High-dimensional density estimation with tensorizing flow
This is an incremental improvement for researchers in machine learning and statistics working on density estimation.
The paper tackles the problem of estimating high-dimensional probability density functions from data by proposing the tensorizing flow method, which combines tensor-train and flow-based generative modeling, and includes numerical results to demonstrate its performance.
We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The method is based on tensor-train and flow-based generative modeling. Our method first efficiently constructs an approximate density in the tensor-train form via solving the tensor cores from a linear system based on the kernel density estimators of low-dimensional marginals. We then train a continuous-time flow model from this tensor-train density to the observed empirical distribution by performing a maximum likelihood estimation. The proposed method combines the optimization-less feature of the tensor-train with the flexibility of the flow-based generative models. Numerical results are included to demonstrate the performance of the proposed method.