Conformal prediction method for NeRF+ — nerfplus

This function generates conformal prediction intervals for a fitted NeRF+ model, using a specified calibration dataset to compute the nonconformity scores (measured as the absolute residuals between the observed responses and the predictions) and a specified test dataset for which predictions and prediction intervals are to be generated.

Usage

nerfplus_conformal(
  object,
  x_cal,
  x_cal_embed = NULL,
  y_cal,
  x_test,
  x_test_embed = NULL,
  A_full,
  nodeids_cal = NULL,
  nodeids_test = NULL,
  alpha = 0.05
)

Arguments

object: A fitted NeRF+ model object.
x_cal: A data frame or matrix of calibration data.
x_cal_embed: Optional embedding data frame or matrix for the calibration data, whose rows are aligned with those in x_cal. If provided, it will be used to augment the input x_cal data. Only needed if training embeddings were manually inputted.
y_cal: A vector of observed responses for the calibration data.
x_test: A data frame or matrix of test data for which predictions are to be made.
x_test_embed: Optional embedding data frame or matrix for the test data, whose rows are aligned with those in x_test. If provided, it will be used to augment the input x_test data. Only needed if training embeddings were manually inputted.
A_full: An adjacency matrix representing the network structure for the full set of nodes (training + calibration + testing nodes in that order, unless nodeids_cal and nodeids_test are provided, in which case the order of nodes in A_full should align with the order of node IDs in nodeids_cal and nodeids_test).
nodeids_cal: (Optional) vector of node IDs for the calibration data, of length equal to nrows in x_cal. If provided, node IDs indicate the rows of A_full, corresponding to each calibration sample. If not provided, the rows of A_full are assumed to be in the order of (x_train, x_cal, x_test).
nodeids_test: (Optional) vector of node IDs for the test data, of length equal to nrows in x_test. If provided, node IDs indicate the rows of A_full, corresponding to each test sample. If not provided, the rows of A_full are assumed to be in the order of (x_train, x_cal, x_test).
alpha: Significance level for conformal prediction intervals. Default is 0.05 for 95% prediction intervals.

Value

A tibble with columns pred, lower_bound, and upper_bound, containing the predicted values and the corresponding lower and upper bounds of the conformal prediction intervals for each sample in the test data.

Examples

data(example_data)
train_idx <- 1:(nrow(example_data$x) / 2)
cal_idx <- (nrow(example_data$x) / 2 + 1):nrow(example_data$x)
x_train <- example_data$x[train_idx, ]
y_train <- example_data$y[train_idx]
x_cal <- example_data$x[cal_idx, ]
y_cal <- example_data$y[cal_idx]
nerfplus_out <- nerfplus(
  x = x_train, y = y_train, A = example_data$A[train_idx, train_idx],
  lambda_netcoh = 1,
  lambda_embed = 0.1,
  lambda_raw = 2,
  lambda_stump = 3,
  family = "linear", embedding = "laplacian", sample_split = "none"
)
conformal_out <- nerfplus_conformal(
  nerfplus_out,
  x_cal = x_cal, y_cal = y_cal,
  x_test = example_data$xtest,
  A_full = example_data$A_full,
  alpha = 0.05
)
conformal_out |>
  dplyr::mutate(
   contains_true_y = y_cal >= lower_bound & y_cal <= upper_bound
  ) |>
  dplyr::summarize(
   coverage = mean(contains_true_y)
  )
#> # A tibble: 1 × 1
#>   coverage
#>      <dbl>
#> 1     0.65