drrglm: Doubly Regularized Matrix-Variate Regression

Description

The doubly regularized matrix-variate regression solves a low-rank-plus-sparse structure for matrix-variate generalized linear models through a weighted combination of nuclear-norm and L1-norm. The methodology implemented by this package is described in the paper "Doubly Regularized Matrix-Variate Regression", which has been tentatively accepted for publication but does not yet have a DOI or URL. A formal citation will be added in a future update once the final publication details are available.

Author(s)

Maintainer: Zengchao Xu zengc.xu@aliyun.com [copyright holder]

Authors:

• Shan Luo

• Binyan Jiang

See Also

Useful links:

• https://github.com/paradoxical-rhapsody/drrglm

• Report bugs at https://github.com/paradoxical-rhapsody/drrglm/issues

ElectroEncephaloGraphy Data

Description

This data arises from a large study to examine EEG correlates of genetic predisposition to alcoholism. See details.

Usage

EEG

Format

list(alcholic, control).

Details

The original data are fully open-access and available in UCI Machine Learning Repository (http://kdd.ics.uci.edu/databases/eeg/). It includes two groups of subjects: 77 alcoholic and 45 control. In the original study, each subject was exposed to either a single stimulus (S1) or two stimuli (S1 and S2), which were pictures chosen from the 1980 Snodgrass and Vanderwart picture set. Each subject underwent 120 trials under each condition.

Here we provide this preprocessed data of the averages of 120 trials under S1 condition, which has been studied in several literature. The dataset is structured as a list containing two arrays,

• EEG$alcholic: Array of dimensions ⁠256 x 64 x 77⁠.

• EEG$control: Array of dimensions ⁠256 x 64 x 45⁠.

References

If you use this dataset, we would be very grateful if you could cite both the original data source and our work:

Zengchao Xu, Shan Luo, and Binyan Jiang. "Doubly Regularized Matrix-Variate Regression". Submitted.

Examples

data(EEG, package="drrglm")

Doubly Regularized Matrix-Variate GLMs

Description

Solve the following problem

\min_{L, S} \Big\lbrace \frac{1}{N} \sum_{n=1}^N \ell(y_n, X_n) + \lambda_1 \|L\|_* + \lambda_2 \|S\|_1 \Big\rbrace,

where \ell(y_n, X_n) refers to the negative-log-likelihood on (y_n, X_n) under pre-specified GLM.

In linear model, the problem has the form

\min_{L, S} \Big\lbrace \frac{1}{2N} \sum_{n=1}^N \big( y_n - \text{tr}(X_n'C) \big)^2 + \lambda_1 \|L\|_* + \lambda_2 \|S\|_1 \Big\rbrace, ~~\text{s.t.}~~ C=L+S.

Usage

drrglm(
  x,
  y,
  family,
  lambda1,
  lambda2,
  C0 = NULL,
  tol = 0.001,
  maxIter = 300,
  verbose = FALSE
)

Arguments

Value

list(L, S, Lsv, iter, lambda1, lambda2, isConvergent).

Examples

set.seed(2025)
r0 <- 13
c0 <- 17
N <- 500
x <- array(runif(r0*c0*N), c(r0, c0, N))
y <- rnorm(N)

family <- "gaussian"
lambda1 <- 0.15
lambda2 <- 0.04

system.time( egg <- drrglm(x, y, family, lambda1, lambda2) )

Initialize Parameters

Description

Initialize \widehat{L} via nuclear-norm regularized regression.

Usage

ini_paras(
  x,
  y,
  family,
  maxRank = min(floor(NROW(x)/2), floor(NCOL(x)/2)),
  tol = 0.001,
  verbose = FALSE
)

Arguments

Value

list( family, grad, lipschitz, sigma0, rankStar, rankStarHat, lambda.star, L0.star )

Simulation: Factor Model with Correlated Noise

Description

y = B u + w with u \sim N(0, I_{r}), w \sim N(0, S) and B \in \mathbb{R}^{p \times r}.

• simu_factor_model_paras: simulate ⁠(B, S)⁠.

• simu_factor_model_data: simulate y.

