TY - JOUR
T1 - Optimal learning rates for distribution regression
AU - Fang, Zhiying
AU - Guo, Zheng-Chu
AU - Zhou, Ding-Xuan
PY - 2020/2
Y1 - 2020/2
N2 - We study a learning algorithm for distribution regression with regularized least squares. This algorithm, which contains two stages of sampling, aims at regressing from distributions to real valued outputs. The first stage sample consists of distributions and the second stage sample is obtained from these distributions. To extract information from samples, we embed distributions to a reproducing kernel Hilbert space (RKHS) and use the second stage sample to form the regressor by a tool of mean embedding. We show error bounds in the L2-norm and prove that the regressor is a good approximation to the regression function. We derive a learning rate which is optimal in the setting of standard least squares regression and improve the existing work. Our analysis is achieved by using a novel second order decomposition to bound operator norms.
AB - We study a learning algorithm for distribution regression with regularized least squares. This algorithm, which contains two stages of sampling, aims at regressing from distributions to real valued outputs. The first stage sample consists of distributions and the second stage sample is obtained from these distributions. To extract information from samples, we embed distributions to a reproducing kernel Hilbert space (RKHS) and use the second stage sample to form the regressor by a tool of mean embedding. We show error bounds in the L2-norm and prove that the regressor is a good approximation to the regression function. We derive a learning rate which is optimal in the setting of standard least squares regression and improve the existing work. Our analysis is achieved by using a novel second order decomposition to bound operator norms.
KW - Distribution regression
KW - Integral operator
KW - Mean embedding
KW - Optimal learning rate
KW - Reproducing kernel Hilbert space
UR - http://www.scopus.com/inward/record.url?scp=85071137664&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85071137664&origin=recordpage
U2 - 10.1016/j.jco.2019.101426
DO - 10.1016/j.jco.2019.101426
M3 - 21_Publication in refereed journal
VL - 56
JO - Journal of Complexity
JF - Journal of Complexity
SN - 0885-064X
M1 - 101426
ER -