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Optimal Binning for Multiclass Targets using JEDI M-WOE

Source: R/obn_jedi_mwoe.R
ob_numerical_jedi_mwoe.Rd

Performs supervised discretization of continuous numerical variables for multiclass target variables (e.g., 0, 1, 2). It extends the Joint Entropy-Driven Interval (JEDI) discretization framework to calculate and optimize the Multinomial Weight of Evidence (M-WOE) for each class simultaneously.

Usage

ob_numerical_jedi_mwoe(
  feature,
  target,
  min_bins = 3,
  max_bins = 5,
  bin_cutoff = 0.05,
  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 excluded prior to execution.

target

An integer vector of multiclass outcomes (0, 1, ..., K-1) corresponding to each observation in feature. Must have at least 2 distinct classes.

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 smaller than this threshold are merged. 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 total Multinomial IV to determine convergence. Defaults to 1e-6.

max_iterations

Integer. Safety limit for the maximum number of 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: A numeric matrix where each column represents the WoE for a specific class (One-vs-Rest).

  • iv: A numeric matrix where each column represents the IV contribution for a specific class.

  • count: Integer vector of total observations per bin.

  • class_counts: A matrix of observation counts per class per bin.

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

  • n_classes: The number of distinct target classes found.

Details

Multinomial Weight of Evidence (M-WOE): For a target with \(K\) classes, the WoE for class \(k\) in bin \(i\) is defined using a "One-vs-Rest" approach: $$WOE_{i,k} = \ln\left(\frac{P(X \in bin_i | Y=k)}{P(X \in bin_i | Y \neq k)}\right)$$

Algorithm Workflow:

  1. Multiclass Initialization: The algorithm starts with quantile-based bins and computes the initial event rates for all \(K\) classes.

  2. Joint Monotonicity: The algorithm attempts to enforce monotonicity for all classes. If bin \(i\) violates the trend for Class 1 OR Class 2, it may be merged. This ensures the variable is predictive across the entire spectrum of outcomes.

  3. Global IV Optimization: When reducing the number of bins to max_bins, the algorithm merges the pair of bins that minimizes the loss of the Sum of IVs across all classes: $$Loss = \sum_{k=0}^{K-1} \Delta IV_k$$

This method is ideal for use cases like:

  • predicting loan status (Current, Late, Default)

  • customer churn levels (Active, Dormant, Churned)

  • ordinal survey responses.

See also

ob_numerical_jedi for the binary version.

Examples

# Example: Multiclass target (0, 1, 2)
set.seed(123)
feature <- rnorm(1000)
# Class 0: low feature, Class 1: medium, Class 2: high
target <- cut(feature + rnorm(1000, 0, 0.5),
  breaks = c(-Inf, -0.5, 0.5, Inf),
  labels = FALSE
) - 1

result <- ob_numerical_jedi_mwoe(feature, target,
  min_bins = 3,
  max_bins = 5
)

# Check WoE for Class 2 (High values)
print(result$woe[, 3]) # Column 3 corresponds to Class 2
#> [1] -20.4501899 -20.4501899 -20.4501899 -20.4501899   0.3630006