mlsanityData to 14 Oct 2026

ReLU integral probability metric and its applications

arXiv 2504.18897 ↗First posted 26 Apr 2025stat.ML cs.LG stat.MEcited by 1

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Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 55 of its 112 references that are in the map. First posted on arXiv 26 Apr 2025.

Builds on

55 of 112 references.

References · 55

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38 more
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  1. 2026A nonparametric two-sample test using a parametric integral probability metriccited by 0