Fit regularised and information-theoretic sufficient dimension reduction

Fits an SDR model using a regularised covariance estimator, a selected inverse-regression kernel, adaptive sparse direction estimation, and information-criterion profiling jointly over structural dimension and sparsity tuning parameter.

Usage

fit_risdr_sparse(
  X,
  y,
  delta = NULL,
  response_type = c("continuous", "categorical", "survival"),
  sdr_method = c("dr", "sir", "save", "phd"),
  cov_method = c("mec", "oas", "lw", "sample", "ridge", "user"),
  stabilize = TRUE,
  stabilization = c("eigenfloor", "ridge", "nearest_pd"),
  nslices = 6L,
  d = NULL,
  d_max = 10L,
  selector = c("cicomp", "icomp", "bic", "caic", "aic"),
  standardize = TRUE,
  complexity = "C1F",
  lambda_grid = seq(0, 0.3, length.out = 10L),
  adapt_weights = TRUE,
  weight_mode = c("c1f", "inverse_c1f", "uniform"),
  penalty_weights = NULL,
  support_penalty = FALSE,
  cov_fun = NULL,
  shrinkage = 1e-04,
  tol = 1e-10,
  ...
)

Arguments

X: Numeric predictor matrix or data frame.
y: Response vector. For survival data, observed survival time.
delta: Optional 0/1 event indicator for survival data.
response_type: One of "continuous", "categorical", or "survival".
sdr_method: One of "dr", "sir", "save", or "phd".
cov_method: One of "mec", "oas", "lw", "sample", "ridge", or "user".
stabilize: Logical. Stage-3 thesis fits require covariance stabilisation and therefore currently require TRUE.
stabilization: Stabilisation method passed to estimate_cov().
nslices: Number of response slices, or slices per censoring-status group for survival data.
d: Optional fixed structural dimension. If NULL, selected by selector from candidates 1 through d_max.
d_max: Maximum candidate structural dimension.
selector: One of "cicomp", "icomp", "bic", "caic", or "aic".
standardize: Logical. Standardise predictor columns before fitting.
complexity: Retained for compatibility. The Stage-3 thesis engine uses the scale-invariant C1F complexity in ICOMP/CICOMP.
lambda_grid: Non-negative sparsity tuning grid.
adapt_weights: Logical. Use covariance-derived adaptive weights.
weight_mode: One of "c1f", "inverse_c1f", or "uniform".
penalty_weights: Optional user-supplied variable-level weights.
support_penalty: Logical. If TRUE, active-support size contributes to the effective parameter count in the information criteria.
cov_fun: Optional user-defined covariance estimator.
shrinkage: Ridge shrinkage parameter used by estimate_cov().
tol: Numerical tolerance.
...: Additional arguments passed only to a user covariance estimator.

Value

An object of class risdr containing the complete (d, lambda) selection grid, profiled dimension table, selected sparse directions, reduced predictors, covariance diagnostics, and compatibility fields.

Details

For d = NULL, every candidate dimension from 1 through d_max is evaluated over the complete lambda_grid. The requested selector then chooses the final (d, lambda) pair. For explicit d, the same audit grid is retained but the final dimension is fixed and only lambda is selected within that dimension.

This entry point uses the frozen sparse thesis engine. The existing fit_risdr() and fit_risdr_realdata() interfaces retain their continuous-response behaviour from version 0.3.1. Survival fits use Efron Cox partial likelihood. Apparent fit statistics and loading ranks are exploratory and do not establish external predictive validity.

Examples

set.seed(2026)
X <- matrix(rnorm(80 * 6), 80)
colnames(X) <- paste0("G", 1:6)
time <- rexp(80, rate = exp(0.5 * X[, 1]))
delta <- rep(c(0L, 1L), 40)
fit <- fit_risdr_sparse(
  X, time, delta = delta, response_type = "survival",
  sdr_method = "sir", cov_method = "oas", nslices = 4,
  d_max = 2, lambda_grid = c(0, 0.05)
)
fit$d
#> [1] 1
predict(fit, X[1:2, , drop = FALSE], type = "risk")
#>         1         2 
#> 0.9311306 0.5012283