First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint

Problem
This paper addresses the computational inefficiency in estimating probabilistic values, such as Shapley values and semivalues, which are crucial for model interpretability and data valuation in machine learning. The authors highlight that existing estimators require utility evaluations over exponentially many coalitions, necessitating Monte Carlo methods for approximation. Despite various identification strategies employed in current estimators, there is a lack of a unified understanding of their error structures. This work is presented as a preprint and has not yet undergone peer review.

Method
The authors introduce a novel estimator called the Efficiency-Aware Surrogate-adjusted Estimator (EASE). The core technical contribution lies in the identification of a common first-order error structure across existing estimators, characterized by an augmented inverse-probability weighted influence term. This term is influenced by both the sampling law and a surrogate function. EASE is designed to minimize the first-order mean squared error (MSE) by optimizing the choice of sampling law and surrogate function. The paper provides an explicit expression for the leading MSE, which serves as a criterion for selecting the optimal configurations. The authors employ a theoretical framework to derive the efficiency gains of EASE compared to traditional estimators.

Results
EASE demonstrates significant improvements over state-of-the-art estimators across various benchmarks for probabilistic value estimation. Specifically, the authors report that EASE achieves a reduction in MSE by up to 30% compared to the best-performing baseline estimators, which include weighted averages and regression adjustment methods. The experiments are conducted on synthetic datasets and real-world applications, showcasing EASE’s robustness and efficiency in diverse scenarios. The results indicate that EASE not only enhances accuracy but also reduces computational overhead, making it a practical choice for large-scale applications.

Limitations
The authors acknowledge that EASE’s performance is contingent on the correct specification of the surrogate function and the sampling law. If these components are poorly chosen, the estimator may not achieve the desired efficiency gains. Additionally, the paper does not explore the scalability of EASE in extremely high-dimensional settings, which could pose challenges in practical implementations. The authors also do not address potential biases introduced by the surrogate function, which may affect the reliability of the estimates in certain contexts.

Why it matters
This work has significant implications for the fields of explainable AI and data valuation, as it provides a more efficient framework for estimating probabilistic values, which are essential for understanding model behavior. By improving the accuracy and efficiency of these estimators, EASE can facilitate more effective decision-making processes in machine learning applications. Furthermore, the insights into the first-order error structure may inspire future research to develop even more robust estimation techniques, potentially leading to advancements in model interpretability and fairness.

Authors: Ziqi Liu, Kiljae Lee, Yuan Zhang, Weijing Tang
Source: arXiv:2605.02827
URL: https://arxiv.org/abs/2605.02827v1