Yevgeniya Semenova
National Academy of Sciences of Ukraine
Nystrom method for functional linear regression model
Abstract:
For the prediction of system response based on an observed curves the functional
linear regression model is usually used. Such investigations can be found in Hongzhi
Tong and Michael Ng (2018), Junhong Lin, Alessandro Rudi, Lorenzo Rosasco, and
Volkan Cevher (2018) and others. Note, that in these publications the problem of
computational complexity of constructed methods in the case of big training set is
not considered. The first attempt to apply some methods to reduce the complexity of
methods was done in the paper Fode Zhang and Heng Lian (2019). In our presentation
we propose to apply the Nystrom type subsampling approaches as tools for dealing
with big data for problem under consideration. Our main result is the following: we
prove that proposed approach can achieve optimal error bounds, provided the subsampling
level is suitably chosen.
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