  Distributions are fundamental statistical elements that play essential
theoretical and practical roles. The article discusses experiences of training
neural networks to classify univariate empirical distributions and to represent
them on the two-dimensional latent space forcing disentanglement based on the
inputs of cumulative distribution functions (CDF). The latent space
representation has been performed using an unsupervised beta variational
autoencoder (beta-VAE). It separates distributions of different shapes while
overlapping similar ones and empirically realises relationships between
distributions that are known theoretically. The synthetic experiment of
generated univariate continuous and discrete (Bernoulli) distributions with
varying sample sizes and parameters has been performed to support the study.
The representation on the latent two-dimensional coordinate system can be seen
as an additional metadata of the real-world data that disentangles important
distribution characteristics, such as shape of the CDF, classification
probabilities of underlying theoretical distributions and their parameters,
information entropy, and skewness. Entropy changes, providing an "arrow of
time", determine dynamic trajectories along representations of distributions on
the latent space. In addition, post beta-VAE unsupervised segmentation of the
latent space based on weight-of-evidence (WOE) of posterior versus standard
isotopic two-dimensional normal densities has been applied detecting the
presence of assignable causes that distinguish exceptional CDF inputs.
