用带ReLU的单节点网络定义新分布度量，适合高维数据
ReLU integral probability metric and its applications
- 用ReLU单节点网络做判别器，构造可优化的分布距离度量
- 估计器收敛速度快，理论保证强，实测效果优于或媲美现有方法
- 适用于因果推断和公平表征学习，超参少、实现简单
我们提出一种参数化的积分概率度量（IPM），用于衡量两个概率分布之间的差异。该度量利用特定参数化判别器族（如带ReLU激活的单节点神经网络）有效区分分布，适用于高维场景。通过优化选定判别器类的参数，所提出的IPM证明其估计器具有良好的收敛速率，并可作为使用平滑非参数判别器类的其他IPM的替代代理。我们提出了一个高效的计算算法，实现简便，所需超参数较少。此外，我们在多种任务中探索了其应用，包括因果推断中的协变量平衡和公平表征学习。在这些多样化任务中，我们展示了该IPM具备强大的理论保障，且实验结果表明其性能可与甚至超过现有方法。
原文摘要 · Abstract (English)
We propose a parametric integral probability metric (IPM) to measure the discrepancy between two probability measures. The proposed IPM leverages a specific parametric family of discriminators, such as single-node neural networks with ReLU activation, to effectively distinguish between distributions, making it applicable in high-dimensional settings. By optimizing over the parameters of the chosen discriminator class, the proposed IPM demonstrates that its estimators have good convergence rates and can serve as a surrogate for other IPMs that use smooth nonparametric discriminator classes. We present an efficient algorithm for practical computation, offering a simple implementation and requiring fewer hyperparameters. Furthermore, we explore its applications in various tasks, such as covariate balancing for causal inference and fair representation learning. Across such diverse applications, we demonstrate that the proposed IPM provides strong theoretical guarantees, and empirical experiments show that it achieves comparable or even superior performance to other methods.
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