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Optimal Binning for Numerical Variables using Dynamic Programming

Source: R/obn_dp.R
ob_numerical_dp.Rd

Performs supervised discretization of continuous numerical variables using a greedy heuristic approach that resembles Dynamic Programming. This method is particularly effective at strictly enforcing monotonic trends (ascending or descending) in the Weight of Evidence (WoE), which is critical for the interpretability of logistic regression models in credit scoring.

Usage

ob_numerical_dp(
  feature,
  target,
  min_bins = 3,
  max_bins = 5,
  bin_cutoff = 0.05,
  max_n_prebins = 20,
  convergence_threshold = 1e-06,
  max_iterations = 1000,
  monotonic_trend = c("auto", "ascending", "descending", "none")
)

Arguments

feature

A numeric vector representing the continuous predictor variable. Missing values (NA) should be handled prior to binning, as they are not supported by this algorithm.

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.

bin_cutoff

Numeric. The minimum fraction of total observations required for a bin to be considered valid. Bins with frequency < bin_cutoff will be merged. Value must be in (0, 1). Defaults to 0.05.

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 metrics 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.

monotonic_trend

Character string specifying the desired direction of the Weight of Evidence (WoE) trend.

  • "auto": Automatically determines the most likely trend (ascending or descending) based on the correlation between the feature and the target.

  • "ascending": Forces the WoE to increase as the feature value increases.

  • "descending": Forces the WoE to decrease as the feature value increases.

  • "none": Does not enforce any monotonic constraint (allows peaks and valleys).

Defaults to "auto".

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.

  • event_rate: Numeric vector of the target event rate in each bin.

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

  • total_iv: The total Information Value of the binned variable.

  • monotonic_trend: The actual trend enforced ("ascending", "descending", or "none").

  • execution_time_ms: Execution time in milliseconds.

Details

Although named "DP" (Dynamic Programming) in some contexts, this implementation primarily uses a greedy heuristic to optimize the Information Value (IV) while satisfying constraints.

Algorithm Steps:

  1. Pre-binning: Generates initial granular bins based on quantiles.

  2. Trend Determination: If monotonic_trend = "auto", calculates the Pearson correlation between the feature and target to decide if the WoE should increase or decrease.

  3. Monotonicity Enforcement: Iteratively merges adjacent bins that violate the determined or requested trend.

  4. Constraint Satisfaction: Merges rare bins (below bin_cutoff) and ensures the number of bins is within [min_bins, max_bins].

  5. Optimization: Greedily merges similar bins (based on WoE difference) to reduce complexity while attempting to preserve information.

This method is often preferred when strict business logic dictates a specific relationship direction (e.g., "higher income must imply lower risk").

See also

ob_numerical_cm, ob_numerical_bb

Examples

# Example: forcing a descending trend
set.seed(123)
feature <- runif(1000, 0, 100)
# Target has a complex relationship, but we want to force a linear view
target <- rbinom(1000, 1, 0.5 + 0.003 * feature) # slightly positive trend

# Force "descending" (even if data suggests ascending) to see enforcement
result <- ob_numerical_dp(feature, target,
  min_bins = 3,
  max_bins = 5,
  monotonic_trend = "descending"
)

print(result$bin)
#> [1] "(-Inf;89.189612]"      "(89.189612;95.310121]" "(95.310121;+Inf]"     
print(result$woe) # Should be strictly decreasing
#> [1] -0.05783551  0.64413073  0.53267052