OptimalBinningWoE (version 1.0.8)

ob_categorical_swb: Optimal Binning for Categorical Variables using Sliding Window Binning (SWB)

Description

This function performs optimal binning for categorical variables using the Sliding Window Binning (SWB) algorithm. This approach combines initial grouping based on frequency thresholds with iterative optimization to achieve monotonic Weight of Evidence (WoE) while maximizing Information Value (IV).

Usage

ob_categorical_swb(
  feature,
  target,
  min_bins = 3L,
  max_bins = 5L,
  bin_cutoff = 0.05,
  max_n_prebins = 20L,
  bin_separator = "%;%",
  convergence_threshold = 1e-06,
  max_iterations = 1000L
)

Value

A list containing the results of the optimal binning procedure:

id

Numeric vector of bin identifiers (1 to n_bins)

bin

Character vector of bin labels, which are combinations of original categories separated by bin_separator

woe

Numeric vector of Weight of Evidence values for each bin

iv

Numeric vector of Information Values for each bin

count

Integer vector of total observations in each bin

count_pos

Integer vector of positive outcomes in each bin

count_neg

Integer vector of negative outcomes in each bin

event_rate

Numeric vector of the observed event rate in each bin

total_iv

Numeric scalar. Total Information Value across all bins

converged

Logical. Whether the algorithm converged within specified tolerances

iterations

Integer. Number of iterations performed

Arguments

feature

A character vector or factor representing the categorical predictor variable. Missing values (NA) will be converted to the string "NA" and treated as a separate category.

target

An integer vector containing binary outcome values (0 or 1). Must be the same length as feature. Cannot contain missing values.

min_bins

Integer. Minimum number of bins to create. Must be at least 1. Default is 3.

max_bins

Integer. Maximum number of bins to create. Must be greater than or equal to min_bins. Default is 5.

bin_cutoff

Numeric. Minimum relative frequency threshold for individual categories. Categories with frequency below this proportion will be grouped together into a single "rare" bin. Value must be between 0 and 1. Default is 0.05 (5%).

max_n_prebins

Integer. Maximum number of initial bins created after the frequency-based grouping step. Used to control early-stage complexity. Default is 20.

bin_separator

Character string used to separate category names when multiple categories are merged into a single bin. Default is "%;%".

convergence_threshold

Numeric. Threshold for determining algorithm convergence based on changes in total Information Value between iterations. Default is 1e-6.

max_iterations

Integer. Maximum number of iterations for the optimization process. Default is 1000.

Details

The SWB algorithm follows these steps:

1. Initialization: Categories are initially grouped based on frequency thresholds (bin_cutoff), separating frequent categories from rare ones.

2. Preprocessing: Initial bins are sorted by their WoE values to establish a baseline ordering.

3. Sliding Window Optimization: An iterative process evaluates adjacent bin pairs and merges those that contribute least to the overall Information Value or violate monotonicity constraints.

4. Constraint Enforcement: The final binning respects the specified min_bins and max_bins limits while maintaining WoE monotonicity.

Key features of this implementation:

• Frequency-based Pre-grouping: Automatically identifies and groups rare categories to reduce dimensionality.

• Statistical Similarity Measures: Utilizes Jensen-Shannon divergence to determine optimal merge candidates.

• Monotonicity Preservation: Ensures final bins exhibit consistent WoE trends (either increasing or decreasing).

• Laplace Smoothing: Employs additive smoothing to prevent numerical instabilities in WoE/IV calculations.

Mathematical concepts:

Weight of Evidence (WoE) with Laplace smoothing: $$WoE = \ln\left(\frac{(p_{pos} + \alpha)/(N_{pos} + 2\alpha)}{(p_{neg} + \alpha)/(N_{neg} + 2\alpha)}\right)$$

Information Value (IV): $$IV = \left(\frac{p_{pos} + \alpha}{N_{pos} + 2\alpha} - \frac{p_{neg} + \alpha}{N_{neg} + 2\alpha}\right) \times WoE$$

where \(p_{pos}\) and \(p_{neg}\) are bin-level counts, \(N_{pos}\) and \(N_{neg}\) are dataset-level totals, and \(\alpha\) is the smoothing parameter (default 0.5).

Jensen-Shannon Divergence between two bins: $$JSD(P||Q) = \frac{1}{2}\left[KL(P||M) + KL(Q||M)\right]$$ where \(M = \frac{1}{2}(P+Q)\) and \(KL\) represents Kullback-Leibler divergence.

Examples

# Generate sample data with varying category frequencies
set.seed(456)
n <- 5000
# Create categories with power-law frequency distribution
categories <- c(
  rep("A", 1500), rep("B", 1000), rep("C", 800),
  rep("D", 500), rep("E", 300), rep("F", 200),
  sample(letters[7:26], 700, replace = TRUE)
)
feature <- sample(categories, n, replace = TRUE)
# Create target with dependency on top categories
target_probs <- ifelse(feature %in% c("A", "B"), 0.7,
  ifelse(feature %in% c("C", "D"), 0.5, 0.3)
)
target <- rbinom(n, 1, prob = target_probs)

# Perform sliding window binning
result <- ob_categorical_swb(feature, target)
print(result[c("bin", "woe", "iv", "count")])

# With stricter bin limits
result_strict <- ob_categorical_swb(
  feature = feature,
  target = target,
  min_bins = 4,
  max_bins = 6
)

# Handling missing values
feature_with_na <- feature
feature_with_na[sample(length(feature_with_na), 100)] <- NA
result_na <- ob_categorical_swb(feature_with_na, target)