DLFM (version 0.2.2)

online_sir_lfm: Online Sufficient Dimension Reduction for Laplace Factor Model (LFM)

Description

Implements an online SIR algorithm tailored for LFM data, using a proxy response constructed from the current subspace estimate and robust updates to handle heavy-tailed noise. The algorithm supports two optimization methods: gradient-based updates and perturbation-based updates.

Usage

online_sir_lfm(
  X,
  K_true = NULL,
  K_max = NULL,
  c_robust = 1.345,
  eta = "auto",
  method = "gradient",
  verbose = FALSE
)

Value

A list with:

B_hat

Final estimated basis matrix (p x K_est)

K_est

Estimated structural dimension

B_path

List of B estimates over time (optional, for debugging)

loss

Reconstruction loss trace (optional)

method_used

The optimization method actually used

Arguments

X

A matrix or data stream of size n x p (rows = observations, cols = features). Can be processed row-by-row in streaming setting.

K_true

Optional true dimension (for monitoring). If NULL, will estimate online via BIC-like criterion.

K_max

Maximum candidate dimension for online selection (default = min(10, ncol(X))).

c_robust

Robustness scale for tanh transformation (default = 1.345, approx. 0.95 efficiency for Gaussian).

eta

Learning rate schedule: either a function of t, or "auto" for 1/t.

method

Optimization method: "gradient" for gradient-based updates with learning rate, or "perturbation" for direct eigenvector computation of the moment matrix (default = "gradient").

verbose

Logical; if TRUE, prints progress and estimated K at each step.

Examples

set.seed(123)
n <- 500; p <- 20; m <- 3
B_true <- qr.Q(qr(matrix(rnorm(p * m), p, m)))
f <- matrix(rnorm(n * m), n, m)
eps <- matrix(rexp(n * p, rate = 1) - 1, n, p) # Asymmetric Laplace-like noise
X <- f %*% t(B_true) + eps

# Using gradient method (default)
out_grad <- online_sir_lfm(X, K_true = m, verbose = TRUE)

# Using perturbation method
out_pert <- online_sir_lfm(X, K_true = m, method = "perturbation", verbose = TRUE)