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

x	$p_1 \times p_2 \times N$ numeric array with mean zero.
y	Numeric vector of length $N$.
family	See glm and family.
lambda1	$\lambda_1$.
lambda2	$\lambda_2$.
C0	Initialization to $C$.
tol	Convergence tolerance.
maxIter	Maximal step of iterations.
verbose	Print iterations?

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) )

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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")

---

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

x	Numeric array.
y	Numeric vector.
family	See glm and family.
maxRank	The maximum of rank to be detected.
tol	Convergence tolerance.
verbose	Print iterations?

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

p	Dimension of data.
r	Number of factors.
noise	Mode of $S$: diag: Diagonal matrix. rand: Nonzero elements at random positions. tridiag: Tri-diagonal matrix. block: Block matrix.
seed	Random seed.
N	Sample size.
B	Matrix $p \times r$.
S	Symmetric matrix $p \times p$.

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

p1	Row dimension.
p2	Column dimension.
rank0	Rank of L.
S.type	Type of S. zero: Zero matrix. rand: Nonzero elements at random positions. block: Block matrix. diag: Diagonal matrix.
seed	Random seed.
family	See glm and family.
N	Sample size.
C0	Coefficient matrix.
err.student.dof	The degree of freedom of Student-$t$ for error term in family="gaussian". By default it is NULL for normal error.

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

N	Sample size.
p1	Row dimension.
p2	Column dimension.
r0	Rank.
s0	signal proportion.
family	gaussian or binomial.

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). https://doi.org/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)

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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

y	Numeric matrix of $N \times p$.
lambda1.factor	Factor on $\lambda_1^8$ (by default 1.1^(-2:2)).
S.diag.penalize	Whether to penalize the diagonal elements of S (by default FALSE).
tol	Convergence tolerance.
maxIter	Maximal step of iterations.

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) )

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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

iniParas	Initial values returned by ini_paras. See examples below.
x	Numeric array.
y	Numeric vector.
lambda1.factor	Factor on initial guess$\lambda_1^2$ (By default 1.3^seq(-3, 3, 0.2)).
maxCard	The maximal cardinality of $S$.
tol	Convergence tolerance.
maxIter	Maximal step of iterations.

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) )

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