gofar_p: Generalize Exclusive factor extraction via co-sparse...

In gofar: Generalized Co-Sparse Factor Regression

Generalize Exclusive factor extraction via co-sparse unit-rank estimation (GOFAR(P)) using k-fold crossvalidation

Description

Divide and conquer approach for low-rank and sparse coefficent matrix estimation: Exclusive extraction

Usage

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

Value

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 (lamMaxlamMaxFac, lamMaxlamMaxFac*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.

References

Mishra, Aditya, Dipak K. Dey, Yong Chen, and Kun Chen. Generalized co-sparse factor regression. Computational Statistics & Data Analysis 157 (2021): 107127

Examples

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
)

gofar documentation built on March 18, 2022, 7:30 p.m.