I have a complicated 20-dimensional multi-modal distribution and consider training a VAE to learn an approximation of it using 2000 samples. But particularly, with the aim to subsequently generate pseudo-random numbers behaving according to the structure of the distribution. However, my problems are the following:

  1. Is my approach fundamentally or logically flawed? Specifically, because unlike image data, the random numbers are of geometric nature and thus take negative values and could also be considered noisy.
  2. How do I find the right architecture aside from simple trial and error? Obviously, I do not necessarily need 2D-Convolutions. But instead, 1D-Convolutions could be considered a good choice to capture the correlations (i.e. modalities of the distribution). I'm also not sure about how I properly decide on the number of hidden layers and nodes.

1 Answer 1


You are describing surrogate modelling.

Because your situation is well studied, I recommend looking at what others have published. See, this paper for example.

  • $\begingroup$ Thanks for the paper recommendation. I will take a closer look at it. However, what I do intend is not to do surrogate modelling or use the network for function approximation. But instead, learn the distribution to such a good degree that correlations in the samples are captured and resampling in the latent space is a good at recreating the correlations in the original distribution. For instance, a correlation could be that in the 4th and 7th position pairs of 0.5 appear for e.g. a sample x=[.4,.3,.1,.5,.1,.6,.5,.1,.9,.3], indicating a peak in the probability distribution. $\endgroup$
    – Steve
    Aug 31, 2020 at 17:54
  • $\begingroup$ I'm sorry @Steve, I'm not understanding your problem well enough to distinguish it from surrogate modelling. Hopefully someone can enlighten us then $\endgroup$
    – Ben
    Aug 31, 2020 at 19:22

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