nbfar: Negative binomial co-sparse factor regression (NBFAR)

In nbfar: Negative Binomial Factor Regression Models ('nbfar')

Negative binomial co-sparse factor regression (NBFAR)

Description

To estimate a low-rank and sparse coefficient matrix in large/high dimensional setting, the approach extracts unit-rank components of required matrix in sequential order. The algorithm automatically stops after extracting sufficient unit rank components.

Usage

nbfar(
  Yt,
  X,
  maxrank = 3,
  nlambda = 40,
  cIndex = NULL,
  ofset = NULL,
  control = list(),
  nfold = 5,
  PATH = FALSE,
  nthread = 1,
  trace = FALSE,
  verbose = TRUE
)

Arguments

Yt	response matrix
X	design matrix; when X = NULL, we set X as identity matrix and perform generalized sparse PCA.
maxrank	an integer specifying the maximum possible rank of the coefficient matrix or the number of factors
nlambda	number of lambda values to be used along each path
cIndex	specify index of control variables in the design matrix X
ofset	offset matrix or microbiome data analysis specific scaling: common sum scaling = CSS (default), total sum scaling = TSS, median-ratio scaling = MRS, centered-log-ratio scaling = CLR
control	a list of internal parameters controlling the model fitting
nfold	number of folds in k-fold crossvalidation
PATH	TRUE/FALSE for generating solution path of sequential estimate after cross-validation step
nthread	number of thread to be used for parallelizing the crossvalidation procedure
trace	TRUE/FALSE checking progress of cross validation error
verbose	TRUE/FALSE checking progress of estimation procedure

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)

References

Mishra, A., Müller, C. (2022) Negative binomial factor regression models with application to microbiome data analysis. https://doi.org/10.1101/2021.11.29.470304

Examples

## Model specification:
SD <- 123
set.seed(SD)
p <- 100; n <- 200
pz <- 0
nrank <- 3                # true rank
rank.est <- 5             # estimated rank
nlam <- 20                # number of tuning parameter
s  = 0.5
q <- 30
control <- nbfar_control()  # control parameters
#
#
## Generate data
D <- rep(0, nrank)
V <- matrix(0, ncol = nrank, nrow = q)
U <- matrix(0, ncol = nrank, nrow = p)
#
U[, 1] <- c(sample(c(1, -1), 8, replace = TRUE), rep(0, p - 8))
U[, 2] <- c(rep(0, 5), sample(c(1, -1), 9, replace = TRUE), rep(0, p - 14))
U[, 3] <- c(rep(0, 11), sample(c(1, -1), 9, replace = TRUE), rep(0, p - 20))
#
  # for similar type response type setting
  V[, 1] <- c(rep(0, 8), sample(c(1, -1), 8,
    replace =
      TRUE
  ) * runif(8, 0.3, 1), rep(0, q - 16))
  V[, 2] <- c(rep(0, 20), sample(c(1, -1), 8,
    replace =
      TRUE
  ) * runif(8, 0.3, 1), rep(0, q - 28))
  V[, 3] <- c(
    sample(c(1, -1), 5, replace = TRUE) * runif(5, 0.3, 1), rep(0, 23),
    sample(c(1, -1), 2, replace = TRUE) * runif(2, 0.3, 1), rep(0, q - 30)
  )
U[, 1:3] <- apply(U[, 1:3], 2, function(x) x / sqrt(sum(x^2)))
V[, 1:3] <- apply(V[, 1:3], 2, function(x) x / sqrt(sum(x^2)))
#
D <- s * c(4, 6, 5) # signal strength varries as per the value of s
or <- order(D, decreasing = TRUE)
U <- U[, or]
V <- V[, or]
D <- D[or]
C <- U %*% (D * t(V)) # simulated coefficient matrix
intercept <- rep(0.5, q) # specifying intercept to the model:
C0 <- rbind(intercept, C)
#
Xsigma <- 0.5^abs(outer(1:p, 1:p, FUN = "-"))
# Simulated data
sim.sample <- nbfar_sim(U, D, V, n, Xsigma, C0,disp = 3, depth = 10)  # Simulated sample
# Dispersion parameter
X <- sim.sample$X[1:n, ]
Y <- sim.sample$Y[1:n, ]
X0 <- cbind(1, X)                     # 1st column accounting for intercept

# Model with known offset
set.seed(1234)
offset <- log(10)*matrix(1,n,q)
control_nbfar <- nbfar_control(initmaxit = 5000, gamma0 = 2, spU = 0.5,
spV = 0.6, lamMinFac = 1e-10, epsilon = 1e-5)
# nbfar_test <- nbfar(Y, X, maxrank = 5, nlambda = 20, cIndex = NULL,
# ofset = offset, control = control_nbfar, nfold = 5, PATH = F)

nbfar documentation built on March 18, 2022, 7:31 p.m.