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Jackknife+ Conformal Prediction Intervals

Source: R/conformal_jackknife.R
conformal_jackknife.Rd

Constructs prediction intervals using the Jackknife+ method of Barber et al. (2021). Uses leave-one-out models to form prediction intervals with finite-sample coverage guarantees.

Usage

conformal_jackknife(
  x,
  y,
  model,
  x_new = NULL,
  alpha = 0.1,
  plus = TRUE,
  verbose = FALSE,
  seed = NULL
)

Arguments

x

A numeric matrix or data frame of predictor variables.

y

A numeric vector of response values.

model

A fitted model object (e.g., from lm()), a make_model() specification, or a formula (which will fit a linear model).

x_new

A numeric matrix or data frame of new predictor variables. If NULL, intervals are computed for the training data.

alpha

Miscoverage level. Default 0.10 gives 90 percent prediction intervals.

plus

Logical. If TRUE (default), uses the Jackknife+ method. If FALSE, uses the basic jackknife.

verbose

Logical. If TRUE, shows a progress bar during LOO fitting. Default FALSE.

seed

Optional random seed for reproducible data splitting.

Value

A predictset_reg object. See conformal_split() for details. The method component is "jackknife_plus" or "jackknife". Additional components include loo_models (list of n leave-one-out fitted models) and loo_residuals (numeric vector of LOO absolute residuals).

Details

The Jackknife+ method fits n leave-one-out models and uses each model's prediction at the test point, shifted by the corresponding LOO residual, to construct the interval. This is distinct from basic jackknife, which centres a single full-model prediction and adds a quantile of the LOO residuals.

The Jackknife+ theoretical coverage guarantee is \(1 - 2\alpha\), not \(1 - \alpha\) (Barber et al. 2021, Theorem 1). This is weaker than split conformal's \(1 - \alpha\) guarantee. In practice, Jackknife+ coverage is typically much closer to \(1 - \alpha\).

References

Barber, R.F., Candes, E.J., Ramdas, A. and Tibshirani, R.J. (2021). Predictive inference with the jackknife+. Annals of Statistics, 49(1), 486–507.

See also

Other regression methods: conformal_aci(), conformal_cqr(), conformal_cv(), conformal_mondrian(), conformal_split(), conformal_weighted()

Examples

set.seed(42)
n <- 50
x <- matrix(rnorm(n * 2), ncol = 2)
y <- x[, 1] + rnorm(n)
x_new <- matrix(rnorm(10 * 2), ncol = 2)

# \donttest{
result <- conformal_jackknife(x, y, model = y ~ ., x_new = x_new)
print(result)
#> 
#> ── Conformal Prediction Intervals (Jackknife+) ─────────────────────────────────
#> • Coverage target: "90%"
#> • Training: 50 | Calibration: 50 | Predictions: 10
#> • Median LOO residual: 0.4319
#> • Median interval width: 3.0956
# }