  Estimation of probability density function from samples is one of the central
problems in statistics and machine learning. Modern neural network-based models
can learn high dimensional distributions but have problems with hyperparameter
selection and are often prone to instabilities during training and inference.
We propose a new efficient tensor train-based model for density estimation
(TTDE). Such density parametrization allows exact sampling, calculation of
cumulative and marginal density functions, and partition function. It also has
very intuitive hyperparameters. We develop an efficient non-adversarial
training procedure for TTDE based on the Riemannian optimization. Experimental
results demonstrate the competitive performance of the proposed method in
density estimation and sampling tasks, while TTDE significantly outperforms
competitors in training speed.
