSEMiPALM(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  lambda,
  rho,
  Wl,
  Wf,
  p,
  maxit = 100,
  inert = inert_opt("linear"),
  threshold = 1e-06,
  verbose = TRUE,
  sparse = TRUE,
  trans = FALSE,
  B2norm = NULL,
  strict = FALSE
)
multiFSSEMiPALM(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  lambda,
  rho,
  Wl,
  Wf,
  p,
  maxit = 100,
  inert = inert_opt("linear"),
  threshold = 1e-06,
  verbose = TRUE,
  sparse = TRUE,
  trans = FALSE,
  B2norm = NULL,
  strict = FALSE
)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance from ridge regression
`lambda`	Hyperparameter of lasso term in FSSEM
`rho`	Hyperparameter of fused-lasso term in FSSEM
`Wl`	weight matrices for adaptive lasso terms
`Wf`	weight matrix for adaptive fused lasso term
`p`	number of genes
`maxit`	maximum iteration number. Default 100
`inert`	inertial function for iPALM. Default as k-1/k+2
`threshold`	convergence threshold. Default 1e-6
`verbose`	Default TRUE
`sparse`	Sparse Matrix or not
`trans`	Fs matrix is transposed to k x p or not. If Fs from ridge regression, trans = TRUE, else, trans = FALSE
`B2norm`	B2norm matrices generated from ridge regression. Default NULL.
`strict`	Converge strictly or not. Default False

Value

fit List of FSSEM model

Bs: coefficient matrices of gene regulatory networks
Fs: coefficient matrices of eQTL-gene effect
mu: Bias vector
sigma2: estimate of covariance in SEM

Examples

seed = 1234
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
library(fssemR)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
## If we assume that different condition has different genetics perturbations (eQTLs)
## gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
##                            N, Ng, Nk)
gamma = 0.6784248     ## optimal gamma computed by cv.multiRegression
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
Xs    = data$Data$X
Ys    = data$Data$Y
Sk    = data$Data$Sk


cvfitc <- cv.multiFSSEMiPALM(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                             sigma2 = fit$sigma2, nlambda = 5, nrho = 5,
                             nfold = 5, p = Ng, q = Nk, wt = TRUE)

fitc0 <- multiFSSEMiPALM(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                         sigma2 = fit$sigma2, lambda = cvfitc$lambda, rho = cvfitc$rho,
                         Wl = inverseB(fit$Bs), Wf = flinvB(fit$Bs),
                         p = Ng, maxit = 100, threshold = 1e-5, sparse = TRUE, 
                         verbose = TRUE, trans = TRUE, strict = TRUE)


(TPR(fitc0$Bs[[1]], data$Vars$B[[1]]) + TPR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
(FDR(fitc0$Bs[[1]], data$Vars$B[[1]]) + FDR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
TPR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
FDR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
seed = 1234
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
library(fssemR)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
## If we assume that different condition has different genetics perturbations (eQTLs)
## gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
##                            N, Ng, Nk)
gamma = 0.6784248     ## optimal gamma computed by cv.multiRegression
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
Xs    = data$Data$X
Ys    = data$Data$Y
Sk    = data$Data$Sk


cvfitc <- cv.multiFSSEMiPALM(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                             sigma2 = fit$sigma2, nlambda = 5, nrho = 5,
                             nfold = 5, p = Ng, q = Nk, wt = TRUE)

fitc0 <- multiFSSEMiPALM(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                         sigma2 = fit$sigma2, lambda = cvfitc$lambda, rho = cvfitc$rho,
                         Wl = inverseB(fit$Bs), Wf = flinvB(fit$Bs),
                         p = Ng, maxit = 100, threshold = 1e-5, sparse = TRUE, 
                         verbose = TRUE, trans = TRUE, strict = TRUE)


(TPR(fitc0$Bs[[1]], data$Vars$B[[1]]) + TPR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
(FDR(fitc0$Bs[[1]], data$Vars$B[[1]]) + FDR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
TPR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
FDR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])

multiFSSEMiPALM2

Description

Implementing FSSELM algorithm for network inference. If Xs is identify for different conditions, multiFSSEMiPALM will be use, otherwise, please use multiFSSEMiPALM2 for general cases

