Performance of Distribution Regression with Doubling Measure under the seek of Closest Point

TL;DR

This paper investigates distribution regression under the assumption of a doubling measure greater than one, developing a geometric theory to find nearest distributions and analyze the regression accuracy.

Contribution

It introduces a new geometric framework for distribution regression with doubling measures and proposes an adaptive method for nearest distribution search and regression.

Findings

Theoretical analysis of the proposed method's accuracy

Development of a geometric theory for distributions with doubling measure > 1

Empirical validation of the regression approach

Abstract

We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small theory around it. Then, we show how to utilize this theory to find one of the nearest distributions adaptively and compute the regression value based on these distributions. Finally, we provide the accuracy of the suggested method here and provide the theoretical analysis for it.