Date of Original Version
Copyright 2013 by the author(s)
Abstract or Description
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.
Journal of Machine Learning Research : Workshop and Conference Proceedings, 28, 3, 1049-1057.