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Distribution to Distribution Regression

Junier Oliva, Barnabas Poczos, Jeff Schneider
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JMLR W&CP 28 (3) : 1049–1057, 2013

Abstract

We analyze ’Distribution to Distribution regression’ where one is regressing a mapping where both the covariate (inputs) and response (outputs) are distributions. No parameters on the input or output distributions are assumed, nor are any strong assumptions made on the measure from which input distributions are drawn from. We develop an estimator and derive an upper bound for the \(L2\) risk; also, we show that when the effective dimension is small enough (as measured by the doubling dimension), then the risk converges to zero with a polynomial rate.

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