Performance of Distribution Regression with Doubling Measure under the seek of Closest Point
This addresses distribution regression for scenarios with specific geometric properties, but appears incremental as it builds on existing doubling measure concepts.
The paper tackles distribution regression by assuming the distribution of distributions has a doubling measure greater than one, developing a geometric theory for such distributions and using it to adaptively find nearest distributions for regression. It provides accuracy results and theoretical analysis for the proposed method.
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.