Perturbation Sampling

The perturbation function must respect the data type to create realistic synthetic instances. Tabular data uses random sampling from feature distributions or quantile-based jittering. Text data relies on token masking—randomly removing words to create document variants. Image data uses superpixel masking, turning contiguous pixel regions on or off to test their impact on the prediction. Using the wrong strategy (e.g., Gaussian noise on text) creates out-of-distribution samples that invalidate the local explanation.

Not all perturbed samples are equally informative. An exponential kernel assigns weights based on cosine or Euclidean distance from the original instance. Samples closer to the original receive weights approaching 1, while distant samples are down-weighted toward 0. This enforces the locality constraint—the surrogate model focuses on approximating the decision boundary precisely where the instance of interest resides, rather than modeling global behavior.

Kernel width controls the effective radius of the local neighborhood. A narrow kernel creates a tight, high-fidelity explanation that may be unstable across runs. A wide kernel smooths the explanation but risks including regions where the black-box model behaves differently. Selecting the optimal kernel width is a bias-variance trade-off—too narrow overfits to sampling noise, too wide underfits the local decision boundary. Frameworks like OptiLIME automate this selection.

The number of perturbed samples determines the statistical reliability of the surrogate model. Typical LIME implementations generate 1,000 to 5,000 samples per explanation. Insufficient samples lead to high variance in feature importance scores, while excessive sampling increases computational cost without meaningful improvement. The goal is to achieve explanation stability—consistent feature rankings across multiple runs with different random seeds.

Perturbed samples exist in the original feature space, but the surrogate model operates on an interpretable representation. For text, this is a binary bag-of-words vector indicating token presence. For images, it's a binary vector of superpixel states. This mapping is critical—the surrogate learns which human-understandable components drive predictions, not which raw pixel values matter. The fidelity of this mapping directly impacts explanation usefulness.

Raw perturbation data often yields dense explanations with many features receiving small importance scores. Lasso regression (L1-regularized linear model) is applied as the surrogate to force coefficients of irrelevant features to exactly zero. This produces a sparse linear model where only 5-10 features have non-zero weights, creating a concise, human-digestible explanation. The regularization strength controls the sparsity-fidelity trade-off.

The specific strategy for creating perturbed data points, which varies by data modality:

• Text: Token masking or random word deletion to create document variations
• Images: Superpixel masking to occlude contiguous regions
• Tabular: Value perturbation by sampling from feature distributions or adding Gaussian noise The quality of the neighborhood directly determines the local fidelity of the resulting explanation.

A distance-based weighting function that enforces the locality constraint in LIME. It assigns weights to perturbed samples using the formula exp(-D(x, z)² / σ²), where:

• D(x, z) is the distance between the original instance and the perturbed sample
• σ (sigma) is the kernel width hyperparameter Samples closer to the original instance receive exponentially higher weight, ensuring the surrogate model focuses on the immediate decision boundary.

A human-understandable transformation of raw features used as the input space for the surrogate model:

• Text: Binary bag-of-words indicating presence or absence of tokens
• Images: Binary vector indicating which superpixels are present or occluded
• Tabular: Discretized bins or quantiles for continuous features This mapping bridges the gap between the model's complex feature space and a human-interpretable domain.

The primary proximity measure used in LIME for text data. It calculates similarity between two documents based on the angle between their TF-IDF vector representations, ignoring differences in document length. This metric is particularly effective for text because:

• It captures semantic similarity through term frequency patterns
• It normalizes for document length, preventing longer perturbed texts from dominating
• It produces values in [0,1], making kernel weight calculations consistent

A critical hyperparameter controlling the effective size of the local neighborhood. It determines how quickly sample weights decay with distance:

• Small kernel width: Tight locality, high fidelity to the immediate point but unstable explanations
• Large kernel width: Broader neighborhood, more stable but may capture non-local behavior OptiLIME provides an automated framework for selecting the optimal kernel width by balancing fidelity and stability.

The process of converting continuous numerical features into categorical bins or quantiles for tabular data. This creates a more human-friendly domain for the surrogate model by:

• Transforming age into brackets like '25-35' or '35-50'
• Converting income into percentile ranges
• Binning sensor readings into 'low', 'medium', 'high' Discretization improves explanation comprehensibility while maintaining sufficient granularity for accurate local approximation.