First-Order Efficiency for Probabilistic Value Estimation via Statistical Viewpoint
A recent preprint on arXiv (2605.02827) presents a comprehensive statistical framework aimed at estimating probabilistic values, including Shapley values and semivalues, which are significant in explainable AI and data valuation. The authors note that various Monte Carlo estimators—such as weighted averages, regression adjustment, self-normalized weighting, and weighted least squares—exhibit a shared first-order error structure. The primary error component is an enhanced inverse-probability weighted influence term influenced by the sampling method and a surrogate function. This first-order approach allows for efficiency gains, leading to optimal convergence rates. The study offers both theoretical assurances and empirical support, presenting a robust method for approximating probabilistic values in high-dimensional contexts.
Key facts
- arXiv:2605.02827v1 is a new submission.
- Probabilistic values include Shapley values and semivalues.
- Exact computation requires utility evaluations over exponentially many coalitions.
- Monte Carlo approximation is essential in modern machine learning.
- Existing estimators include weighted averages, self-normalized weighting, regression adjustment, and weighted least squares.
- The key observation is a common first-order error structure.
- The leading term is an augmented inverse-probability weighted influence term.
- The framework yields first-order efficiency.
Entities
Institutions
- arXiv