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Distribution to Distribution Regression
Authors: Junier Oliva, Barnabas Poczos and Jeff Schneider
Conference: Proceedings of the 30th International Conference on Machine Learning (ICML-13)
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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