SHAP & LIME

SHAP and LIME are the two most common model explainability methods. SHAP performs strictly additive feature attribution based on the game-theoretic Shapley value: $\phi_i = \sum_{S \subseteq N\setminus\{i\}} \frac{|S|!(|N|-|S|-1)!}{|N|!}[v(S\cup\{i\}) - v(S)]$, where $v(S)$ is the expected prediction given feature subset $S$ and the weight $\frac{|S|!(|N|-|S|-1)!}{|N|!}$ is the ordering share of feature $i$ among coalition permutations; Shapley values are the unique attribution satisfying efficiency, symmetry, dummy and additivity, decomposing the output exactly as $\sum_i \phi_i = f(x) - E[f]$. TreeSHAP exploits the tree structure to compute exact values in $O(TLD^2)$ without sampling, while LIME fits a local interpretable surrogate $\min_g \mathcal{L}(f, g, \pi_x)$ — a sparse linear/decision model $g$ approximating $f$ in a $\pi_x$-weighted neighborhood around $x$.

feature explanation for production risk/credit/recommendation models; interview questions like "SHAP vs LIME, how do you choose" or "how to attribute a black-box model"; global explanations via SHAP importance/dependence plots, local ones via force plots or LIME weights; in industry TreeSHAP is the default for tree ensembles.

linear coefficients only explain additive-linear relationships, while SHAP decomposes any nonlinear model's output fairly across features — additivity guarantees $\sum_i \phi_i = f(x) - E[f]$, so attributions exactly sum to prediction minus baseline and stay comparable across models and samples; unlike LIME whose random sampling is non-reproducible, TreeSHAP is exact, fast and deterministic for trees.

Write the Shapley formula $\phi_i = \sum_{S \subseteq N\setminus\{i\}} \frac{|S|!(|N|-|S|-1)!}{|N|!}[v(S\cup\{i\}) - v(S)]$, explain the weight $\frac{|S|!(|N|-|S|-1)!}{|N|!}$, and why it is the unique attribution satisfying efficiency/symmetry/dummy/additivity?

SHAP's additivity: why does $\sum_i \phi_i = f(x) - E[f]$? How does it fundamentally differ from linear-model coefficients (LIME weights)?

Why can TreeSHAP compute exact values for trees? Decode $O(TLD^2)$ and explain why no sampling is needed.

Write LIME's surrogate objective $\min_g \mathcal{L}(f, g, \pi_x)$: what are $g$, $\pi_x$, $\mathcal{L}$? Why are LIME results unstable?

SHAP vs LIME: global vs local explanations, when to use which; applicability on tabular/image/text tasks?