so Silverman in his 1986 book mentioned about approximate distributions with the Gaussian mixing models, but did not go into the subject very deeply … I wonder, let's say they gave me a box of N-dimensional uniforms (and as a additional point). extension to this, any arbitrary distribution) $ u ( bar {x}) $ , Is there a clear way to do it with a Gaussian k-kernel mixing model (truncated) $ g ( bar {x}) = sum_ {i} omega_i N ( mu_i, sigma ^ 2_i) $?

I tried this by trying to minimize some kind of measurable divergence between the two, for example, the Hellinger distance or the Kullback-Leibler divergence, but the analytical solutions do not seem plausible and in terms of numerical approaches, the computational costs rise too quickly to As the number of cores / dimension increases.

I wonder if there have been previous studies on this topic before, but I have not been successful in finding something useful … if someone can give me some clues or perhaps refer me to the relevant literature on this, it would be great appreciated!

Cheers!