Usage

multiFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  lambda,
  rho,
  Wl,
  Wf,
  p,
  maxit = 100,
  inert = inert_opt("linear"),
  threshold = 1e-06,
  verbose = TRUE,
  sparse = TRUE,
  trans = FALSE,
  B2norm = NULL,
  strict = FALSE
)
multiFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  lambda,
  rho,
  Wl,
  Wf,
  p,
  maxit = 100,
  inert = inert_opt("linear"),
  threshold = 1e-06,
  verbose = TRUE,
  sparse = TRUE,
  trans = FALSE,
  B2norm = NULL,
  strict = FALSE
)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance from ridge regression
`lambda`	Hyperparameter of lasso term in FSSEM
`rho`	Hyperparameter of fused-lasso term in FSSEM
`Wl`	weight matrices for adaptive lasso terms
`Wf`	weight matrix for adaptive fused lasso term
`p`	number of genes
`maxit`	maximum iteration number. Default 100
`inert`	inertial function for iPALM. Default as k-1/k+2
`threshold`	convergence threshold. Default 1e-6
`verbose`	Default TRUE
`sparse`	Sparse Matrix or not
`trans`	Fs matrix is transposed to k x p or not. If Fs from ridge regression, trans = TRUE, else, trans = FALSE
`B2norm`	B2norm matrices generated from ridge regression. Default NULL.
`strict`	Converge strictly or not. Default False

Value

fit List of FSSEM model

Bs: coefficient matrices of gene regulatory networks
Fs: coefficient matrices of eQTL-gene effect
mu: Bias vector
sigma2: estimate of covariance in SEM

Examples

seed = 1234
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
library(fssemR)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
## If we assume that different condition has different genetics perturbations (eQTLs)
data$Data$X = list(data$Data$X, data$Data$X)
## gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
##                            N, Ng, Nk)
gamma = 0.6784248     ## optimal gamma computed by cv.multiRegression
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
Xs    = data$Data$X
Ys    = data$Data$Y
Sk    = data$Data$Sk


cvfitc <- cv.multiFSSEMiPALM2(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                             sigma2 = fit$sigma2, nlambda = 5, nrho = 5,
                             nfold = 5, p = Ng, q = Nk, wt = TRUE)

fitc0 <- multiFSSEMiPALM2(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                          sigma2 = fit$sigma2, lambda = cvfitc$lambda, rho = cvfitc$rho,
                          Wl = inverseB(fit$Bs), Wf = flinvB(fit$Bs),
                          p = Ng, maxit = 100, threshold = 1e-5, sparse = TRUE, 
                          verbose = TRUE, trans = TRUE, strict = TRUE)


(TPR(fitc0$Bs[[1]], data$Vars$B[[1]]) + TPR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
(FDR(fitc0$Bs[[1]], data$Vars$B[[1]]) + FDR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
TPR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
FDR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
seed = 1234
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
library(fssemR)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
## If we assume that different condition has different genetics perturbations (eQTLs)
data$Data$X = list(data$Data$X, data$Data$X)
## gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
##                            N, Ng, Nk)
gamma = 0.6784248     ## optimal gamma computed by cv.multiRegression
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
Xs    = data$Data$X
Ys    = data$Data$Y
Sk    = data$Data$Sk


cvfitc <- cv.multiFSSEMiPALM2(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                             sigma2 = fit$sigma2, nlambda = 5, nrho = 5,
                             nfold = 5, p = Ng, q = Nk, wt = TRUE)

fitc0 <- multiFSSEMiPALM2(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                          sigma2 = fit$sigma2, lambda = cvfitc$lambda, rho = cvfitc$rho,
                          Wl = inverseB(fit$Bs), Wf = flinvB(fit$Bs),
                          p = Ng, maxit = 100, threshold = 1e-5, sparse = TRUE, 
                          verbose = TRUE, trans = TRUE, strict = TRUE)


(TPR(fitc0$Bs[[1]], data$Vars$B[[1]]) + TPR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
(FDR(fitc0$Bs[[1]], data$Vars$B[[1]]) + FDR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
TPR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
FDR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])

multiNFSSEMiPALM2

Description

Implementing NFSSEM algorithm for network inference. If Xs is identify for different conditions, multiNFSSEMiPALM will be use, otherwise, please use multiNFSSEMiPALM2 for general cases

