sofar: Sparse orthogonal factor regression

In rrpack: Reduced-Rank Regression

Sparse orthogonal factor regression

Description

Compute solution paths of sparse orthogonal factor regression

Usage

sofar(
  Y,
  X,
  nrank = 1,
  su = NULL,
  sv = NULL,
  ic.type = c("GIC", "BIC", "AIC", "GCV"),
  modstr = list(),
  control = list(),
  screening = FALSE
)

Arguments

Y	response matrix
X	covariate matrix
nrank	an integer specifying the desired rank/number of factors
su	a scaling vector for U such that U^TU = diag(s_u).
sv	a scaling vector for V such that V^TV = diag(s_v).
ic.type	select tuning method; the default is GIC
modstr	a list of internal model parameters controlling the model fitting
control	a list of internal computation parameters controlling optimization
screening	If TRUE, marginal screening via lasso is performed before sofar fitting.

Details

The model parameters can be specified through argument modstr. The available elements include

• mu: parameter in the augmented Lagrangian function.

• mugamma: increament of mu along iterations to speed up computation.

• WA: weight matrix for A.

• WB: weight matrix for B.

• Wd: weight matrix for d.

• wgamma: power parameter in constructing adaptive weights.

The model fitting can be controled through argument control. The avilable elements include

• nlam: number of lambda triplets to be used.

• lam.min.factor: set the smallest lambda triplets as a fraction of the estimation lambda.max triplets.

• lam.max.factor: set the largest lambda triplets as a multiple of the estimation lambda.max triplets.

• lam.AB.factor: set the relative penalty level between A/B and D.

• penA,penB,penD: if TRUE, penalty is applied.

• lamA: sequence of tuning parameters for A.

• lamB: sequence of tuning parameters for B.

• lamD: sequence of tuning parameters for d.

• methodA: penalty for penalizing A.

• methodB: penalty for penalizing B.

• epsilon: convergence tolerance.

• maxit: maximum number of iterations.

• innerEpsilon: convergence tolerance for inner subroutines.

• innerMaxit: maximum number of iterations for inner subroutines.

• sv.tol: tolerance for singular values.

Value

A sofar object containing

call	original function call
Y	input response matrix
X	input predictor matrix
Upath	solution path of U
Dpath	solution path of D
Vpath	solution path of D
Rpath	path of estimated rank
icpath	path of information criteria
lam.id	ids of selected lambda for GIC, BIC, AIC and GCV
p.index	ids of predictors which passed screening
q.index	ids of responses which passed screening
lamA	tuning sequence for A
lamB	tuning sequence for B
lamD	tuning sequence for D
U	estimated left singular matrix that is orthogonal (factor weights)
V	estimated right singular matrix that is orthogonal (factor loadings)
D	estimated singular values
rank	estimated rank

References

Uematsu, Y., Fan, Y., Chen, K., Lv, J., & Lin, W. (2019). SOFAR: large-scale association network learning. IEEE Transactions on Information Theory, 65(8), 4924–4939.

Examples

## Not run: 
library(rrpack)
## Simulate data from a sparse factor regression model
p <- 100; q <- 50; n <- 100; nrank <- 3
mydata <- rrr.sim1(n, p, q, nrank, s2n = 1,
                   sigma = NULL, rho_X = 0.5, rho_E = 0.3)
Y <- mydata$Y
X <- mydata$X

fit1 <- sofar(Y, X, ic.type = "GIC", nrank = nrank + 2,
              control = list(methodA = "adlasso", methodB = "adlasso"))
summary(fit1)
plot(fit1)

fit1$U
crossprod(fit1$U) #check orthogonality
fit1$V
crossprod(fit1$V) #check orthogonality

## End(Not run)

rrpack documentation built on June 16, 2022, 9:05 a.m.