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

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