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I am thinking how to use GAN or KL Divergence as a loss function to enforce specific specific distribution on the feature space:

Let $X \sim D$ where $D$ is some distribution. Assume we know a reference asymptotic distribution $Y \sim D_2$.

We would like to find a polynomial transformation of $X \to f(X)$ such that $f(X) \sim Y \sim D_2$.

For the case of $Y \sim D_2=N(0,1)$ the network potentially will find the z-score normalization or some mapping $f$, so $f(x) \sim Y$.

I would like to get advice how to formalize this problem in order to be able to solve it using Neural Network.

Someone mentioned something like: Quantile Transforms, but I want to use neural network.

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