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

crossval function