Package {oesir}

Generate Elliptical Streaming Data

Description

Generate elliptical normal / student‑t heavy‑tailed covariate stream. Simulate streaming high‑dimensional elliptical predictors and response, with true subspace and covariance matrix returned for subspace evaluation.

Usage

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

Arguments

Value

A list containing:

X

numeric matrix of dimension n * p, simulated predictor matrix.

Y

numeric vector of length n, simulated response variable.

B.true

numeric matrix, true effective dimension reduction subspace.

Sigma

numeric matrix, true population covariance matrix.

Examples

# tiny toy example for CRAN automatic checking (run <5s)
set.seed(123)
dat <- generate_elliptical(n = 80, p = 6, nu = 3, sigma = 0.3, heavy = TRUE)
dim(dat$X)
length(dat$Y)
dim(dat$B.true)

# larger simulation example, skipped in auto‑check

set.seed(123)
dat_large <- generate_elliptical(n = 2000, p = 30)

Online Elliptical SIR (Two Online Solvers)

Description

Streaming recursive OE‑SIR algorithm, supporting gradient‑based and perturbation‑based two recursive updating strategies for streaming elliptical high‑dimensional data.

Usage

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

Arguments

Value

A list containing:

B_hat

numeric matrix of dimension p * K, estimated effective dimension reduction subspace directions.

Examples

# tiny toy example for CRAN automatic checking (run <5s)
set.seed(123)
dat <- generate_elliptical(n = 80, p = 6)
res <- oe_sir(X = dat$X, Y = dat$Y, H = 5, K = 2, method = "grad")
dim(res$B_hat)

# larger streaming example, skipped in auto‑check

set.seed(123)
dat_large <- generate_elliptical(n = 2000, p = 30)
res_pert <- oe_sir(X = dat_large$X, Y = dat_large$Y, method = "pert")

Offline Batch SIR (Baseline Comparison Algorithm)

Description

Classical full‑data sliced inverse regression, offline batch‑mode baseline algorithm for estimating the central subspace.

Usage

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

Arguments

Value

Numeric matrix p * K, the estimated central subspace basis directions.

Examples

# tiny toy example for CRAN automatic checking (run <5s)
set.seed(123)
dat <- generate_elliptical(n = 80, p = 6)
res_off <- offline_sir(X = dat$X, Y = dat$Y, H = 5, K = 2)
dim(res_off)

# larger example, skipped in auto‑check

set.seed(123)
dat_large <- generate_elliptical(n = 2000, p = 30)
res_off_large <- offline_sir(X = dat_large$X, Y = dat_large$Y)

Batch Ablation Simulation Tool

Description

Generate simulation result table for numerical experiment and paper visualization. Run repeated experiments over grids of sample size and dimension, compare OE‑SIR and offline SIR subspace estimation error.

Usage

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

Arguments

Value

A data.frame containing simulation summary results: sample size n, dimension p, averaged MSE for OESIR and offline SIR.

Examples

# tiny toy example for CRAN automatic checking (small rep to save time)
set.seed(123)
sim_res <- sim_ablation(heavy = TRUE, n_vec = c(200), p_vec = c(6), rep = 2)
print(sim_res)

# full simulation, skipped in auto‑check due to computation cost

sim_full <- sim_ablation(heavy = TRUE, n_vec = c(2000,4000), p_vec = c(8,10), rep = 5)

Subspace Projection MSE Loss Function

Description

Calculate mean‑squared estimation error between estimated subspace projection matrix and true subspace projection matrix.

Usage

subspace_mse(est, true)

Arguments

Value

Numeric scalar, mean squared error between two projection matrices.

Examples

# tiny runnable example for CRAN check
set.seed(123)
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)