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Wasserstein distance

The Wasserstein distance is a distance function for measuring the distance between two probability distributions.

Also known as the Earth Mover’s distance, the metric It is defined as the minimum amount of "energy cost" required to transform one distribution into the other. 

It is calculated as:

W:= W(FP,FQ) = (01 ∣FP−1(u) − FQ−1(u) ∣2 du)1/2


P and Q = two different conditions 

FP and FQ = corresponding cumulative distribution functions (CDFs)

FP−1 and FQ−1   = quantile functions

The Wasserstein distance has several advantages, such as the ability to take into account the geometry of the space in which the distributions are defined and the ability to handle distributions with different support sizes.

Wasserstein distance is used for numerical features. The default threshold in AryaXAI is 0.05.

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