High-dimensional density estimation with tensorizing flow

We propose the tensorizing flow method for estimating high-dimensional probability density functions from observed data. Our method combines the optimization-less feature of the tensor-train with the flexibility of flow-based generative models, providing an accurate and efficient approach for density estimation. Specifically, our method first constructs an approximate density in the tensor-train form by efficiently solving the tensor cores from a linear system based on kernel density estimators of low-dimensional marginals. Subsequently, a continuous-time flow model is trained from this tensor-train density to the observed empirical distribution using maximum likelihood estimation. Numerical results are presented to demonstrate the performance of our method.