One Sample Fits All: Approximating All Probabilistic Values Simultaneously and Efficiently

TL;DR

This paper introduces a unified, efficient framework for approximating all probabilistic values, such as Beta Shapley and weighted Banzhaf values, simultaneously with optimal convergence rates, significantly improving computational efficiency.

Contribution

The authors propose the first one-sample-fits-all framework that approximates all probabilistic values simultaneously and efficiently, with theoretical convergence guarantees and practical improvements.

Findings

Achieves the best average time complexity for all probabilistic values.

Provides the fastest convergence rate for Beta Shapley values.

Connects probabilistic values with least squares regression in data models.

Abstract

The concept of probabilistic values, such as Beta Shapley values and weighted Banzhaf values, has gained recent attention in applications like feature attribution and data valuation. However, exact computation of these values is often exponentially expensive, necessitating approximation techniques. Prior research has shown that the choice of probabilistic values significantly impacts downstream performance, with no universally superior option. Consequently, one may have to approximate multiple candidates and select the best-performing one. Although there have been many efforts to develop efficient estimators, none are intended to approximate all probabilistic values both simultaneously and efficiently. In this work, we embark on the first exploration of achieving this goal. Adhering to the principle of maximum sample reuse, we propose a one-sample-fits-all framework parameterized by a sampling vector to approximate intermediate terms that can be converted to any probabilistic value without amplifying scalars. Leveraging the concept of $ (\epsilon, \delta) $-approximation, we theoretically identify a key formula that effectively determines the convergence rate of our framework. By optimizing the sampling vector using this formula, we obtain i) a one-for-all estimator that achieves the currently best time complexity for all probabilistic values on average, and ii) a faster generic estimator with the sampling vector optimally tuned for each probabilistic value. Particularly, our one-for-all estimator achieves the fastest convergence rate on Beta Shapley values, including the well-known Shapley value, both theoretically and empirically. Finally, we establish a connection between probabilistic values and the least square regression used in (regularized) datamodels, showing that our one-for-all estimator can solve a family of datamodels simultaneously.