Hello

I want to construct a map from given samples ( from unknown distrubution) that has standard normal distribution as target distribution so that I can get standard normal samples when samples from unknown distribution are plugged into the map.

I followed the tutorial example: Inverse transport from samples, where samples from Gumbel distribution are used to construct the map:Gumbel to Standard normal. However in the code, I could not understand in the following block ( where map is constructed):

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S = TM.Default_IsotropicIntegratedSquaredTriangularTransportMap( 1, 3, 'total') rho = DIST.StandardNormalDistribution(1) push_L_pi = DIST.PushForwardTransportMapDistribution(L, pi) push_SL_pi = DIST.PushForwardTransportMapDistribution( S, push_L_pi) qtype = 0 # Monte-Carlo quadratures from pi qparams = 500 # Number of MC points reg = None # No regularization tol = 1e-3 # Optimization tolerance ders = 2 # Use gradient and Hessian log = push_SL_pi.minimize_kl_divergence( rho, qtype=qtype, qparams=qparams, regularization=reg, tol=tol, ders=ders) ######################################################### specifically the line "push_L_pi = DIST.PushForwardTransportMapDistribution(L, pi)". Here we are explicitly specifying the "Gumbel distribution" ,defined by pi, instead of the samples, arent we supposed to not know the distribution in the first place ( instead we only have samples, like the situation that I have i.e. only samples without having any knowledge about its distribution) Could you kindly clear my misunderstanding,if possible with an example code. I would be very grateful thanks saad