ReLU integral probability metric and its applications
This work addresses the need for efficient and theoretically sound distribution discrepancy measures in high-dimensional settings, with incremental improvements in algorithm simplicity and hyperparameter reduction.
The authors tackled the problem of measuring discrepancies between probability distributions by proposing a parametric integral probability metric (IPM) using ReLU-based discriminators, which achieves good convergence rates and comparable or superior performance in applications like causal inference and fair representation learning.
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.