Usage

simu_factor_model_paras(p, r, noise, seed = 2023)

simu_factor_model_data(N, B, S)

Arguments

Value

• simu_factor_model_paras: list(B, S).

• simu_factor_model_data: Numeric matrix y of N \times p.

Examples

set.seed(2025)
N <- 50
p <- 15
r <- 7

paras <- simu_factor_model_paras(p, r, 'diag')
paras <- simu_factor_model_paras(p, r, 'rand')
paras <- simu_factor_model_paras(p, r, 'tridiag')
paras <- simu_factor_model_paras(p, r, 'block')

DT <- simu_factor_model_data(N, paras[["B"]], paras[["S"]])

Simulation: Matrix-Variate GLM

Description

Simulation: Matrix-Variate GLM

Usage

simu_reg_coefs(p1, p2, rank0, S.type, seed = 2023)

simu_reg_data(family, N, C0, err.student.dof = NULL)

Arguments

Value

• simu_reg_coefs: list(L, S).

• simu_reg_data: list( train=list(x, y), test=list(x, y) ).

Examples

p1 <- 10
p2 <- 9
rank0 <- 3

coefs <- simu_reg_coefs(p1, p2, rank0, "zero")
coefs <- simu_reg_coefs(p1, p2, rank0, "rand")
coefs <- simu_reg_coefs(p1, p2, rank0, "block")
coefs <- simu_reg_coefs(p1, p2, rank0, "diag")

N <- 100
S.type <- "rand"
family <- "binomial"

coefs <- simu_reg_coefs(p1, p2, rank0, S.type)
C0 <- coefs[["L"]] + coefs[["S"]]

set.seed(2025)
DT <- simu_reg_data(family, N, C0)
DT <- simu_reg_data("gaussian", N, C0, err.student.dof=3)

Simulation: Setups in Regularized Matrix Regression

Description

Simulation: Setups in Regularized Matrix Regression

Usage

simu_zhouandli2014(N, p1, p2, r0, s0, family)

Arguments

Value

list( C0, train=list(x, y), test=list(x, y) ).

References

Zhou Hua and Li Lexin (2014). Regularized Matrix Regression. Journal of the Royal Statistical Society (Series B). doi:10.1111/rssb.12031

Examples

N <- 100
p1 <- 64
p2 <- 64
r0 <- 1
s0 <- 0.05
family <- 'gaussian'

set.seed(2026)
DT <- simu_zhouandli2014(N, p1, p2, r0, s0, family)

Doubly Regularized Regression for Matrix-Variate Data

Description

Tune the (\lambda_1, \lambda_2) in drr.

Usage

tune_drrglm(
  iniParas,
  x,
  y,
  lambda1.factor = 1.3^seq(-3, 3, 0.2),
  maxCard = 30,
  tol = 0.001,
  maxIter = 500
)

Arguments

Value

List.

Examples

p1 <- 10
p2 <- 9
rank0 <- 3
S.type <- "rand"
coefs <- simu_reg_coefs(p1, p2, rank0, S.type)

N <- 500
family <- "gaussian"
L0 <- coefs[["L"]]
S0 <- coefs[["S"]]
C0 <- L0 + S0
DT <- simu_reg_data(family, N, C0)

x <- DT[["train"]][["x"]]
y <- DT[["train"]][["y"]]

lambda1.factor <- 1.1^(0:1)
maxRank <- 5

system.time( iniParas <- ini_paras(x, y, family, maxRank) )
system.time( drrObj <- tune_drrglm(iniParas, x, y, lambda1.factor) )

Simulating Data for Factor Model with Correlated Noise

Description

Doubly regularized decomposition for covariance matrix in factor model.

Usage

tune_drr_factor_model(
  y,
  lambda1.factor = 1.1^(-2:2),
  S.diag.penalize = FALSE,
  tol = 0.001,
  maxIter = 500
)

Arguments

Value

List.

Examples

set.seed(2025)
N <- 500
p <- 30
r <- 10
noise <- "diag"
paras <- simu_factor_model_paras(p, r, noise)
y <- simu_factor_model_data(N, paras[["B"]], paras[["S"]])
lambda1.factor <- 1.1^(-1:1)
system.time( egg <- tune_drr_factor_model(y, lambda1.factor) )