Data distribution modelling or probability density estimation is an important problem of statistical inference. This work presents variational autoencoders, one of the modern deep machine learning methods for solving this challenge. It addresses their mathematical background, explains the training process of the distribution model, and demonstrates how the learned model can be used to generate new data. It also presents two modern extensions of variational autoencoders that enable learning disentangled latent representations and modelling recursive data types, and the results of testing the model on selected datasets.
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