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Select a stable high-dimensional submodel core with CPSS

Source: R/cpss-selection.R
cpss_select_core.Rd

cpss_select_core() implements complementary-pairs stability selection (CPSS) with a size-budgeted LASSO or MCP base selector. Selection must be performed on data independent of any sample later used for the conditional-Gaussian exact-null test. CPSS itself is due to Shah and Samworth (2013); this function supplies the core-selection stage used by the package's CPSS–SM endpoint.

Usage

cpss_select_core(
  X,
  y,
  selector = c("lasso", "mcp"),
  complementary_pairs = 50L,
  base_selection_size = 20L,
  stability_threshold = 0.6,
  seed = NULL,
  path_points = 100L,
  lambda_min_ratio = 0.01,
  coefficient_tolerance = 1e-08,
  lasso_maxit = 100000L,
  mcp_gamma = 3,
  mcp_max_iter = 100000L,
  no_top_k_fallback = TRUE,
  strata = NULL,
  mandatory_core = NULL,
  candidate_set = NULL,
  rank_tolerance = 1e-10
)

Arguments

X

Numeric selection-sample design matrix.

y

Numeric selection-sample response.

selector

Base selector, either "lasso" or "mcp".

complementary_pairs

Number of complementary half-sample pairs.

base_selection_size

Maximum support size of each base fit.

stability_threshold

Inclusion-frequency threshold. The usual Meinshausen–Buehlmann PFER expression is only reported above one half.

seed

Optional reproducible resampling seed.

path_points

Number of penalty-path points per base fit.

lambda_min_ratio

Path lower-bound control. It is passed as lambda.min.ratio to glmnet for LASSO and as the lambda.min fraction of lambda.max to grpreg for the singleton-group MCP sensitivity path.

coefficient_tolerance

Numerical support threshold.

lasso_maxit

Maximum glmnet iterations.

mcp_gamma

MCP concavity parameter.

mcp_max_iter

Maximum total grpreg iterations over the MCP path.

no_top_k_fallback

Must be TRUE. An empty thresholded core is returned without a data-dependent top-k replacement. If a mandatory core is supplied, an empty CPSS extension leaves the mandatory core unchanged.

strata

Optional resampling strata with one entry per row.

mandatory_core

Optional one-based indices or feature names that are always retained. Within every half-sample they are centered and projected out by a checked economy SVD before the base selector is fitted. Mandatory variables are outside the CPSS frequency and PFER family.

candidate_set

Optional one-based indices or feature names eligible for CPSS selection. The default is every predictor outside mandatory_core.

rank_tolerance

Relative SVD tolerance for mandatory-core residualization.

Value

A cpss_core_selection object containing the selected indices, selection frequencies, feature identities, and base-fit diagnostics.

References

Meinshausen, N. and Buehlmann, P. (2010). Stability selection. Journal of the Royal Statistical Society: Series B, 72, 417–473. doi:10.1111/j.1467-9868.2010.00740.x

Shah, R. D. and Samworth, R. J. (2013). Variable selection with error control: another look at stability selection. Journal of the Royal Statistical Society: Series B, 75, 55–80. doi:10.1111/j.1467-9868.2011.01034.x