crossval {gsbm}

Parameter selection by cross validation

Description

Selection by cross validation of the regularization parameters (lambda1 and lambda2) for estimating the probabilities of connection in a Generalized Stochastic Block Model.

Usage

crossval(
  A,
  epsilon = 0.1,
  nb.boot = 5,
  thresh = 1e-05,
  maxit = 100,
  lambda1.max = NULL,
  lambda2.max = NULL,
  lambda1.min = NULL,
  lambda2.min = NULL,
  length = 10,
  S0 = NULL,
  L0 = NULL,
  trace.it = FALSE
)

Arguments

A

nxn adjacency matrix

epsilon

regularization parameter for the L^2-norm penalty (positive number, if NULL, default method is applied)

nb.boot

number of folds for cross validation (integer)

thresh

convergence tolerance (positive number)

maxit

maximum number of iterations (positive integer)

lambda1.max

maximum regularization parameter for nuclear norm penalty (positive number)

lambda2.max

maximum regularization parameter for 2,1-norm norm penalty (positive number)

lambda1.min

minimum regularization parameter for nuclear norm penalty (positive number)

lambda2.min

minimum regularization parameter for 2,1-norm norm penalty (positive number)

length

size of cross-validation grid (integer)

S0

initial value for the sparse component

L0

initial value for the low-rank component

trace.it

whether messages about convergence should be printed (boolean)

Value

The values selected by cross-validation for the regularization parameters lambda1 and lambda2. The return value is a list of components

• lambda1 selected value for the parameter of the nuclear norm penalization.

• lambda2 selected value for the parameter of the 2,1-norm penalization.

• estim.cv result of the gsbm_mcgd function for the parameters selected.

• error a table containing the errors for all pairs of parameters on the grid.

• lambda1.grid grid of value for the parameter lambda1.

• lambda2.grid grid of value for the parameter lambda2.

Examples

# Draw a 50x50 adjacency matrix
# Generalized SBM with 2 communities and 2 outliers
# Create low-rank matrix L
L <- matrix(0,50,50) # low-rank component
L[1:25, 1:25] <- 0.6 # connection probabilities within community 1
L[1:25, 26:48] <- 0.1 # connection probabilities between communities 1 and 2
L[26:48, 1:25] <- 0.1 # connection probabilities between communities 1 and 2
L[26:48, 26:48] <- 0.6 # connection probabilities within community 2

# Create column-sparse matrix S
S <- matrix(0,50,50) # column sparse component
S[49:50,1:48] <- 0.6 # connection probabilities between outliers and inliers

# Draw connections and create the adjacency matrix
undir <- rbinom(n=50*(50-1)/2, size=1, prob=(L+S+t(S))[upper.tri(L+S+t(S))]) # draw edges
A <- matrix(0,50,50)
A[upper.tri(A)] <- undir
A <- (A+t(A))