Woman writing calculations on whiteboard. Illustration from unsplash.com, by @thisisengineering.

A mathematical "quiz" solved for data science

Pedro Lind has together with researchers from Germany published an article deriving an approximate solution of an old equation in statistical physics.

– Imagine you have a time series such as the measurements from an EEG or fNIRS device (tests that detects electrical activity in your brain), the power output of a wind turbine, or the series of a financial index in the stock market, says professor Pedo Lind at the OsloMet Artificial Intelligence Lab.

– How about deriving from that series a (simple) equation that describes the evolution of the series of values you measured or observed? More or less like the equation of Newton describing the chaotic trajectory of planets around a star.

It would be an equation more complex than the one describing the gravitational law for planets since it would involve quite a lot of statistics. But it would still be an equation. Which means, something able to describe how such complex signals evolve in a statistical sense.

These equations are called stochastic equations and how to derive them from data is not an easy task.

Together with researchers in Germany, from the Department of Epileptology, the Institute for Energy and Climate Research, and the Interdisciplinary Center for Complex Systems, Pedro Lind published an article deriving an approximate solution of an old equation in statistical physics.

– While it is an approximation, it is good enough to improve several previous challenges researchers had when modeling stochastic signals. The solution is basically maths, but it can now be easily implemented to better describe how stochastic signals evolve, says Pedro.

For those who like maths or/and to solve hard quizzes, the article is published here (open access):

Arbitrary-order finite time corrections for the Kramers-Moyal operator, L.R. Gorjão, D. Witthaut, K. Lehnertz, P.G. Lind, Entropy 2021, 23(5), 517 (mdpi.com)

For those who don't like maths or are more focused on its applications there is another paper under submission more focused on the implementation of these derivations.

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