Help for package fssemR

Title:

Fused Sparse Structural Equation Models to Jointly Infer Gene Regulatory Network

Version:

0.1.8

Author:

Xin Zhou, Xiaodong Cai

Maintainer:

Xin Zhou <xxz220@miami.edu>

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>).

License:

GPL (≥ 3)

Encoding:

UTF-8

Depends:

methods

Imports:

Rcpp, Matrix, stats, igraph, mvtnorm, qtl, stringr, glmnet, MASS, qpdf

Suggests:

plotly, knitr, rmarkdown, network, ggnetwork

LinkingTo:

Rcpp, RcppEigen

RoxygenNote:

7.1.2

URL:

https://github.com/Ivis4ml/fssemR

NeedsCompilation:

yes

Repository:

CRAN

VignetteBuilder:

knitr

Packaged:

2022-02-11 10:02:31 UTC; xxzhou

Date/Publication:

2022-02-11 13:00:02 UTC

FDR

Description

False discovery rate for network prediction

Usage

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.

TPR

Description

Power of detection for network prediction

Usage

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.

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
)

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
)

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
)

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)

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)

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

flinvB

Description

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

Usage

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)

Arguments

Bs

list of network matrices

Value

matrix whose entries are all 1

Solving Sparse Structural Equation Model

Description

Author(s)

Xin Zhou <xxz220@miami.edu>

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]])

implFSSEM

Description

implementor function of FSSEM solver

Usage

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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
)

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]])

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
)

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]])

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
)

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

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)

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)

obj.multiRegression

Description

obj.multiRegression

Usage

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
)

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]])

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
)

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]])

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
)

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)

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)

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)

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)

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
)

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
)

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
)

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

transx

Description

transx

Usage

transx(data)

Arguments

data

Collecting data structure generated by randomFSSEMdata function

Value

transformed list of eQTL matrices