Distribution regression model with a Reproducing Kernel Hilbert Space approach

TL;DR

This paper presents a novel distribution regression model using RKHS with Wasserstein-based kernels, demonstrating its universality and effectiveness on simulated and real-world data, including biomedical signals and age prediction.

Contribution

Introduces a new RKHS-based distribution regression model with Wasserstein kernels, proving their universality and applying to functional and biomedical data.

Findings

The Wasserstein-based kernels are universal for distribution regression.

The proposed model outperforms existing methods on simulated data.

Effective in predicting age from TEOAE distribution responses.

Abstract

In this paper, we introduce a new distribution regression model for probability distributions. This model is based on a Reproducing Kernel Hilbert Space (RKHS) regression framework, where universal kernels are built using Wasserstein distances for distributions belonging to W 2 ($\Omega$) and $\Omega$ is a compact subspace of R. We prove the universal kernel property of such kernels and use this setting to perform regressions on functions. Different regression models are first compared with the proposed one on simulated functional data. We then apply our regression model to transient evoked otoascoutic emission (TEOAE) distribution responses and real predictors of the age.