BICforPCAwithSparseWeights: BIC for sparse weight based PCA methods

In trbKnl/sparseWeightBasedPCA: Sparse weight based PCA

Description

A function that returns the Bayesian information criterion (BIC) given a set of tuning parameters and a sparse weight based PCA method

Usage

BICforPCAwithSparseWeights(X, ncomp, FUN, ...)

Arguments

X	A data matrix of class 'matrix'
ncomp	An integer specifying the number of components
FUN	A pointer to a function (i.e. the function name with no brackets) that performs sparse weight based PCA. The function should return a list containing a matrix object called "W" that contains the component weights
...	specify all the arguments the function in FUN needs

Value

The following items in a list
BIC The BIC given the set of tuning parameters
nNonZeroCoef The number of non-zero coefficients in the model

Examples

 
J  <- 10
ncomp <- 3
X <- matrix(rnorm(100 * J), 100, J)

BICforPCAwithSparseWeights(X = X, ncom = ncomp, FUN = scads, ncomp, ridge = 0, lasso = rep(0.1, ncomp),
                constraints = matrix(1, J, ncomp), Wstart = matrix(0, J, ncomp),
                itr = 100000, nStarts = 1, printLoss = FALSE, tol = 10^-5)


#Extended example: select LASSO parameter using BICforPCAwithSparseWeights with scads()
#create sammple data
ncomp <- 3 
J <- 30
comdis <- matrix(1, J, ncomp)
comdis <- sparsify(comdis, 0.7) #set 70 percent of the 1's to zero
variances <- makeVariance(varianceOfComps = c(100, 80, 90), J = J, error = 0.05) #create realistic eigenvalues
dat <- makeDat(n = 100, comdis = comdis, variances = variances)
X <- dat$X


#Use cross-validation to look for the data generating structure 
lasso <- seq(0, 1, length.out = 500)
BIC <- rep(NA, length(lasso))
nNonZeroCoef <- rep(NA, length(lasso))
for (i in 1:length(lasso)) {
    print(i)
    res <- BICforPCAwithSparseWeights(X = X, ncomp = ncomp, FUN = scads, ncomp, ridge = 0, lasso = rep(lasso[i], ncomp),
                    constraints = matrix(1, J, ncomp), Wstart = matrix(0, J, ncomp),
                    itr = 100000, nStarts = 1, printLoss = FALSE, tol = 10^-5)
    BIC[i]  <- res$BIC #store BIC for each lasso
}

#make a plot of all the BIC's choose the minimal BIC or a model with a small BIC
#BIC tends to select very sparse models
x <- 1:length(BIC)
plot(x, BIC)

#Select the model with the lowest BIC (or alternatively select a model around the model with the lowest BIC)
best <- which.min(BIC)

#Do the analysis with the "winning" structure
results <- scads(X = X, ncomp = ncomp, ridge = 0, lasso = rep(lasso[best], ncomp),
                constraints = matrix(1, J, ncomp), Wstart = matrix(0, J, ncomp),
                itr = 100000, nStarts = 1, printLoss = TRUE , tol = 10^-5)

results$W #inspect results of the estimation
dat$P[, 1:ncomp] #inspect data generating model

trbKnl/sparseWeightBasedPCA documentation built on July 22, 2020, 10:29 p.m.