Package 'gofar' reference manual

Title:	Generalized Co-Sparse Factor Regression
Description:	Divide and conquer approach for estimating low-rank and sparse coefficient matrix in the generalized co-sparse factor regression. Please refer the manuscript 'Mishra, Aditya, Dipak K. Dey, Yong Chen, and Kun Chen. Generalized co-sparse factor regression. Computational Statistics & Data Analysis 157 (2021): 107127' for more details.
Authors:	Aditya Mishra [aut, cre], Kun Chen [aut]
Maintainer:	Aditya Mishra <[email protected]>
License:	GPL (>= 3.0)
Version:	0.1
Built:	2024-11-21 06:46:01 UTC
Source:	CRAN

Control parameters for the estimation procedure of GOFAR(S) and GOFAR(P)

Description

Default control parameters for Generalized co-sparse factor regresion

Usage

gofar_control(
  maxit = 5000,
  epsilon = 1e-06,
  elnetAlpha = 0.95,
  gamma0 = 1,
  se1 = 1,
  spU = 0.5,
  spV = 0.5,
  lamMaxFac = 1,
  lamMinFac = 1e-06,
  initmaxit = 2000,
  initepsilon = 1e-06,
  equalphi = 1,
  objI = 1,
  alp = 60
)
gofar_control(
  maxit = 5000,
  epsilon = 1e-06,
  elnetAlpha = 0.95,
  gamma0 = 1,
  se1 = 1,
  spU = 0.5,
  spV = 0.5,
  lamMaxFac = 1,
  lamMinFac = 1e-06,
  initmaxit = 2000,
  initepsilon = 1e-06,
  equalphi = 1,
  objI = 1,
  alp = 60
)

Arguments

`maxit`	maximum iteration for each sequential steps
`epsilon`	tolerence value set for convergene of gcure
`elnetAlpha`	elastic net penalty parameter
`gamma0`	power parameter in the adaptive weights
`se1`	apply 1se sule for the model;
`spU`	maximum proportion of nonzero elements in each column of U
`spV`	maximum proportion of nonzero elements in each column of V
`lamMaxFac`	a multiplier of calculated lambda_max
`lamMinFac`	a multiplier of determing lambda_min as a fraction of lambda_max
`initmaxit`	maximum iteration for initialization problem
`initepsilon`	tolerence value for convergene in the initialization problem
`equalphi`	dispersion parameter for all gaussian outcome equal or not 0/1
`objI`	1 or 0 convergence on the basis of objective function or not
`alp`	scaling factor corresponding to poisson outcomes

Value

a list of controling parameter.

References

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

Examples


# control variable for GOFAR(S) and GOFAR(P)
control <- gofar_control()

# control variable for GOFAR(S) and GOFAR(P)
control <- gofar_control()

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
)
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
)

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
)

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

Description

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

Usage

gofar_s(
  Yt,
  X,
  nrank = 3,
  nlambda = 40,
  family,
  familygroup = NULL,
  cIndex = NULL,
  ofset = NULL,
  control = list(),
  nfold = 5,
  PATH = FALSE
)
gofar_s(
  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 folds in k-fold crossvalidation
`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
`familygroup`	spcified familygroup of outcome variables.
`fitCV`	output from crossvalidation step, for each sequential step

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(S) (full data)
set.seed(SD)
rank.est <- 5
fit.seq <- gofar_s(Y, X,
  nrank = rank.est, family = family,
  nlambda = nlam, familygroup = familygroup,
  control = control, nfold = 5
)


# Model fitting: GOFAR(S) (missing data)
set.seed(SD)
rank.est <- 5
fit.seq.m <- gofar_s(Ym, X,
  nrank = rank.est, family = family,
  nlambda = nlam, familygroup = familygroup,
  control = control, nfold = 5
)

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(S) (full data)
set.seed(SD)
rank.est <- 5
fit.seq <- gofar_s(Y, X,
  nrank = rank.est, family = family,
  nlambda = nlam, familygroup = familygroup,
  control = control, nfold = 5
)


