cv.edgenet {netReg}R Documentation

Find the optimal shrinkage parameters for edgenet

Description

Finds the optimal shrinkage parameters using cross-validation for edgenet. We use the BOBYQA algorithm to find the optimial regularization parameters and coordinate descent in order to minimize the objective function of the linear model.

Usage

cv.edgenet(X, Y, G.X = NULL, G.Y = NULL, lambda = NULL, psigx = NULL,
  psigy = NULL, thresh = 1e-05, maxit = 1e+05, family = c("gaussian"),
  optim.epsilon = 0.001, optim.maxit = 10000, nfolds = 10)

Arguments

X

input matrix, of dimension (n x p) where n is the number of observations and p is the number of covariables. Each row is an observation vector.

Y

output matrix, of dimension (n x q) where n is the number of observations and q is the number of response variables Each row is an observation vector.

G.X

non-negativ affinity matrix for n, of dimensions (p x p) where p is the number of covariables X. Providing a graph G.X will optimize the regularization parameter psi.gx. If this is not desired just set G.X to NULL.

G.Y

non-negativ affinity matrix for n, of dimensions (q x q) where q is the number of responses Y. Providing a graph G.Y will optimize the regularization parameter psi.gy. If this is not desired just set G.Y to NULL.

lambda

numerical shrinkage parameter for LASSO. Per default this parameter is set to NULL which means that lambda is going to be estimated using cross-validation. If any numerical value for lambda is set, estimation of the optimal parameter will not be conducted.

psigx

numerical shrinkage parameter for graph-regularization of G.X. Per default this parameter is set to NULL which means that psigx is going to be estimated in the cross-validation. If any numerical value for psigx is set, estimation of the optimal parameter will not be conducted.

psigy

numerical shrinkage parameter for graph-regularization of G.Y. Per default this parameter is set to NULL which means that psigy is going to be estimated in the cross-validation. If any numerical value for psigy is set, estimation of the optimal parameter will not be conducted.

thresh

numerical threshold for coordinate descent

maxit

maximum number of iterations for the coordinate descent (integer)

family

family of response, e.g. gaussian

optim.epsilon

numerical threshold criterion for the optimization to stop. Usually 1e-3 is a good choice.

optim.maxit

the maximum number of iterations for the optimization (integer). Usually 1e4 is a good choice.

nfolds

the number of folds to be used - default is 10 (minimum 3, maximum nrow(X)).

Value

An object of class cv.edgenet

call

the call that produced the object

lambda

the estimated (p x q)-dimensional coefficient matrix B.hat

psigx

the estimated (q x 1)-dimensional vector of intercepts

psigy

the estimated (q x 1)-dimensional vector of intercepts

References

Dirmeier, Simon and Fuchs, Christiane and Mueller, Nikola S and Theis, Fabian J (2018), netReg: Network-regularized linear models for biological association studies.
Friedman J., Hastie T., Hoefling H. and Tibshirani R. (2007), Pathwise coordinate optimization.
The Annals of Applied Statistics

Friedman J., Hastie T. and Tibshirani R. (2010), Regularization Paths for Generalized Linear Models via Coordinate Descent.
Journal of Statistical Software

Fu W. J. (1998), Penalized Regression: The Bridge Versus the Lasso.
Journal of Computational and Graphical Statistics

Cheng W. and Wang W. (2014), Graph-regularized dual Lasso for robust eQTL mapping.
Bioinformatics

Powell M.J.D. (2009), The BOBYQA algorithm for bound constrained optimization without derivatives.
http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf

Examples

X <- matrix(rnorm(100*10), 100, 10)
b <- rnorm(10)
G.X <- matrix(rpois(10*10,1),10)
G.X <- t(G.X) + G.X
diag(G.X) <- 0

# fit a Gaussian model
Y <- X%*%b + rnorm(100)
cv.edge <- cv.edgenet(X=X, Y=Y, G.X=G.X, family="gaussian")

[Package netReg version 1.6.0 Index]