Laboratory of Structural Methods of Data Analysis in Predictive
Modeling Moscow Institute of Physics and Technology
ENG
Логин:
Пароль:
Approximation of data generated by Cartesian product
We propose an approximation method for data samples generated by the Cartesian product of an arbitrary number of multi-dimensional factors. The method is based on an expansion of the functions dictionary, which is constructed as the tensor product of other dictionaries. Such smaller dictionaries are obtained as a solutions of approximation problems in each factor of the Cartesian product. We also introduce a special kind of penalty in order to control smoothness of the model in each factor. Decomposition coefficients of the global dictionary are found in optimal way as a solution of regularized least squares. Regularization parameters that specify model smoothness are calculated using the leave-one-out error. Factorized data structure allows to make all calculations with the global dictionary computationally efficient. The proposed approach is successfully used in real applications.

Авторы: Belyaev Mikhail

Дата: 17 ноября 2014

Статус: опубликована

Журнал: Proceedings of Moscow Institute of Physics and Technology

Том: 5

Выпуск: 3

Страницы: 11-23

Год: 2013

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Statistical methods

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