Tensor-Train Density Estimation
This work addresses density estimation challenges in statistics and machine learning, offering a stable and efficient alternative to neural network-based models, though it appears incremental as it builds on tensor train methods.
The authors tackled the problem of probability density estimation from samples by proposing a tensor train-based model (TTDE) that enables exact sampling and efficient computation of density functions, achieving competitive performance and significantly faster training speed compared to existing methods.
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.