Conformal Prediction with Spatial Dependence

Constructs distribution-free prediction intervals with finite-sample coverage guarantees, adjusted for spatial autocorrelation. Standard conformal prediction assumes exchangeability, which spatial data violates. This function uses spatially-blocked calibration residuals as nonconformity scores, producing intervals that maintain coverage even under dependence.

Usage

borg_conformal(
  model,
  data,
  new = NULL,
  target,
  coords = NULL,
  alpha = 0.1,
  method = c("split", "block_jackknife", "block_cv"),
  folds = NULL,
  n_blocks = 10,
  type = c("regression", "classification"),
  seed = 42
)

Arguments

model

A fitted model with a predict() method.

data

Data frame used to compute nonconformity scores (calibration set).

new

Data frame of new locations for prediction. If NULL, computes intervals for data via leave-one-block-out.

target

Character. Target variable name in data.

coords

Character vector of length 2. Coordinate column names. If provided, uses spatial blocking for calibration.

alpha

Numeric. Miscoverage level. Default: 0.1 (90% intervals).

method

Character. Conformal method: "split" (default) uses a held-out calibration set, "block_jackknife" uses leave-one-block-out, "block_cv" uses blocked cross-validation residuals.

folds

A borg_cv object or fold list. If provided, residuals are computed from these folds (respecting spatial structure). Overrides internal blocking.

n_blocks

Integer. Number of spatial blocks if folds is NULL and coords is provided. Default: 10.

type

Character. For classification: "regression" (default) or "classification". Classification uses adaptive prediction sets.

seed

Integer. Random seed. Default: 42.

Value

A data frame with class "borg_conformal" containing:

prediction

Point prediction

lower

Lower bound of prediction interval

upper

Upper bound of prediction interval

width

Interval width (upper - lower)

x and y

Coordinates (if coords provided and new has them)

Attributes include alpha, method, coverage_estimate, and quantile_score (the nonconformity threshold).

Details

Why spatial conformal?

Standard split conformal prediction computes residuals on a random calibration set. Under spatial autocorrelation, nearby calibration points produce correlated residuals, leading to underestimated interval widths and actual coverage below the nominal level.

By using spatially-blocked calibration (where residuals come from predictions on spatially separated test folds), the effective sample size of nonconformity scores is honest, and coverage guarantees hold approximately even under dependence.

Methods

"split"

Splits data into training and calibration sets using spatial blocks. Fast, but uses only part of the data.

"block_jackknife"

Leave-one-block-out: refit the model excluding each block, predict on the held-out block. More data-efficient but slower.

"block_cv"

Use pre-computed blocked CV residuals from a borg_cv object. Requires folds.

References

Mao, H., Martin, R., & Reich, B. J. (2024). Valid prediction inference with spatial conformal methods. arXiv preprint arXiv:2403.14058.

Johnstone, C., & Cox, D. (2023). Conformal prediction with spatial data.

Vovk, V., Gammerman, A., & Shafer, G. (2005). Algorithmic Learning in a Random World. Springer.

Examples

set.seed(42)
d <- data.frame(x = runif(200), y = runif(200), a = rnorm(200))
d$z <- 2 * d$a + sin(d$x * 10) + rnorm(200, sd = 0.5)
model <- lm(z ~ a + x + y, data = d)

# Split conformal with spatial blocking
conf <- borg_conformal(model, d, target = "z", coords = c("x", "y"))
conf

# Predict on new locations
new <- data.frame(x = runif(50), y = runif(50), a = rnorm(50))
pred <- borg_conformal(model, d, new = new, target = "z",
                        coords = c("x", "y"))