Usage

multiNFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  lambda,
  rho,
  Wl,
  Wf,
  p,
  maxit = 100,
  inert = inert_opt("linear"),
  threshold = 1e-06,
  verbose = TRUE,
  sparse = TRUE,
  trans = FALSE,
  B2norm = NULL,
  strict = FALSE
)
multiNFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  lambda,
  rho,
  Wl,
  Wf,
  p,
  maxit = 100,
  inert = inert_opt("linear"),
  threshold = 1e-06,
  verbose = TRUE,
  sparse = TRUE,
  trans = FALSE,
  B2norm = NULL,
  strict = FALSE
)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance from ridge regression
`lambda`	Hyperparameter of lasso term in NFSSEM
`rho`	Hyperparameter of fused-lasso term in NFSSEM
`Wl`	weight matrices for adaptive lasso terms
`Wf`	weight matrix for columnwise l2 norm adaptive group lasso
`p`	number of genes
`maxit`	maximum iteration number. Default 100
`inert`	inertial function for iPALM. Default as k-1/k+2
`threshold`	convergence threshold. Default 1e-6
`verbose`	Default TRUE
`sparse`	Sparse Matrix or not
`trans`	Fs matrix is transposed to k x p or not. If Fs from ridge regression, trans = TRUE, else, trans = FALSE
`B2norm`	B2norm matrices generated from ridge regression. Default NULL.
`strict`	Converge strictly or not. Default False
`zstart`	TRUE for zero matrix start

Value

fit List of NFSSEM model

Bs: coefficient matrices of gene regulatory networks
Fs: coefficient matrices of eQTL-gene effect
mu: Bias vector
sigma2: estimate of covariance in SEM

multiRegression

Description

Ridge regression on multiple conditions, initialization of FSSEM algorithm

Usage

multiRegression(Xs, Ys, Sk, gamma, n, p, k, trans = FALSE)
multiRegression(Xs, Ys, Sk, gamma, n, p, k, trans = FALSE)

Arguments

`Xs`	eQTL matrices. eQTL matrix can be matrix/list of multiple conditions
`Ys`	Gene expression matrices
`Sk`	eQTL index of genes
`gamma`	Hyperparameter for ridge regression
`n`	number of observations
`p`	number of genes
`k`	number of eQTLs
`trans`	if rows for sample, trans = TRUE, otherwise, trans = FALSE. Default FALSE

Value

fit List of SEM model

Bs: coefficient matrices of gene regulatory networks
fs: eQTL's coefficients w.r.t each gene
Fs: coefficient matrices of eQTL-gene effect
mu: Bias vector
sigma2: estimate of covariance in SEM

Examples

seed = 1234
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
## If we assume that different condition has different genetics perturbations (eQTLs)
## data$Data$X = list(data$Data$X, data$Data$X)
gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
                           N, Ng, Nk)
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
seed = 1234
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
## If we assume that different condition has different genetics perturbations (eQTLs)
## data$Data$X = list(data$Data$X, data$Data$X)
gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
                           N, Ng, Nk)
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)

obj.multiRegression

Description

obj.multiRegression

Usage

obj.multiRegression(Xs, Ys, fit, trans = F)
obj.multiRegression(Xs, Ys, fit, trans = F)

Arguments

`Xs`	eQTL matrices
`Ys`	gene expression matrices
`fit`	regression fit result object
`trans`	if rows for sample, trans = TRUE, otherwise, trans = FALSE. Default FALSE

Value

error squared norm of ||(I-B)Y - FX||_2^2

opt.multiFSSEMiPALM

Description

optimize multiFSSEMiPALM's parameters by minimize BIC, when feature size is large (> 300), BIC methods will be much faster than Cross-validation

Usage

opt.multiFSSEMiPALM(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  p,
  q,
  wt = TRUE
)
opt.multiFSSEMiPALM(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  p,
  q,
  wt = TRUE
)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`nlambda`	number of hyper-parameter of lasso term in CV
`nrho`	number of hyper-parameter of fused-lasso term in CV
`p`	number of genes
`q`	number of eQTLs
`wt`	use adaptive lasso or not. Default TRUE.

