sgdgmf.rank: Rank selection via eigenvalue-gap methods

In sgdGMF: Estimation of Generalized Matrix Factorization Models via Stochastic Gradient Descent

Rank selection via eigenvalue-gap methods

Description

Select the number of significant principal components of a GMF model via exploitation of eigenvalue-gap methods

Usage

sgdgmf.rank(
  Y,
  X = NULL,
  Z = NULL,
  maxcomp = ncol(Y),
  family = gaussian(),
  weights = NULL,
  offset = NULL,
  method = c("evr", "onatski", "act", "oht"),
  type.reg = c("ols", "glm"),
  type.res = c("deviance", "pearson", "working", "link"),
  normalize = FALSE,
  maxiter = 10,
  parallel = FALSE,
  nthreads = 1,
  return.eta = FALSE,
  return.mu = FALSE,
  return.res = FALSE,
  return.cov = FALSE
)

Arguments

Y	matrix of responses (n \times m)
X	matrix of row-specific fixed effects (n \times p)
Z	matrix of column-specific fixed effects (q \times m)
maxcomp	maximum number of eigenvalues to compute
family	a family as in the glm interface (default gaussian())
weights	matrix of optional weights (n \times m)
offset	matrix of optional offsets (n \times m)
method	rank selection method
type.reg	regression method to be used to profile out the covariate effects
type.res	residual type to be decomposed
normalize	if TRUE, standardize column-by-column the residual matrix
maxiter	maximum number of iterations
parallel	if TRUE, allows for parallel computing using foreach
nthreads	number of cores to be used in parallel (only if parallel=TRUE)
return.eta	if TRUE, return the linear predictor martix
return.mu	if TRUE, return the fitted value martix
return.res	if TRUE, return the residual matrix
return.cov	if TRUE, return the covariance matrix of the residuals

Value

A list containing the method, the selected latent rank ncomp, and the eigenvalues used to select the latent rank lambdas. Additionally, if required, in the output list will also provide the linear predictor eta, the predicted mean matrix mu, the residual matrix res, and the implied residual covariance matrix covmat.

References

Onatski, A. (2010). Determining the number of factors from empirical distribution of eigenvalues. Review of Economics and Statistics, 92(4): 1004-1016

Ahn, S.C., Horenstein, A.R. (2013). Eigenvalue ratio test for the number of factors. Econometrica, 81, 1203-1227

Gavish, M., Donoho, D.L. (2014) The optimal hard thresholding for singular values is 4/sqrt(3). IEEE Transactions on Information Theory, 60(8): 5040–5053

Fan, J., Guo, J. and Zheng, S. (2020). Estimating number of factors by adjusted eigenvalues thresholding. Journal of the American Statistical Association, 117(538): 852–861

Wang, L. and Carvalho, L. (2023). Deviance matrix factorization. Electronic Journal of Statistics, 17(2): 3762-3810

Examples

library(sgdGMF)

# Set the data dimensions
n = 100; m = 20; d = 5

# Generate data using Poisson, Binomial and Gamma models
data_pois = sim.gmf.data(n = n, m = m, ncomp = d, family = poisson())
data_bin = sim.gmf.data(n = n, m = m, ncomp = d, family = binomial())
data_gam = sim.gmf.data(n = n, m = m, ncomp = d, family = Gamma(link = "log"), dispersion = 0.25)

# Initialize the GMF parameters assuming 3 latent factors
ncomp_pois = sgdgmf.rank(data_pois$Y, family = poisson(), normalize = TRUE)
ncomp_bin = sgdgmf.rank(data_bin$Y, family = binomial(), normalize = TRUE)
ncomp_gam = sgdgmf.rank(data_gam$Y, family = Gamma(link = "log"), normalize = TRUE)

# Get the selected number of components
print(paste("Poisson:", ncomp_pois$ncomp))
print(paste("Binomial:", ncomp_bin$ncomp))
print(paste("Gamma:", ncomp_gam$ncomp))

# Plot the screeplot used for the component determination
oldpar = par(no.readonly = TRUE)
par(mfrow = c(3,1))
barplot(ncomp_pois$lambdas, main = "Poisson screeplot")
barplot(ncomp_bin$lambdas, main = "Binomial screeplot")
barplot(ncomp_gam$lambdas, main = "Gamma screeplot")
par(oldpar)

sgdGMF documentation built on June 8, 2025, 12:05 p.m.