Regularised and Information-Theoretic Sufficient Dimension Reduction

Implements covariance-stabilised sufficient dimension reduction for continuous responses, with an additional sparse engine for continuous, categorical, and right-censored survival responses and information-theoretic structural dimension selection. Supported methods include sliced inverse regression, sliced average variance estimation, directional regression, and principal Hessian directions. Sample, ridge, Oracle Approximating Shrinkage, Ledoit-Wolf, and Maximum Entropy Covariance (MEC) estimators are provided alongside prediction, resampling, simulation, and diagnostic utilities. The sufficient dimension reduction methods build on Li (1991) , Li (1992) , and Li and Wang (2007) . Covariance shrinkage follows Olorede and Yahya (2019) , Ledoit and Wolf (2004) and Chen et al. (2010) .

risdr

risdr provides a reproducible framework for comparative sufficient dimension reduction with covariance regularisation and information-theoretic structural dimension selection. The existing fit_risdr() interface supports continuous responses. Version 0.4.0 adds explicit sparse, categorical, and survival interfaces without changing the 0.3.1 API.

The package implements:

• sliced inverse regression (SIR);
• sliced average variance estimation (SAVE);
• directional regression (DR);
• principal Hessian directions (pHd);
• sample, ridge, Oracle Approximating Shrinkage (OAS), Ledoit-Wolf (LW), and Maximum Entropy Covariance (MEC) estimators;
• AIC, BIC, CAIC, ICOMP, and CICOMP structural dimension criteria;
• V-fold, repeated, and complexity-aware cross-validation;
• prediction diagnostics, subspace recovery measures, simulation utilities, and base R plotting methods.

Sparse and survival workflow

fit_risdr_sparse() implements the frozen thesis engine, including joint selection of structural dimension and sparsity. fit_risdr_dual() performs sample-space PCA for large predictor sets. fit_risdr_sparse_realdata() adds outcome cleaning and a variance screen.

set.seed(2026)
X <- matrix(rnorm(100 * 8), nrow = 100)
colnames(X) <- paste0("Gene", seq_len(ncol(X)))
event_time <- rexp(100, rate = exp(0.5 * X[, 1]))
censor_time <- rexp(100, rate = 0.5)
time <- pmin(event_time, censor_time)
delta <- as.integer(event_time <= censor_time)
fit <- fit_risdr_sparse(
  X, time, delta = delta, response_type = "survival",
  sdr_method = "sir", cov_method = "oas", nslices = 4,
  d_max = 3, lambda_grid = c(0, 0.05, 0.1)
)
fit$selection_grid
predict(fit, X[1:2, , drop = FALSE], type = "risk")

Survival selection uses Efron Cox partial likelihood and defaults to support_penalty = FALSE. C1F weights are contributions in predictor coordinates. Dual variable rankings use the selected mapped directions; thresholding PCA coordinates does not imply a sparse original-gene support. These are exploratory methods. Independent validation and proportional-hazards diagnostics must be performed separately for a particular application.

See vignette("sparse-survival", package = "risdr") and THESIS_PROVENANCE.md for migration and provenance.

Development status

Version 0.4.0 is the sparse and survival release candidate. CRAN currently publishes 0.3.1. The frozen thesis package was locally versioned 0.3.2; its analysis provenance remains tied to that frozen version.

Version 0.3.1 is the first CRAN release of risdr, published on 28 July 2026. It is available from CRAN with DOI [10.32614/CRAN.package.risdr] (https://doi.org/10.32614/CRAN.package.risdr). The release is also archived on Zenodo under version DOI [10.5281/zenodo.21728851] (https://doi.org/10.5281/zenodo.21728851). The Zenodo concept DOI [10.5281/zenodo.21728850] (https://doi.org/10.5281/zenodo.21728850) identifies all archived versions.

Installation

Install the current CRAN release with:

install.packages("risdr")
library(risdr)

Install the current development version from GitHub with:

install.packages(
  paste0(
    "https://github.com/ilovemaths/risdr/",
    "archive/refs/heads/main.tar.gz"
  ),
  repos = NULL,
  type = "source"
)

Minimal example

library(risdr)

set.seed(2026)

sim <- simulate_risdr_data(
  n = 160,
  p = 20,
  d = 2,
  rho = 0.6,
  model = "linear_quadratic",
  seed = 2026
)

fit <- fit_risdr(
  X = sim$X,
  y = sim$y,
  sdr_method = "dr",
  cov_method = "oas",
  nslices = 6,
  d_max = 6,
  selector = "cicomp"
)

fit
summary(fit)

prediction <- predict(fit, sim$X[1:10, , drop = FALSE])
evaluate_prediction(sim$y[1:10], prediction, d = fit$d)

Component-specific arguments are separated explicitly:

fit_ridge <- fit_risdr(
  X = sim$X,
  y = sim$y,
  sdr_method = "sir",
  cov_method = "ridge",
  d = 2,
  d_max = 4,
  cov_args = list(lambda = 0.15),
  stabilization_args = list(eps = 1e-7),
  sdr_args = list(slice_type = "quantile")
)

Structural dimension assessment

cv <- select_dimension_cv(
  X = sim$X,
  y = sim$y,
  sdr_method = "dr",
  cov_method = "oas",
  d_max = 5,
  v = 5,
  seed = 2026
)

cv$selected_d
cv$cv_table

See the package vignettes for the complete workflow, EPI case study, simulation design, covariance regularisation, and structural dimension selection.

Scope and reproducibility

All stochastic examples expose seeds. Training-set centring and scaling are stored in fitted objects and reused for prediction. The package records failed resampling fits rather than silently discarding them.

The supplied processed EPI training and test matrices are included under inst/extdata/epi, together with selected summary outputs from the completed thesis. The original single-file EPI corpus is not redistributed. Simulation fixtures are legacy records and must not be treated as newly validated results.

The corrected Simulation A, B1, and B2 workflow is configured in config.yml and can be run from the repository root with:

Rscript analysis/reproduce_simulations.R config.yml

Corrected files receive a _corrected_v0_3_0 suffix, so the workflow cannot overwrite the supplied legacy results.

Licence

risdr is released under GPL version 3 or later.