Value

list of model selection result

Examples

seed = 1234
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
library(fssemR)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
## If we assume that different condition has different genetics perturbations (eQTLs)
## data$Data$X = list(data$Data$X, data$Data$X)
## gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
##                            N, Ng, Nk)
gamma = 0.6784248     ## optimal gamma computed by cv.multiRegression
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
Xs    = data$Data$X
Ys    = data$Data$Y
Sk    = data$Data$Sk

fitm <- opt.multiFSSEMiPALM(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                           sigma2 = fit$sigma2, nlambda = 10, nrho = 10,
                           p = Ng, q = Nk, wt = TRUE)

fitc0 <- fitm$fit

(TPR(fitc0$Bs[[1]], data$Vars$B[[1]]) + TPR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
(FDR(fitc0$Bs[[1]], data$Vars$B[[1]]) + FDR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
TPR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
FDR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
seed = 1234
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
library(fssemR)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
## If we assume that different condition has different genetics perturbations (eQTLs)
## data$Data$X = list(data$Data$X, data$Data$X)
## gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
##                            N, Ng, Nk)
gamma = 0.6784248     ## optimal gamma computed by cv.multiRegression
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
Xs    = data$Data$X
Ys    = data$Data$Y
Sk    = data$Data$Sk

fitm <- opt.multiFSSEMiPALM(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                           sigma2 = fit$sigma2, nlambda = 10, nrho = 10,
                           p = Ng, q = Nk, wt = TRUE)

fitc0 <- fitm$fit

(TPR(fitc0$Bs[[1]], data$Vars$B[[1]]) + TPR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
(FDR(fitc0$Bs[[1]], data$Vars$B[[1]]) + FDR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
TPR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
FDR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])

opt.multiFSSEMiPALM2

Description

optimize multiFSSEMiPALM's parameters by minimize BIC, when feature size is large (> 300), BIC methods will be much faster than Cross-validation

Usage

opt.multiFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  p,
  q,
  wt = TRUE
)
opt.multiFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  p,
  q,
  wt = TRUE
)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`nlambda`	number of hyper-parameter of lasso term in CV
`nrho`	number of hyper-parameter of fused-lasso term in CV
`p`	number of genes
`q`	number of eQTLs
`wt`	use adaptive lasso or not. Default TRUE.

Value

list of model selection result

Examples

seed = 1234
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
library(fssemR)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
## If we assume that different condition has different genetics perturbations (eQTLs)
data$Data$X = list(data$Data$X, data$Data$X)
## gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
##                            N, Ng, Nk)
gamma = 0.6784248     ## optimal gamma computed by cv.multiRegression
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
Xs    = data$Data$X
Ys    = data$Data$Y
Sk    = data$Data$Sk

fitm <- opt.multiFSSEMiPALM2(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                           sigma2 = fit$sigma2, nlambda = 10, nrho = 10,
                           p = Ng, q = Nk, wt = TRUE)

fitc0 <- fitm$fit

(TPR(fitc0$Bs[[1]], data$Vars$B[[1]]) + TPR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
(FDR(fitc0$Bs[[1]], data$Vars$B[[1]]) + FDR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
TPR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
FDR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
seed = 1234
N = 100                                           # sample size
Ng = 5                                            # gene number
Nk = 5 * 3                                        # eQTL number
Ns = 1                                            # sparse ratio
sigma2 = 0.01                                     # sigma2
set.seed(seed)
library(fssemR)
data = randomFSSEMdata(n = N, p = Ng, k = Nk, sparse = Ns, df = 0.3, sigma2 = sigma2,
                       u = 5, type = "DG", nhub = 1, dag = TRUE)
## If we assume that different condition has different genetics perturbations (eQTLs)
data$Data$X = list(data$Data$X, data$Data$X)
## gamma = cv.multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, ngamma = 20, nfold = 5,
##                            N, Ng, Nk)
gamma = 0.6784248     ## optimal gamma computed by cv.multiRegression
fit   = multiRegression(data$Data$X, data$Data$Y, data$Data$Sk, gamma, N, Ng, Nk,
                      trans = FALSE)
Xs    = data$Data$X
Ys    = data$Data$Y
Sk    = data$Data$Sk

fitm <- opt.multiFSSEMiPALM2(Xs = Xs, Ys = Ys, Bs = fit$Bs, Fs = fit$Fs, Sk = Sk,
                           sigma2 = fit$sigma2, nlambda = 10, nrho = 10,
                           p = Ng, q = Nk, wt = TRUE)