# Model fitting: GOFAR(S) (missing data)
set.seed(SD)
rank.est <- 5
fit.seq.m <- gofar_s(Ym, X,
  nrank = rank.est, family = family,
  nlambda = nlam, familygroup = familygroup,
  control = control, nfold = 5
)

Simulate data for GOFAR

Description

Genertate random samples from a generalize sparse factor regression model

Usage

gofar_sim(U, D, V, n, Xsigma, C0, familygroup, snr)
gofar_sim(U, D, V, n, Xsigma, C0, familygroup, snr)

Arguments

`U`	specified value of U
`D`	specified value of D
`V`	specified value of V
`n`	sample size
`Xsigma`	covariance matrix for generating sample of X
`C0`	Specified coefficient matrix with first row being intercept
`familygroup`	index set of the type of multivariate outcomes: "1" for Gaussian, "2" for Bernoulli, "3" for Poisson outcomes
`snr`	signal to noise ratio specified for gaussian type outcomes

Value

`Y`	Generated response matrix
`X`	Generated predictor matrix
`sigmaG`	standard deviation for gaussian error

References

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

Examples


## Model specification:
SD <- 123
set.seed(SD)
n <- 200
p <- 100
pz <- 0
# Model I in the paper
# n <- 200; p <- 300; pz <- 0 ;           # Model II in the paper
# q1 <- 0; q2 <- 30; q3 <- 0               # Similar response cases
q1 <- 15
q2 <- 15
q3 <- 0 # mixed response cases
nrank <- 3 # true rank
rank.est <- 4 # estimated rank
nlam <- 40 # number of tuning parameter
s <- 1 # multiplying factor to singular value
snr <- 0.25 # SNR for variance Gaussian error
#
q <- q1 + q2 + q3
respFamily <- c("gaussian", "binomial", "poisson")
family <- list(gaussian(), binomial(), poisson())
familygroup <- c(rep(1, q1), rep(2, q2), rep(3, q3))
cfamily <- unique(familygroup)
nfamily <- length(cfamily)
#
control <- gofar_control()
#
#
## 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))
#
if (nfamily == 1) {
  # 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)
  )
} else {
  # for mixed type response setting
  # V is generated such that joint learning can be emphasised
  V1 <- matrix(0, ncol = nrank, nrow = q / 2)
  V1[, 1] <- c(sample(c(1, -1), 5, replace = TRUE), rep(0, q / 2 - 5))
  V1[, 2] <- c(
    rep(0, 3), V1[4, 1], -1 * V1[5, 1],
    sample(c(1, -1), 3, replace = TRUE), rep(0, q / 2 - 8)
  )
  V1[, 3] <- c(
    V1[1, 1], -1 * V1[2, 1], rep(0, 4),
    V1[7, 2], -1 * V1[8, 2], sample(c(1, -1), 2, replace = TRUE),
    rep(0, q / 2 - 10)
  )
  #
  V2 <- matrix(0, ncol = nrank, nrow = q / 2)
  V2[, 1] <- c(sample(c(1, -1), 5, replace = TRUE), rep(0, q / 2 - 5))
  V2[, 2] <- c(
    rep(0, 3), V2[4, 1], -1 * V2[5, 1],
    sample(c(1, -1), 3, replace = TRUE), rep(0, q / 2 - 8)
  )
  V2[, 3] <- c(
    V2[1, 1], -1 * V2[2, 1], rep(0, 4),
    V2[7, 2], -1 * V2[8, 2],
    sample(c(1, -1), 2, replace = TRUE), rep(0, q / 2 - 10)
  )
  #
  V <- rbind(V1, V2)
}
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 <- gofar_sim(U, D, V, n, Xsigma, C0, familygroup, snr)
# Dispersion parameter
pHI <- c(rep(sim.sample$sigmaG, q1), rep(1, q2), rep(1, q3))
X <- sim.sample$X[1:n, ]
Y <- sim.sample$Y[1:n, ]
simulate_gofar <- list(Y = Y,X = X, U = U, D = D, V = V, n=n,
Xsigma = Xsigma, C0 = C0, familygroup = familygroup)


