Optimal Binning using Fisher's Exact Test

Performs supervised discretization of continuous numerical variables using Fisher's Exact Test. This method iteratively merges adjacent bins that are statistically similar (highest p-value) while strictly enforcing a monotonic Weight of Evidence (WoE) trend.

Usage

ob_numerical_fetb(
  feature,
  target,
  min_bins = 3,
  max_bins = 5,
  max_n_prebins = 20,
  convergence_threshold = 1e-06,
  max_iterations = 1000
)

Arguments

feature

A numeric vector representing the continuous predictor variable. Missing values (NA) should be handled prior to binning.

target

An integer vector of binary outcomes (0/1) corresponding to each observation in feature. Must have the same length as feature.

min_bins

Integer. The minimum number of bins to produce. Must be \(\ge\) 2. Defaults to 3.

max_bins

Integer. The maximum number of bins to produce. Must be \(\ge\) min_bins. Defaults to 5.

max_n_prebins

Integer. The number of initial quantiles to generate during the pre-binning phase. Defaults to 20.

convergence_threshold

Numeric. The threshold for the change in Information Value (IV) to determine convergence during the iterative merging process. Defaults to 1e-6.

max_iterations

Integer. Safety limit for the maximum number of merging iterations. Defaults to 1000.

Value

A list containing the binning results:

• id: Integer vector of bin identifiers.

• bin: Character vector of bin labels in interval notation.

• woe: Numeric vector of Weight of Evidence for each bin.

• iv: Numeric vector of Information Value contribution per bin.

• count: Integer vector of total observations per bin.

• count_pos: Integer vector of positive cases.

• count_neg: Integer vector of negative cases.

• cutpoints: Numeric vector of upper boundaries (excluding Inf).

• converged: Logical indicating if the algorithm converged.

• iterations: Integer count of iterations performed.

Details

The Fisher's Exact Test Binning (FETB) algorithm provides a robust statistical alternative to ChiMerge.

Key Differences from ChiMerge:

• Exact Probability: Instead of relying on the Chi-Square asymptotic approximation (which can be unreliable for small bin counts), FETB calculates the exact hypergeometric probability of independence between the bin index and the target.

• Merge Criterion: In each step, the algorithm identifies the pair of adjacent bins with the highest p-value (indicating they are the most statistically indistinguishable) and merges them.

• Monotonicity: The algorithm incorporates a check after every merge to ensure the WoE trend remains monotonic, merging strictly violating bins immediately.

This method is particularly recommended when working with smaller datasets or highly imbalanced target classes, where the assumptions of the Chi-Square test might be violated.

See also

ob_numerical_cm

Examples

# Example: Binning a small dataset where Fisher's Exact Test excels
set.seed(123)
feature <- rnorm(100)
target <- rbinom(100, 1, 0.2)

result <- ob_numerical_fetb(feature, target,
  min_bins = 2,
  max_bins = 4,
  max_n_prebins = 10
)

print(result$bin)
#> [1] "(-inf; -1.06782]"    "(-1.06782; 1.36065]" "(1.36065; inf]"     
print(result$woe)
#> [1] -1.6521490  0.1035344  0.1685980