Tensor-Train Density Estimation

TL;DR

The paper introduces a tensor train-based density estimation model that enables efficient, stable, and exact density computations with intuitive hyperparameters, outperforming neural network models in speed.

Contribution

It presents a novel tensor train-based density estimation method with exact sampling and efficient training, addressing limitations of neural network approaches.

Findings

Competitive density estimation performance

Faster training compared to competitors

Exact sampling and density calculations

Abstract

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.