## Model specification:
SD <- 123
set.seed(SD)
n <- 200
p <- 100
pz <- 0
# Model I in the paper
# n <- 200; p <- 300; pz <- 0 ;           # Model II in the paper
# q1 <- 0; q2 <- 30; q3 <- 0               # Similar response cases
q1 <- 15
q2 <- 15
q3 <- 0 # mixed response cases
nrank <- 3 # true rank
rank.est <- 4 # estimated rank
nlam <- 40 # number of tuning parameter
s <- 1 # multiplying factor to singular value
snr <- 0.25 # SNR for variance Gaussian error
#
q <- q1 + q2 + q3
respFamily <- c("gaussian", "binomial", "poisson")
family <- list(gaussian(), binomial(), poisson())
familygroup <- c(rep(1, q1), rep(2, q2), rep(3, q3))
cfamily <- unique(familygroup)
nfamily <- length(cfamily)
#
control <- gofar_control()
#
#
## 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))
#
if (nfamily == 1) {
  # 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)
  )
} else {
  # for mixed type response setting
  # V is generated such that joint learning can be emphasised
  V1 <- matrix(0, ncol = nrank, nrow = q / 2)
  V1[, 1] <- c(sample(c(1, -1), 5, replace = TRUE), rep(0, q / 2 - 5))
  V1[, 2] <- c(
    rep(0, 3), V1[4, 1], -1 * V1[5, 1],
    sample(c(1, -1), 3, replace = TRUE), rep(0, q / 2 - 8)
  )
  V1[, 3] <- c(
    V1[1, 1], -1 * V1[2, 1], rep(0, 4),
    V1[7, 2], -1 * V1[8, 2], sample(c(1, -1), 2, replace = TRUE),
    rep(0, q / 2 - 10)
  )
  #
  V2 <- matrix(0, ncol = nrank, nrow = q / 2)
  V2[, 1] <- c(sample(c(1, -1), 5, replace = TRUE), rep(0, q / 2 - 5))
  V2[, 2] <- c(
    rep(0, 3), V2[4, 1], -1 * V2[5, 1],
    sample(c(1, -1), 3, replace = TRUE), rep(0, q / 2 - 8)
  )
  V2[, 3] <- c(
    V2[1, 1], -1 * V2[2, 1], rep(0, 4),
    V2[7, 2], -1 * V2[8, 2],
    sample(c(1, -1), 2, replace = TRUE), rep(0, q / 2 - 10)
  )
  #
  V <- rbind(V1, V2)
}
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 <- gofar_sim(U, D, V, n, Xsigma, C0, familygroup, snr)
# Dispersion parameter
pHI <- c(rep(sim.sample$sigmaG, q1), rep(1, q2), rep(1, q3))
X <- sim.sample$X[1:n, ]
Y <- sim.sample$Y[1:n, ]
simulate_gofar <- list(Y = Y,X = X, U = U, D = D, V = V, n=n,
Xsigma = Xsigma, C0 = C0, familygroup = familygroup)

Simulated data for GOFAR

Description

Simulated data with low-rank and sparse coefficient matrix.

Usage

data(simulate_gofar)
data(simulate_gofar)

Format

A list of variables for the analysis using GOFAR(S) and GOFAR(P):

Y: Generated response matrix
X: Generated predictor matrix
U: specified value of U
V: specified value of V
D: specified value of D
n: sample size
Xsigma: covariance matrix used to generate predictors in X
C0: intercept value in the coefficient matrix
familygroup: index set of the type of multivariate outcomes: "1" for Gaussian, "2" for Bernoulli, "3" for Poisson outcomes

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

Package 'gofar'

Help Index

Control parameters for the estimation procedure of GOFAR(S) and GOFAR(P)

Description

Usage

Arguments

Value

References

Examples

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

Description

Usage

Arguments

Value

References

Examples

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

Description

Usage

Arguments

Value

References

Examples

Simulate data for GOFAR

Description

Usage

Arguments

Value

References

Examples

Simulated data for GOFAR

Description

Usage

Format