fitc0 <- fitm$fit

(TPR(fitc0$Bs[[1]], data$Vars$B[[1]]) + TPR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
(FDR(fitc0$Bs[[1]], data$Vars$B[[1]]) + FDR(fitc0$Bs[[2]], data$Vars$B[[2]])) / 2
TPR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])
FDR(fitc0$Bs[[1]] - fitc0$Bs[[2]], data$Vars$B[[1]] - data$Vars$B[[2]])

opt.multiNFSSEMiPALM2

Description

optimize multiNFSSEMiPALM's parameters by minimize BIC, when feature size is large (> 300), BIC methods will be much faster than Cross-validation

Usage

opt.multiNFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  p,
  q,
  wt = TRUE
)
opt.multiNFSSEMiPALM2(
  Xs,
  Ys,
  Bs,
  Fs,
  Sk,
  sigma2,
  nlambda = 20,
  nrho = 20,
  p,
  q,
  wt = TRUE
)

Arguments

`Xs`	eQTL matrices
`Ys`	Gene expression matrices
`Bs`	initialized GRN-matrices
`Fs`	initialized eQTL effect matrices
`Sk`	eQTL index of genes
`sigma2`	initialized noise variance
`nlambda`	number of hyper-parameter of lasso term in CV
`nrho`	number of hyper-parameter of fused-lasso term in CV
`p`	number of genes
`q`	number of eQTLs
`wt`	use adaptive lasso or not. Default TRUE.

Value

list of model selection result

pninvB

Description

inversed column l2 norm for perturbed group lasso penalty

Usage

pninvB(Bs)
pninvB(Bs)

Arguments

`Bs`	list of network matrices

Value

inversed l2 norm of B2 - B1

pnoneB

Description

if you do not want adaptive group lasso penalty, pnoneB replace pninvB

Usage

pnoneB(Bs)
pnoneB(Bs)

Arguments

`Bs`	list of network matrices

Value

inversed l2 norm of B2 - B1 with all entries is 1

proc.centerFSSEM

Description

proc.centerFSSEM

Usage

proc.centerFSSEM(Xs, Ys)
proc.centerFSSEM(Xs, Ys)

Arguments

`Xs`	eQTL matrices
`Ys`	list of gene expression matrices

Value

centered Xs and Ys and mean vectors

proc.centerFSSEM2

Description

proc.centerFSSEM2

Usage

proc.centerFSSEM2(Xs, Ys)
proc.centerFSSEM2(Xs, Ys)

Arguments

`Xs`	list of eQTL matrices
`Ys`	list of gene expression matrices

Value

centered Xs and Ys and mean vectors

randomFSSEMdata

Description

randomFSSEMdata

Usage

randomFSSEMdata(
  n,
  p,
  k,
  sparse = 0.1,
  df = 0.2,
  sigma2 = 0.01,
  u = 5,
  type = c("DG", "ER"),
  dag = TRUE,
  coef = c(0.2, 0.4),
  nhub = 2
)
randomFSSEMdata(
  n,
  p,
  k,
  sparse = 0.1,
  df = 0.2,
  sigma2 = 0.01,
  u = 5,
  type = c("DG", "ER"),
  dag = TRUE,
  coef = c(0.2, 0.4),
  nhub = 2
)

Arguments

`n`	number of observations
`p`	number of genes
`k`	number of eQTLs
`sparse`	ratio of edges / gene_number
`df`	ratio of differential edges among two network
`sigma2`	noise variance of error
`u`	variance of bias in SEM model.
`type`	type of generated network, can be selected as DG, ER, Scale-free network
`dag`	network is directed-acyclic or not. Default TRUE
`coef`	Range of absolute value of coefficients in simulated network matrices. Default (0.2, 0.4), or (0.5, 1)
`nhub`	If you select to generate ER network, nhub is the number of pre-defined hub node number. Default 2

