Find the optimal shrinkage parameters for edgenet

Finds the optimal regulariztion parameters using cross-validation for edgenet. We use the BOBYQA algorithm to find the optimial regularization parameters in a cross-validation framework.

cv.edgenet(
  X,
  Y,
  G.X = NULL,
  G.Y = NULL,
  lambda = NA_real_,
  psigx = NA_real_,
  psigy = NA_real_,
  thresh = 1e-05,
  maxit = 1e+05,
  learning.rate = 0.01,
  family = gaussian,
  optim.maxit = 100,
  optim.thresh = 0.01,
  nfolds = 10
)

# S4 method for matrix,numeric
cv.edgenet(
  X,
  Y,
  G.X = NULL,
  G.Y = NULL,
  lambda = NA_real_,
  psigx = NA_real_,
  psigy = NA_real_,
  thresh = 1e-05,
  maxit = 1e+05,
  learning.rate = 0.01,
  family = gaussian,
  optim.maxit = 100,
  optim.thresh = 0.01,
  nfolds = 10
)

# S4 method for matrix,matrix
cv.edgenet(
  X,
  Y,
  G.X = NULL,
  G.Y = NULL,
  lambda = NA_real_,
  psigx = NA_real_,
  psigy = NA_real_,
  thresh = 1e-05,
  maxit = 1e+05,
  learning.rate = 0.01,
  family = gaussian,
  optim.maxit = 100,
  optim.thresh = 0.01,
  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 `X`, of dimensions (`p` x `p`) where `p` is the number of covariables. 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 `Y`, 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 `NA_real_` 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 `NA_real_` 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 `NA_real_` 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 the optimizer
maxit	maximum number of iterations for the optimizer (`integer`)
learning.rate	step size for Adam optimizer (`numerical`)
family	family of response, e.g. gaussian or binomial
optim.maxit	the maximum number of iterations for the optimization (`integer`). Usually 1e4 is a good choice.
optim.thresh	`numerical` threshold criterion for the optimization to stop. Usually 1e-3 is a good choice.
nfolds	the number of folds to be used - default is 10

Value

An object of class cv.edgenet

parameters

the estimated, optimal regularization parameters

lambda

optimal estimated value for regularization parameter lambda (or, if provided as argument, the value of the parameter)

psigx

optimal estimated value for regularization parameter psigx (or, if provided as argument, the value of the parameter)

psigy

optimal estimated value for regularization parameter psigy (or, if provided as argument, the value of the parameter)

estimated.parameters

names of parameters that were estimated

family

family used for estimated

fit

an edgenet object fitted with the optimal, estimated paramters

call

the call that produced the object

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 and estimate lambda
fit <- cv.edgenet(
  X = X, Y = Y, family = gaussian,
  maxit = 1, optim.maxit = 1
)
## only provide one matrix and estimate lambda
fit <- cv.edgenet(
  X = X, Y = Y, G.X = G.X, psigx = 1, family = gaussian,
  maxit = 1, optim.maxit = 1
)
## estimate only lambda with two matrices
fit <- cv.edgenet(
  X = X, Y = Y, G.X = G.X, G.Y, psigx = 1, psigy = 1,
  family = gaussian, maxit = 1, optim.maxit = 1
)
## estimate only psigx
fit <- cv.edgenet(
  X = X, Y = Y, G.X = G.X, G.Y, lambda = 1, psigy = 1,
  family = gaussian, maxit = 1, optim.maxit = 1
)
## estimate all parameters
fit <- cv.edgenet(
  X = X, Y = Y, G.X = G.X, G.Y,
  family = gaussian, maxit = 1, optim.maxit = 1
)
## if Y is vectorial, we cannot use an affinity matrix for Y
fit <- cv.edgenet(
  X = X, Y = Y[, 1], G.X = G.X,
  family = gaussian, maxit = 1, optim.maxit = 1
)