Distribution to Distribution Regression

  title={Distribution to Distribution Regression},
  author={Junier B. Oliva and Barnab{\'a}s P{\'o}czos and Jeff G. Schneider},
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… CONTINUE READING
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