Valuation problems, such as feature interpretation, data valuation and model valuation for ensembles, become increasingly more important in many machine learning applications. Such problems are commonly solved by well-known game-theoretic criteria, such as Shapley value or Banzhaf index. In this work, we present a novel energy-based treatment for cooperative games, with a theoretical justification by the maximum entropy framework. Surprisingly, by conducting variational inference of the energy-based model, we recover various game-theoretic valuation criteria through conducting one-step gradient ascent for maximizing the mean-field ELBO objective. This observation also verifies the rationality of existing criteria, as they are all attempting to decouple the correlations among the players through the mean-field approach. By running gradient ascent for multiple steps, we achieve a trajectory of the valuations, among which we define the valuation with the best conceivable decoupling error as the Variational Index. We experimentally demonstrate that the proposed Variational Index enjoys intriguing properties on certain synthetic and real-world valuation problems.
翻译:在许多机器学习应用中,诸如地貌解释、数据估值和群装模型估值等估值问题越来越重要,在许多机器学习应用中,这些问题通常通过众所周知的游戏理论标准,如Shapley 值或Banzhaf 指数,加以解决。在这项工作中,我们为合作游戏提出了一个新型的基于能源的处理办法,其理论依据是最大英特普框架。令人惊讶的是,我们通过对基于能源的模式进行不同的推论,通过对各种游戏理论性估价标准进行分级,我们通过进行一步梯度的梯度,将各种游戏性估价标准作为最大限度地实现平均地ELBO目标的中心,从而恢复了各种游戏性估价标准。这一观察还验证了现有标准的合理性,因为这些标准都试图通过平均地方法将各参与者之间的相互关系分解开来。我们通过将梯度作为多个步骤的精度,从而实现估值的轨迹,其中我们用最有可能发生的脱钩错误来界定估值。我们实验性地证明,拟议的挥发性指数在某些合成和现实世界估值问题中具有令人触动的特性。