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Title: Fast Rate of Estimating Perfect Classifier on Functional Data Authors:  Masaaki Imaizumi - The University of Tokyo (Japan) [presenting]
Abstract: We investigate a possibility of perfect classification of binary classification on functional data with finite samples. It is known that the classification problem on functional data is easier to guarantee the existence of a perfect classifier than finite dimensional data. However, a very huge sample size may be required to build the classifier from finite observations, due to the large complexity of functional data. Specifically, the rate of convergence of the excess risk in the sample size is shown to have a logarithm order of the sample size. This study solves this complication by proving that a sufficient condition for the perfect classification also provides very fast convergence. We define a classifier with empirical risk minimization using RKHS and analyze its convergence rate under the conditions for perfect classification. The result shows that the convergence rate of our classifier has an exponential order in sample size. Its proof relies on that condition for perfect classification manipulating margins of the distribution of functional data and the entropy control of a space of functionals using empirical processes.