Weighted Conformal Prediction Intervals

Constructs prediction intervals using weighted split conformal inference, designed for settings with covariate shift where calibration and test data may have different distributions. Importance weights re-weight the calibration scores to account for this shift.

Usage

conformal_weighted(
  x,
  y,
  model,
  x_new,
  weights = NULL,
  alpha = 0.1,
  cal_fraction = 0.5,
  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, a make_model() specification, or a formula.

x_new

A numeric matrix or data frame of new predictor variables.

weights

A numeric vector of importance weights for each observation in x, with length equal to nrow(x). Weights must be non-negative. If NULL, uniform weights are used (equivalent to standard split conformal).

alpha

Miscoverage level. Default 0.10.

cal_fraction

Fraction of data used for calibration. Default 0.5.

seed

Optional random seed.

Value

A predictset_reg object. See conformal_split() for details. The method component is "weighted".

Details

The test-point weight \(w_{n+1}\) is set to the mean of calibration weights, following standard practice when the true test weight is unknown. See Tibshirani et al. (2019), Equation 5.

References

Tibshirani, R.J., Barber, R.F., Candes, E.J. and Ramdas, A. (2019). Conformal prediction under covariate shift. Advances in Neural Information Processing Systems, 32.

See also

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

Examples

set.seed(42)
n <- 400
x <- matrix(rnorm(n * 3), ncol = 3)
y <- x[, 1] * 2 + rnorm(n)
x_new <- matrix(rnorm(50 * 3, mean = 1), ncol = 3)
weights <- rep(1, n)

# \donttest{
result <- conformal_weighted(x, y, model = y ~ ., x_new = x_new,
                              weights = weights)
print(result)
#> 
#> ── Conformal Prediction Intervals (Weighted Conformal) ─────────────────────────
#> • Coverage target: "90%"
#> • Training: 200 | Calibration: 200 | Predictions: 50
#> • Conformal quantile: 1.648
#> • Median interval width: 3.296
# }