Value

list of generated data

Data: List of observed, Xs, Ys, Sk
Vars: List of model, Bs, Fs, mu, n, p, k

randomFSSEMdata2

Description

randomFSSEMdata2

Usage

randomFSSEMdata2(
  n,
  p,
  k,
  sparse = 0.1,
  df = 0.2,
  sigma2 = 0.01,
  u = 5,
  type = c("DG", "ER"),
  dag = TRUE,
  coef = c(0.2, 0.4),
  nhub = 2
)
randomFSSEMdata2(
  n,
  p,
  k,
  sparse = 0.1,
  df = 0.2,
  sigma2 = 0.01,
  u = 5,
  type = c("DG", "ER"),
  dag = TRUE,
  coef = c(0.2, 0.4),
  nhub = 2
)

Arguments

`n`	number of observations. Vector for unbalance observations
`p`	number of genes
`k`	number of eQTLs
`sparse`	ratio of edges / gene_number
`df`	ratio of differential edges among two network
`sigma2`	noise variance of error
`u`	variance of bias in SEM model.
`type`	type of generated network, can be selected as DG, ER, Scale-free network
`dag`	network is directed-acyclic or not. Default TRUE
`coef`	Range of absolute value of coefficients in simulated network matrices. Default (0.2, 0.4), or (0.5, 1)
`nhub`	If you select to generate ER network, nhub is the number of pre-defined hub node number. Default 2

Value

list of generated data

Data: List of observed, Xs, Ys, Sk
Vars: List of model, Bs, Fs, mu, n, p, k

randomFSSEMdata4Cor

Description

randomFSSEMdata4Cor

Usage

randomFSSEMdata4Cor(
  n,
  p,
  k,
  sparse = 0.1,
  df = 0.2,
  sigma2 = 0.01,
  u = 5,
  type = c("DG", "ER"),
  dag = TRUE,
  coef = c(0.2, 0.4),
  nhub = 2,
  r = 0.5
)
randomFSSEMdata4Cor(
  n,
  p,
  k,
  sparse = 0.1,
  df = 0.2,
  sigma2 = 0.01,
  u = 5,
  type = c("DG", "ER"),
  dag = TRUE,
  coef = c(0.2, 0.4),
  nhub = 2,
  r = 0.5
)

Arguments

`n`	number of observations. Vector for unbalance observations
`p`	number of genes
`k`	number of eQTLs
`sparse`	ratio of edges / gene_number
`df`	ratio of differential edges among two network
`sigma2`	noise variance of error
`u`	variance of bias in SEM model.
`type`	type of generated network, can be selected as DG, ER, Scale-free network
`dag`	network is directed-acyclic or not. Default TRUE
`coef`	Range of absolute value of coefficients in simulated network matrices. Default (0.2, 0.4), or (0.5, 1)
`nhub`	If you select to generate ER network, nhub is the number of pre-defined hub node number. Default 2
`r`	correlation between different observations

Value

list of generated data

Data: List of observed, Xs, Ys, Sk
Vars: List of model, Bs, Fs, mu, n, p, k

TPR

Description

Power of detection for network prediction

Usage

TPR(X, B, PREC = 0)
TPR(X, B, PREC = 0)

Arguments

`X`	list of predicted network matrices
`B`	list of true network matrices
`PREC`	precision threshold for FDR test. Default 0.

transx

Description

transx

Usage

transx(data)
transx(data)

Arguments

data

Collecting data structure generated by randomFSSEMdata function

Value

transformed list of eQTL matrices

Package 'fssemR'

Help Index

cv.multiFSSEMiPALM

Description

Usage

Arguments

Value

cv.multiFSSEMiPALM2

Description

Usage

Arguments

Value

cv.multiNFSSEMiPALM2

Description

Usage

Arguments

Value

cv.multiRegression

Description

Usage

Arguments

Value

cwiseGradient4FSSEM

Description

Usage

Arguments

Value

FDR

Description

Usage

Arguments

flinvB

Description

Usage

Arguments

Value

floneB

Description

Usage

Arguments

Value

Solving Sparse Structural Equation Model

Description

Author(s)

Examples

implFSSEM

Description

Usage

Arguments

Value

initLambdaiPALM

Description

Usage

Arguments

Value

initLambdaiPALM2

Description

Usage

Arguments

Value

initLambdaiPALM3

Description

Usage

Arguments

Value

initRhoiPALM

Description

Usage

Arguments

Value

initRhoiPALM2

Description

Usage

Arguments

Value

initRhoiPALM3

Description

Usage

Arguments

Value