Conformal Local Influence Screening — clis

Performs scalable, FDR-controlled influence screening for a fitted zero-or-one inflated beta regression model. The conformal normal curvature score of each observation is used as a non-conformity score within a split-conformal procedure: the data are partitioned into a calibration set (presumed clean) and a screening set; conformal p-values are computed for the screening set; and Benjamini-Hochberg adjustment declares an influential subset with false discovery rate controlled at level alpha.

Usage

clis_screen(
  object,
  scheme = "caseweights",
  p = 1L,
  alpha = 0.1,
  calib_frac = 0.5,
  calib_idx = NULL,
  use_fisher = TRUE,
  r_max = 4L,
  score = c("B_Et", "m_r"),
  penalised = FALSE,
  penalty = NULL,
  seed = NULL
)

Arguments

object: A fitted gamlss model of family BEZI or BEOI.
scheme: Character; the perturbation scheme. One of "caseweights" (default), "disccovar", "meancovar", or "preccovar".
p: Integer; covariate index for the covariate-perturbation schemes.
alpha: Numeric in (0, 1); target false discovery rate. Default 0.1.
calib_frac: Numeric in (0, 1); fraction of observations used for conformal calibration when calib_idx is not supplied. Default 0.5.
calib_idx: Optional integer vector of observation indices to use as the calibration set. The conformal false discovery rate guarantee requires the calibration set to be (nearly) free of influential points; when a trusted clean subset is known, supply it here. If NULL (default) a random subset of size floor(calib_frac * n) is drawn, which is appropriate only when influential points are rare.
use_fisher: Logical; use the Fisher information (default TRUE).
r_max: Integer; order for aggregate contributions used as the score.
score: Character; which CNC quantity to use as the non-conformity score: "B_Et" (basic perturbation, default) or "m_r" (aggregate contribution at order r_max).
penalised: Logical; if TRUE, use the penalised information J + S obtained from the smooth terms of an additive gamlss fit, implementing the semiparametric extension. The penalty is extracted with bic_penalty(). Default FALSE.
penalty: Optional penalty matrix, of the dimension of the full coefficient vector, added to the information before inversion. Use this when the smooth basis is supplied explicitly as design columns.
seed: Optional integer for reproducible calibration splitting.

Value

An object of class clis with components:

influential: Integer indices (into the screening set) declared influential at FDR level alpha.
influential_global: Integer indices into the original data.
pvalues: Conformal p-values for the screening set.
padj: Benjamini-Hochberg adjusted p-values.
scores: Non-conformity scores for all observations.
calib_idx, screen_idx: Calibration and screening indices.
alpha, scheme: Inputs echoed back.
decomp: Block decomposition (case-weights scheme only).

Details

Classical local influence diagnostics rank observations by a curvature measure and rely on visual inspection of an index plot against an ad-hoc threshold. This neither scales to large \(n\) nor provides any control of the type-I error rate. CLIS addresses both limitations: the conformal wrapper supplies a finite-sample FDR guarantee, and the per-observation score is computed in linear time after a single model fit.

The calibration set is assumed to be predominantly free of influential observations. Because influential points are typically rare, a random split satisfies this approximately; for adversarial settings, a robust pre-filter can be applied before calibration.

Examples

# \donttest{
if (requireNamespace("gamlss", quietly = TRUE) &&
    requireNamespace("betareg", quietly = TRUE)) {
  data("ReadingSkills", package = "betareg")
  ReadingSkills$dys <- as.numeric(ReadingSkills$dyslexia == "yes")
  fit <- gamlss::gamlss(accuracy1 ~ dys * iq,
                        sigma.formula = ~ dys, nu.formula = ~ iq,
                        family = gamlss.dist::BEOI, data = ReadingSkills,
                        control = gamlss::gamlss.control(trace = FALSE))
  res <- clis_screen(fit, alpha = 0.1, seed = 1)
  print(res)
}
#> Conformal Local Influence Screening
#>   Scheme:        caseweights
#>   Score:         B_Et
#>   Target FDR:    0.1
#>   Observations:  44 (22 calibration, 22 screening)
#>   Declared influential: 0 (FDR <= 0.1)
# }