Fit a graph-regularized linear regression model using edge-based regularization.

Fit a graph-regularized linear regression model using edge-penalization. The coefficients are computed using graph-prior knowledge in the form of one/two affinity matrices. Graph-regularization is an extension to previously introduced regularization techniques, such as the LASSO. See the vignette for details on the objective function of the model: vignette("edgenet", package="netReg")

edgenet(
  X,
  Y,
  G.X = NULL,
  G.Y = NULL,
  lambda = 0,
  psigx = 0,
  psigy = 0,
  thresh = 1e-05,
  maxit = 1e+05,
  learning.rate = 0.01,
  family = gaussian
)

# S4 method for matrix,numeric
edgenet(
  X,
  Y,
  G.X = NULL,
  G.Y = NULL,
  lambda = 0,
  psigx = 0,
  psigy = 0,
  thresh = 1e-05,
  maxit = 1e+05,
  learning.rate = 0.01,
  family = gaussian
)

# S4 method for matrix,matrix
edgenet(
  X,
  Y,
  G.X = NULL,
  G.Y = NULL,
  lambda = 0,
  psigx = 0,
  psigy = 0,
  thresh = 1e-05,
  maxit = 1e+05,
  learning.rate = 0.01,
  family = gaussian
)

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 `X`, of dimensions (`p` x `p`) where `p` is the number of covariables
G.Y	non-negativ affinity matrix for `Y`, of dimensions (`q` x `q`) where `q` is the number of responses
lambda	`numerical` shrinkage parameter for LASSO.
psigx	`numerical` shrinkage parameter for graph-regularization of `G.X`
psigy	`numerical` shrinkage parameter for graph-regularization of `G.Y`
thresh	`numerical` threshold for optimizer
maxit	maximum number of iterations for optimizer (`integer`)
learning.rate	step size for Adam optimizer (`numerical`)
family	family of response, e.g. gaussian or binomial

Value

An object of class edgenet

beta

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

alpha

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

parameters

regularization parameters

lambda

regularization parameter lambda)

psigx

regularization parameter psigx

psigy

regularization parameter psigy

family

a description of the error distribution and link function to be used. Can be a netReg::family function or a character string naming a family function, e.g. gaussian or "gaussian".

call

the call that produced the object

References

Cheng, Wei and Zhang, Xiang and Guo, Zhishan and Shi, Yu and Wang, Wei (2014), Graph-regularized dual Lasso for robust eQTL mapping.
Bioinformatics

Examples

X <- matrix(rnorm(100 * 10), 100, 10)
b <- matrix(rnorm(100), 10)
G.X <- abs(rWishart(1, 10, diag(10))[, , 1])
G.Y <- abs(rWishart(1, 10, diag(10))[, , 1])
diag(G.X) <- diag(G.Y) <- 0

# estimate the parameters of a Gaussian model
Y <- X %*% b + matrix(rnorm(100 * 10), 100)
## dont use affinity matrices
fit <- edgenet(X = X, Y = Y, family = gaussian, maxit = 10)
## only provide one matrix
fit <- edgenet(X = X, Y = Y, G.X = G.X, psigx = 1, family = gaussian, maxit = 10)
## use two matrices
fit <- edgenet(X = X, Y = Y, G.X = G.X, G.Y, family = gaussian, maxit = 10)
## if Y is vectorial, we cannot use an affinity matrix for Y
fit <- edgenet(X = X, Y = Y[, 1], G.X = G.X, family = gaussian, maxit = 10)