first (version 2.1)

first.rank: Factor Ranking via Cumulative Variance that can be explained.

Description

first.tank implements FIRST-RANK algorithm in Huang and Joseph (2025). Parallel computation is available to accelerate the estimation. For categorical inputs, please convert them to factor before calling this function. For large datasets, we support the use of subsample to reduce the computational cost.

Usage

first.rank(
  X,
  y,
  noise,
  n.knn = NULL,
  n.mc = nrow(X),
  twin.mc = FALSE,
  rescale = TRUE,
  parl = NULL
)

Value

ranking

Indices of the factors, ordered from most to least importance

explained.variance

Cumulative variance explained by the factors in the ranking order

Arguments

X

a matrix or data frame for the factors / predictors.

y

a vector for the responses.

noise

a logical indicating whether the responses are noisy.

n.knn

number of nearest-neighbors for the inner loop conditional variance estimation. n.knn=2 is recommended for regression, and n.knn=3 for binary classification.

n.mc

number of Monte Carlo samples for the outer loop expectation estimation.

twin.mc

a logical indicating whether to use twinning subsamples, otherwise random subsamples are used. It is supported when the reduction ratio is at least 2.

rescale

a logical logical indicating whether to standardize the factors / predictors.

parl

number of cores on which to parallelize the computation. If NULL, then no parallelization is done.

Author

Chaofan Huang and V. Roshan Joseph

Details

first.rank provdes factor ranking directly from scattered data via cumulative variance that can be explained. Please see Huang and Joseph (2025) for a more detailed discussion and comparison.

For integer/numeric output, n.knn=2 nearest-neighbors is recommended for the noisy data (Huang and Joseph, 2025), and n.knn=3 nearest-neighbors is suggested for the clean/noiseless data (Broto et al., 2020). For numeric inputs, it is recommended to standardize them via setting the argument rescale=TRUE. Categorical inputs are transformed via one-hot encoding for the nearest-neighbor search. To speed up the nearest-neighbor search, k-d tree from the FNN package is used. Also, parallel computation is also supported via the parallel package.

Last, for large datasets, we support the use of subsamples for further acceleration. Use argument n.mc to specify the number of subsamples. Two options are available for finding the subsamples: random and twinning (Vakayil and Joseph, 2022). Twinning is able to find subsamples that better represent the big data, i.e., providing a more accurate estimation, but at a slightly higher computational cost. For more details, please see the twinning package.

References

Huang, C., & Joseph, V. R. (2025). Factor Importance Ranking and Selection using Total Indices. Technometrics.

Sobol', I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and computers in simulation, 55(1-3), 271-280.

Broto, B., Bachoc, F., & Depecker, M. (2020). Variance reduction for estimation of Shapley effects and adaptation to unknown input distribution. SIAM/ASA Journal on Uncertainty Quantification, 8(2), 693-716.

Vakayil, A., & Joseph, V. R. (2022). Data twinning. Statistical Analysis and Data Mining: The ASA Data Science Journal, 15(5), 598-610.

Examples

ishigami <- function(x) {
  x <- -pi + 2*pi*x
  y <- sin(x[1]) + 7*sin(x[2])^2 + 0.1*x[3]^4*sin(x[1])
  return (y)
}

set.seed(123)
n <- 10000
p <- 3
X <- matrix(runif(n*p), ncol=p)
y <- apply(X,1,ishigami) + rnorm(n)
res <- first.rank(X, y, noise=TRUE, n.knn=2, rescale=FALSE)
res