Package {conforest}

Plot method for rfok

Description

A conformal RF based on Johansson et al. (2014). Rather than using a traditional calibration set, conformal intervals are constructed using out-of-bag samples for each tree. K-nearest neighbors is used to calibrate the prediction intervals for each prediction location.

Usage

## S3 method for class 'rfok'
plot(x, conf = 0.95, ...)

Arguments

Value

Invisibly returns x.

Examples

# Friedman function
f <-  function(x){
  10 * sin(pi * x[1] * x[2]) + 20 * (x[3] - 0.5)^2 + 10 * x[4] + 5 * x[5]
}
X <- matrix(runif(250), nrow=50, ncol=5)
y <- apply(X, 1, f)
fit <- rfok(X, y)

plot(fit)

Predict method for rfok

Description

A conformal RF based on Johansson et al. (2014). Rather than using a traditional calibration set, conformal intervals are constructed using out-of-bag samples for each tree. K-nearest neighbors is used to calibrate the prediction intervals for each prediction location.

Usage

## S3 method for class 'rfok'
predict(
  object,
  newdata = NULL,
  samples = 1000,
  conf = NULL,
  smoothing = TRUE,
  eps = 0,
  ...
)

Arguments

Details

Prediction intervals are constructed by estimating a local scale for each prediction point using the k nearest training observations. The conformal margin of error is the requested quantile of the training non-conformity scores multiplied by this local scale.

If samples = NULL, the function returns point predictions and margins of error for the confidence levels supplied in conf. For example, conf = 0.95 uses the 0.95 quantile of the non-conformity scores.

If samples is a positive integer, the function returns simulated predictive samples. When smoothing = TRUE, signed non-conformity scores are generated using quantiles of the symmetrized empirical distribution. When smoothing = FALSE, non-conformity scores are sampled directly with replacement and assigned random signs.

Value

A matrix of predictions with 1 column per test point.

Examples

# Friedman function
f <-  function(x){
  10 * sin(pi * x[1] * x[2]) + 20 * (x[3] - 0.5)^2 + 10 * x[4] + 5 * x[5]
}
X <- matrix(runif(250), nrow=50, ncol=5)
y <- apply(X, 1, f)
fit <- rfok(X, y)

Xnew <- matrix(runif(250), nrow=50, ncol=5)
predict(fit, Xnew)

Print method for rfok objects

Description

Print method for rfok objects

Usage

## S3 method for class 'rfok'
print(x, ...)

Arguments

Value

Invisibly returns x.

Conformal Random Forest with Out-of-bag KNN

Description

A conformal RF based on Johansson et al. (2014). Rather than using a traditional calibration set, conformal intervals are constructed using out-of-bag samples for each tree. K-nearest neighbors is used to calibrate the prediction intervals for each prediction location.

Usage

rfok(X, y, k = 5, beta = sd(y)/30, eps = 0, ...)

Arguments

Details

This function fits a random forest and constructs conformal prediction intervals using out-of-bag (OOB) predictions. For each training observation, an OOB prediction is computed using only trees for which that observation was not included in the bootstrap sample. These OOB predictions are used to form residuals without requiring a separate calibration set.

Local scale estimates are computed using the k nearest neighbors in the predictor space. For observation i, the local scale estimate \mu_i is the average absolute OOB residual among its nearest neighbors. The non-conformity score is

\alpha_i = \frac{|y_i - \hat{y}^{OOB}_i|}{\mu_i + \beta}.

The parameter k controls the locality of the scale estimate. Smaller values make the intervals more locally adaptive, while larger values produce smoother, more stable local scale estimates.

The parameter beta is a non-negative stabilization parameter added to the local scale estimate. Smaller values make the intervals more sensitive to local changes in the OOB residuals. Larger values reduce this sensitivity and make the intervals behave more like globally scaled conformal intervals. The default, sd(y) / 30, is a scale-aware value intended to provide mild stabilization.

The parameter eps is passed to the nearest-neighbor search. Setting eps = 0 uses exact nearest neighbors. Larger values allow approximate nearest-neighbor search and may be faster for large data sets.

Value

An object with class "rfok"

References

Johansson, U., Boström, H., Löfström, T., & Linusson, H. (2014). Regression conformal prediction with random forests. Machine learning, 97, 155-176.

Examples

# Friedman function
f <-  function(x){
  10 * sin(pi * x[1] * x[2]) + 20 * (x[3] - 0.5)^2 + 10 * x[4] + 5 * x[5]
}
X <- matrix(runif(250), nrow=50, ncol=5)
y <- apply(X, 1, f)
fit <- rfok(X, y)

Xnew <- matrix(runif(250), nrow=50, ncol=5)
predict(fit, Xnew)

Cross-validate the rfok sensitivity parameter

Description

Cross-validates the sensitivity parameter beta for an rfok model over a user-supplied or automatically generated grid.

Usage

rfok_cv_beta(
  X,
  y,
  beta = NULL,
  beta_mult = c(0, 1/100, 1/50, 1/30, 1/20, 1/10),
  k = 5,
  num_folds = 5,
  selection_rule = c("crps", "interval_score", "coverage_width"),
  conf = 0.95,
  samples = 1000,
  smoothing = TRUE,
  eps = 0,
  return_fit = FALSE,
  verbose = TRUE,
  ...
)

Arguments

Details

The parameter beta controls the sensitivity of the conformal interval widths to the local out-of-bag residual scale estimate. Smaller values make intervals more locally adaptive, while larger values make intervals more stable and more similar to globally scaled conformal intervals.

This function evaluates candidate beta values using cross-validation. For selection_rule = "crps", predictive samples are generated for each held-out observation and the candidate with the smallest average continuous ranked probability score is selected.

For selection_rule = "interval_score", conformal intervals are constructed at level conf and the candidate with the smallest average interval score is selected. The interval score rewards narrow intervals but penalizes observations that fall outside the interval.

For selection_rule = "coverage_width", the selected candidate is the one with the smallest average interval width among candidates with empirical coverage at least conf. If no candidate reaches the desired coverage, the candidate with the largest empirical coverage is selected, with ties broken by average interval width.

Value

A data frame with one row per candidate beta. The selected beta is marked in the selected column. If return_fit = TRUE, a list is returned with elements results, best_beta, and fit.

Summary method for rfok objects

Description

Summary method for rfok objects

Usage

## S3 method for class 'rfok'
summary(object, ...)

Arguments

Value

An object of class "summary.rfok".