Learning rate of distribution regression with dependent samples.

In this paper, we study the learning rate of distribution regression for strong mixing sequences. The distribution regression containing two stages of sampling aims at regressing from distributions to real valued outputs. In order to form our regressor, we embed distributions to a reproducing kernel Hilbert space by utilizing the tool of mean embedding. By using the property of integral operator and the covariance inequality for strong mixing sequence, we show that under some priori conditions of regression function, the distribution regression still reaches the optimal learning rate with dependent samples. Hence, we extend the applicable range of distribution regression to the identically distributed but dependent samples. [ABSTRACT FROM AUTHOR]