How we can massively speedup statistical interpolation (Kriging)

What is it about?

Assume we have some observations and we would like to interpolate these data onto new locations. A typical example is: weather stations in Germany measure weather only locally around these stations, how to predict weather on the whole territory of Germany? One of the methods is Kriging (also called statistical interpolation). From linear algebra point of view, this is only solution of a linear system and matrix-vector product. Another task is how to improve already existing weather prediction model is some new measurement data become available? Or another task, where are the optimal positions for the weather stations to maximize the information gain. All these are very time-consuming tasks. We speed up computations by combining low-rank tensor methods and Fats Fourier Transformation. We can achieve speed up factors 10, 100 or even 1000. This is not for free; we do certain assumptions about the covariance matrix and require axes parallel mesh.

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Photo by Wim van 't Einde on Unsplash

Photo by Wim van 't Einde on Unsplash

Why is it important?

Nowadays we deal with huge amount of data, the data are high-dimensional. In spatio-temporal statistics the time intervals and the spatial areas are huge. The satellite data are huge. All these require very fast and efficient numerical techniques.

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