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For dynamical systems we can determine whether a system is chaotic by finding how much it diverges over time from two close starting points. We can also apply this concept to raw data instead of a set of differential equations to find maximum lyaponuv exponents. This provides an easy metric to see how hard it would be for a machine learning model to learn trends in the data. Does a similar system exist for categorical data? Specifically, say I have measures of x, y, and z variables over t time steps and categorical outcome a. Is there a way to easily measure the "chaos" of this system, or, how hard it is to fit a model to the data?
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