Structures and algorithms for post-processing large data sets and multi-variate functions in spatio-temporal statistics

摘要

Matrices began in the 2nd century BC with the Chinese. One can find traces, which go to the 4th century BC to the Babylonians. The text ``Nine Chapters of the Mathematical Art'' written during the Han Dynasty in China gave the first known example of matrix methods. They were used to solve simultaneous linear equations (more in http://math.nie.edu.sg/bwjyeo/it/MathsOnline_AM/livemath/the/IT3AMMatricesHistory.html).udThe first ideas of the maximum likelihood estimation (MLE) was introduces by Laplace (1749-1827), by Gauss (1777-1855), the Likelihood was defined by Thiele Thorvald (1838-1910). Why we still use matrices? The matrix data format is more than 2200 years old. Our world is multi-dimensional! Why not to introduce a more appropriate data format and why not to reformulate the MLE method for it?udIn this work we are utilizing the low-rank tensor formats for multi-dimansional functions, which appear in spatial statistics.