Feature Discretization

Divides the continuous range into k intervals of identical width. The formula is bin_width = (max - min) / k.

• Advantage: Computationally trivial and preserves the original distribution shape.
• Disadvantage: Highly sensitive to outliers; a single extreme value can create many empty bins.
• Example: For age data ranging 18-80 with k=4, bins become [18-33.5), [33.5-49), [49-64.5), [64.5-80].

Partitions data so that each bin contains approximately the same number of instances. This is achieved by dividing on percentile boundaries.

• Advantage: Handles skewed distributions and outliers gracefully; no empty bins.
• Disadvantage: Can group semantically distinct values together if data is sparse in certain regions.
• Example: For income data, quartile binning creates 4 bins each containing 25% of the population, regardless of dollar-value gaps.

A supervised method that recursively splits the continuous variable to maximize information gain with respect to the target class. It uses the Minimum Description Length Principle (MDLP) as a stopping criterion.

• Advantage: Creates bins that are maximally predictive of the outcome, directly optimizing for the surrogate model's task.
• Disadvantage: Computationally expensive and can overfit to noise in small datasets.
• Origin: Derived from decision tree splitting algorithms like ID3 and C4.5.

Applies 1D k-means clustering to the continuous feature values. Each data point is assigned to the cluster whose centroid is nearest, and cluster boundaries become the discretization cut points.

• Advantage: Data-driven; bins naturally conform to the underlying density structure of the feature.
• Disadvantage: Requires pre-specifying k and is sensitive to initialization.
• Use Case: Effective when the continuous variable exhibits natural multi-modal distributions with distinct peaks.

Uses expert knowledge or regulatory standards to define bin boundaries rather than statistical properties of the data.

• Example (Medical): BMI categories: Underweight (<18.5), Normal (18.5-24.9), Overweight (25-29.9), Obese (≥30).
• Example (Finance): FICO credit score bands: Poor (<580), Fair (580-669), Good (670-739), Very Good (740-799), Exceptional (≥800).
• Advantage: Produces bins with immediate semantic meaning for human operators, critical for high-stakes explanations.

In the LIME framework, discretization serves a dual purpose: it creates the interpretable representation and defines the perturbation space.

• Tabular Data: Continuous features are discretized into quartiles before generating perturbed samples, ensuring the surrogate model operates on human-friendly categorical inputs.
• Stability Impact: The choice of discretization strategy directly affects explanation stability. Quantile binning typically yields more robust feature importance scores than equal-width binning when data is skewed.
• Trade-off: Finer bins increase local fidelity but reduce interpretability; coarser bins simplify the explanation but may obscure subtle decision boundary effects.

The human-understandable transformation of raw inputs that serves as the foundation for the surrogate model. For tabular data, this often involves feature discretization—converting continuous values like 'Age' into categorical bins such as '18-25', '26-35', etc. For text, it might be a bag-of-words; for images, superpixels. The key is that the explanation is presented in terms of these meaningful, high-level concepts rather than raw pixel intensities or floating-point numbers.

An intrinsically interpretable model, such as a sparse linear model or a shallow decision tree, trained to mimic the black-box model's predictions locally. Feature discretization is critical here because a linear surrogate can only provide a single coefficient per feature. A continuous feature discretized into quartiles allows the surrogate to learn a non-linear, step-wise relationship, dramatically improving local fidelity without sacrificing human readability.

The process of creating perturbed samples around the instance being explained to train the local surrogate. For continuous features, this involves sampling from a normal distribution centered on the instance's value. However, the explanation is built on the discretized version of these features. The strategy must define how perturbations map to bins:

• Quantile-based: Bins defined by data distribution
• Uniform-width: Bins of equal range
• Domain-specific: Bins based on expert knowledge (e.g., 'Normal', 'Elevated', 'Critical' for blood pressure)

The fundamental balancing act in local explanations. High fidelity requires a complex surrogate that precisely matches the black-box boundary, but this often becomes uninterpretable. Feature discretization is a key lever in this trade-off:

• Too few bins: Low fidelity, as the surrogate cannot capture the model's granular decision surface.
• Too many bins: High fidelity, but the explanation becomes a long list of narrow categories, defeating the purpose of human interpretability.
• Optimal binning: Uses decision tree splits on the black-box's predictions to find the most informative cut points.

The most common surrogate model in LIME, which uses Lasso (L1) regularization to force the coefficients of less important features to exactly zero. When combined with discretized features, this creates an explanation like: 'Prediction = +0.2 (if Age is 30-40) + 0.5 (if Income > $100k)'. The discretization ensures each selected feature represents a specific, actionable condition rather than a vague continuous slope. The sparsity constraint guarantees only the top K bins survive, keeping the explanation concise.

A successor to LIME that generates high-precision if-then rules called anchors. An anchor is a set of feature conditions that 'anchors' the prediction—meaning changes to any other feature not in the rule will not change the outcome with high probability. Feature discretization is mandatory here, as anchors are defined on categorical predicates. For example: 'If EDUCATION is Bachelors or higher AND HOURS_PER_WEEK > 40, then predicted INCOME > $50k with 97% precision.'