LIME: Local Interpretable Model-agnostic Explanations

Intuition

A complex model may be curved globally but almost linear in a small neighbourhood of one input. LIME samples variations of the instance, asks the model about them, and fits a simple linear model that is accurate near the instance.

Precise explanation (Ribeiro et al., 2016, tabular variant used here)

1. Interpretable representation: binary masks $z \in \{0,1\}^d$; $z_j = 1$ keeps $x_j$, $z_j = 0$ replaces it with the baseline value. Input for mask z: $x(z) = z\odot x + (1-z)\odot x'$.
2. Sample masks (always include the all-ones mask = the instance itself).
3. Proximity weights: with distance $D(z) = 1 - \frac{1}{d}\sum_j z_j$ (fraction of features removed), $\pi(z) = \exp(-D^2/\sigma^2)$, σ = kernel width.
4. Weighted least squares: fit $g(z) = \beta_0 + \beta\cdot z$ minimising $\sum \pi(z)(f(x(z)) - g(z))^2$: solve with rows scaled by $\sqrt{\pi}$. The coefficient $\beta_j$ estimates the effect of including feature j. For a linear model $f$, LIME recovers $\beta_j = w_j(x_j - x'_j)$ exactly (same as XA-01/XA-11).

Worked example

f(x) = 2x₀ − x₁, x = (3, 1), baseline 0 → β = [6, −1], β₀ = 0, for any set of masks that spans the space.

Common mistakes

• Fitting on raw perturbed features instead of the binary masks (changes what β means).
• Forgetting the weights (fits a global, not local, model).
• Too few samples → unstable explanations (re-run with other seeds to check).

Why this matters

LIME is a widely used model-agnostic local explainer; implementing it shows exactly which design choices (baseline, kernel width, sampling) affect explanations.

References

• "Why Should I Trust You?": Explaining the Predictions of Any Classifier — Marco Tulio Ribeiro, Sameer Singh, Carlos Guestrin (S025)
• Interpretable Machine Learning (3rd edition) — Christoph Molnar (S024)