Laboratory of Structural Methods of Data Analysis in Predictive
Modeling Moscow Institute of Physics and Technology
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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Направления исследований

Statistical methods

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