How to speed up typical statistical tasks in high-dimensions and for large data sets

What is it about?

How to speed up typical linear algebra tasks in spatio-temporal statistics? Especially if there are a lot of data and these data are high dimensional. During last yeas quite a lot was done in the multi-linear algebra and low-rank tensor calculus. It is time to reconsider standard data structures, methods and algorithms, some of which were developed 100 years ago, when matrices were very small (3x3). We suggest to extend existing matrices tools to tensors, standard linear algebra to multi-linear algebra.

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Why is it important?

With various tensor formats and tensor calculus we will be able to perform statistics with huge data sets (e.g., 100^100 samples) and with very high-dimensional data. Examples of dimensions are (user, sex, age, country, what he is buying, when he is buying, how much, how often, his preferences). We will be able to solve completely new tasks, which were not possible earlier, e.g., how to find the largest element in a sample with 100^100 elements? Or how to sort this set and build a histogram, or how to select 1% of objects which fulfill certain criteria? or how to do sensitivity analysis ? Or the simplest ones how to compute the mean and the variance if N=100^100?

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