# Generalize Exclusive factor extraction via co-sparse unit-rank estimation (GOFAR(P)) using k-fold crossvalidation Divide and conquer approach for low-rank and sparse coefficent matrix estimation: Exclusive extraction ```r gofar_p( Yt, X, nrank = 3, nlambda = 40, family, familygroup = NULL, cIndex = NULL, ofset = NULL, control = list(), nfold = 5, PATH = FALSE ) ``` ## Arguments - `Yt`: response matrix - `X`: covariate matrix; when X = NULL, the fucntion performs unsupervised learning - `nrank`: an integer specifying the desired rank/number of factors - `nlambda`: number of lambda values to be used along each path - `family`: set of family gaussian, bernoulli, possion - `familygroup`: index set of the type of multivariate outcomes: "1" for Gaussian, "2" for Bernoulli, "3" for Poisson outcomes - `cIndex`: control index, specifying index of control variable in the design matrix X - `ofset`: offset matrix specified - `control`: a list of internal parameters controlling the model fitting - `nfold`: number of fold for cross-validation - `PATH`: TRUE/FALSE for generating solution path of sequential estimate after cross-validation step ## Returns - **C**: estimated coefficient matrix; based on GIC - **Z**: estimated control variable coefficient matrix - **Phi**: estimted dispersion parameters - **U**: estimated U matrix (generalize latent factor weights) - **D**: estimated singular values - **V**: estimated V matrix (factor loadings) - **lam**: selected lambda values based on the chosen information criterion - **lampath**: sequences of lambda values used in model fitting. In each sequential unit-rank estimation step, a sequence of length nlambda is first generated between (lamMax**lamMaxFac, lamMax**lamMaxFac*lamMinFac) equally spaced on the log scale, in which lamMax is estimated and the other parameters are specified in gofar_control. The model fitting starts from the largest lambda and stops when the maximum proportion of nonzero elements is reached in either u or v, as specified by spU and spV in gofar_control. - **IC**: values of information criteria - **Upath**: solution path of U - **Dpath**: solution path of D - **Vpath**: solution path of D - **ObjDec**: boolian type matrix outcome showing if objective function is monotone decreasing or not. - **familygroup**: spcified familygroup of outcome variables. ## Examples ```r family <- list(gaussian(), binomial(), poisson()) control <- gofar_control() nlam <- 40 # number of tuning parameter SD <- 123 # Simulated data for testing data('simulate_gofar') attach(simulate_gofar) q <- ncol(Y) p <- ncol(X) # Simulate data with 20% missing entries miss <- 0.20 # Proportion of entries missing t.ind <- sample.int(n * q, size = miss * n * q) y <- as.vector(Y) y[t.ind] <- NA Ym <- matrix(y, n, q) naind <- (!is.na(Ym)) + 0 # matrix(1,n,q) misind <- any(naind == 0) + 0 # # Model fitting begins: control$epsilon <- 1e-7 control$spU <- 50 / p control$spV <- 25 / q control$maxit <- 1000 # Model fitting: GOFAR(P) (full data) set.seed(SD) rank.est <- 5 fit.eea <- gofar_p(Y, X, nrank = rank.est, nlambda = nlam, family = family, familygroup = familygroup, control = control, nfold = 5 ) # Model fitting: GOFAR(P) (missing data) set.seed(SD) rank.est <- 5 fit.eea.m <- gofar_p(Ym, X, nrank = rank.est, nlambda = nlam, family = family, familygroup = familygroup, control = control, nfold = 5 ) ``` ## References **Mishra, Aditya, Dipak K. Dey, Yong Chen, and Kun Chen. Generalized co-sparse factor regression. Computational Statistics & Data Analysis 157 (2021): 107127**

gofar_p function