Shrinkage Principal Fitted Components with Information Complexity-Based Model Selection

Implements shrinkage principal fitted components for sufficient dimension reduction in high-dimensional regression and classification. Provides regularised covariance estimation using Oracle Approximating Shrinkage and Maximum Entropy Covariance, structural-dimension selection using conventional and information-complexity criteria, response-guided feature screening, reduced-space prediction, and simulation utilities. Methodological foundations include Cook and Forzani (2008) , Chen et al. (2010) , Bozdogan (2000) , and Olorede and Yahya (2019) .

spfcICOMP

spfcICOMP implements Shrinkage Principal Fitted Components (SPFC) for high-dimensional sufficient dimension reduction, structural-dimension selection, feature screening, regression, and classification.

The package currently provides:

• regularised covariance estimation, including Oracle Approximating Shrinkage (OAS) and Maximum Entropy Covariance (MEC);
• Principal Fitted Components estimation for continuous and categorical responses;
• structural-dimension selection using AIC, BIC, CAIC, ICOMP(IFIM), and CICOMP;
• C1F-calibrated original-feature screening;
• reduced-space regression and classification;
• simulation and benchmarking utilities.

Release status

Version 0.1.0 is the initial CRAN release candidate. The exact source tarball has passed the local test suite and CRAN-style check. The release commit remains subject to the five-platform GitHub Actions matrix before submission.

Installation from GitHub

The development version can be installed from GitHub with either pak or remotes:

pak::pak("ilovemaths/spfcICOMP")
# or
remotes::install_github("ilovemaths/spfcICOMP")

Basic example

library(spfcICOMP)

set.seed(123)
X <- matrix(rnorm(40 * 10), nrow = 40, ncol = 10)
y <- X[, 1] - 0.5 * X[, 2] + rnorm(40)

fit <- spfc_fit(
  X = X,
  y = y,
  d = 1,
  ytype = "continuous",
  cov_method = "mec",
  nslices = 5,
  poly_degree = 2
)

fit
summary(fit)
head(fitted(fit))

Automatic structural-dimension selection is available through spfc_select_dimension():

dsel <- spfc_select_dimension(
  X = X,
  y = y,
  d_grid = 1:3,
  cov_method = "mec",
  ytype = "continuous"
)

dsel$selected

Benchmark data and thesis reproducibility

Third-party Riboflavin and Golub gene-expression datasets are not bundled in the CRAN package. The research scripts under thesis_analysis/ obtain the benchmarks from their established statistical-data packages when required:

• Riboflavin from the archived CRAN hdi 0.1-10 source via an archive-safe loader;
• Golub leukaemia from Bioconductor package multtest.

These optional research-data packages are not required for the normal installation, tests, vignettes, or examples of spfcICOMP. See thesis_analysis/README.md for the frozen empirical-analysis settings and run order.

Methodological references

• Cook, R. D. and Forzani, L. (2008). Principal Fitted Components for dimension reduction in regression. Statistical Science, 23(4), 485-501. doi:10.1214/08-STS275.
• Chen, Y., Wiesel, A., Eldar, Y. C. and Hero, A. O. (2010). Shrinkage algorithms for MMSE covariance estimation. IEEE Transactions on Signal Processing, 58(10), 5016-5029. doi:10.1109/TSP.2010.2053029.
• Bozdogan, H. (2000). Akaike's Information Criterion and recent developments in information complexity. Journal of Mathematical Psychology, 44(1), 62-91. doi:10.1006/jmps.1999.1277.
• Olorede, K. O. and Yahya, W. B. (2019). A new covariance estimator for sufficient dimension reduction in high-dimensional and undersized sample problems. arXiv. doi:10.48550/arXiv.1909.13017.

Licence

MIT.