Package {osir}

Type: Package
Title: Online Sliced Inverse Regression for Elliptical Model with Streaming Data
Version: 0.3.2
Author: Sirui Yan [aut], Guangbao Guo [aut, cre]
Maintainer: Guangbao Guo <ggb11111111@163.com>
Description: For high-dimensional streaming heavy-tailed elliptical data, traditional sliced inverse regression methods require full offline data and cannot adapt to incremental data arrival. This package implements Online Sliced Inverse Regression for Elliptical Model with Streaming Data (OSIR) algorithm with two recursive updating strategies, including offline batch SIR as benchmark, elliptical heavy-tailed data simulator, subspace evaluation metric and batch simulation tools for numerical experiments. Cai, Z., Li, R., & Zhu, L. (2020) <doi:10.48550/arXiv.2002.02795>.
License: MIT + file LICENSE
Encoding: UTF-8
Depends: R (≥ 3.5.0)
Imports: stats, Matrix, MASS
NeedsCompilation: no
Language: en-US
Config/roxygen2/version: 8.0.0
Packaged: 2026-10-28 14:54:47 UTC; Lenovo
Repository: CRAN
Date/Publication: 2026-11-13 22:20:02 UTC

Generate Elliptical Streaming Data Generate elliptical normal / student-t heavy-tailed covariate stream

Description

Generate Elliptical Streaming Data Generate elliptical normal / student-t heavy-tailed covariate stream

Usage

generate_elliptical(n, p, nu = 3, sigma = 0.3, heavy = TRUE)

Arguments

n

total sample size

p

covariate dimension

nu

t-distribution freedom

sigma

scale coefficient

heavy

TRUE = elliptical-t, FALSE = elliptical normal

Value

A list with components:

X

An n by p numeric matrix of generated elliptically distributed covariates.

Y

A numeric response vector of length n.

B.true

A p by 2 orthonormal matrix; its first column spans the true central direction.

Sigma

A p by p positive definite covariance matrix used to scale X.

Examples

set.seed(1)
dat <- generate_elliptical(n = 100, p = 6)
dim(dat$X)
length(dat$Y)

Offline Batch SIR (Baseline Comparison Algorithm) Classical full-data sliced inverse regression

Description

Offline Batch SIR (Baseline Comparison Algorithm) Classical full-data sliced inverse regression

Usage

offline_sir(X, Y, H = 5, K = 2)

Arguments

X

n*p covariate matrix

Y

response vector

H

slice number

K

target central subspace dimension

Value

A p by K numeric matrix whose columns are the estimated SIR directions, i.e. the leading K eigenvectors of the sliced covariance matrix.

Examples

set.seed(1)
dat <- generate_elliptical(n = 100, p = 6)
offline_sir(dat$X, dat$Y)

Online SIR (Two Online Solvers) Streaming recursive OSIR, gradient / perturbation two update methods

Description

Online SIR (Two Online Solvers) Streaming recursive OSIR, gradient / perturbation two update methods

Usage

osir(X, Y, H = 5, K = 2, method = c("grad", "pert"), C = 1)

Arguments

X

full streaming matrix

Y

response vector

H

slice count

K

target subspace dimension

method

"grad" gradient descent / "pert" perturbation update

C

gradient step constant

Value

A list with component B_hat: a p by K numeric matrix of the recursively updated estimated directions after scanning the whole stream X.

Examples

set.seed(1)
dat <- generate_elliptical(n = 80, p = 5)
osir(dat$X, dat$Y, method = "grad")$B_hat

Batch Ablation Simulation Tool Generate experiment table for paper drawing

Description

Batch Ablation Simulation Tool Generate experiment table for paper drawing

Usage

sim_ablation(
  heavy = TRUE,
  n_vec = c(2000, 4000, 6000),
  p_vec = c(8, 10, 12),
  rep = 5
)

Arguments

heavy

TRUE = heavy-tailed elliptical-t

n_vec

sample size grid

p_vec

dimension grid

rep

repeat experiment times

Value

A data.frame with one row per (n,p) setting and columns n, p, OSIR_MSE and Offline_MSE, giving the averaged subspace projection MSE over rep replications for the online and offline solvers.

Subspace Projection MSE Loss Function

Description

Calculate estimation error between true & estimated subspace

Usage

subspace_mse(est, true)

Arguments

est

estimated subspace matrix

true

real true subspace basis

Value

A non-negative numeric scalar giving the mean squared error between the projection matrices of the estimated and true subspaces.

Examples

set.seed(123)
# Generate demo subspace
true_sub <- matrix(rnorm(10*2), 10, 2)
est_sub  <- true_sub + matrix(rnorm(10*2, sd = 0.01), 10, 2)
subspace_mse(est = est_sub, true = true_sub)