# week-5 : xai 2

1. marginal contribution
   • contribution of an element j to a function f when j is added, holding everything else fixed

• 4 shapley axioms:
  • efficiency - the shapley values sum to the gap between full coalition and empty one
  • symmetry - if v(S U {j}) = v(S U {k}) for S that excludes both then MC_j= MC_k
  • dummy - if v(S U {j}) = v(S) for every S then MC_j= 0
  • additivity - for split in value function, the players shapley values also split MC_J(v+w) = MC_j(v) + MC_j(w)
• Uniqueness theorem - shapley values satisfy all 4 axioms so it is probably fair!
• computational challenge - since there are 2^p coallitions for mc_j exact computation is infeasible!
• shapley values
  • strengths:
    • axiomatic - satisfies axioms
    • model-agnostic - works for any value function
    • interpretable - MC_j has a per player meaning
  • limitations:
    • cost - 2^p coalitions
    • missing-feature semantic - feature absent not possible in ML
    • correlated features - credit can leak to features not used by models

2. SHAP

• we need a data matrix “X” - because in ML we can’t skip features, to evaluate coalition S, we plug in stand-in values for feat not is S, drawn from X
• SHAP - Shapley Additive exPlanations
• explains individual predictions of an ML model using Shapley values
  • Shapley - uses shapley values
  • Additive - output = baseline + each feat contribution
  • exPlanation - local explanation properties of SHAP:
• post-hoc → analyzes the model after it has already been trained.
• model-agnostic → works with any architecture - xgboost, nn, random forest, svm etc.

SHAP axioms:

• local accuracy - baseline + sum of feat contribution = model pred
• missingness - if feat j is missing from input then mc_j=0
• consistency - changing model such that feat j’s marginal contribution increases or decreases but SHAP guaranteed it will never decrease

Links:

202608131549