We propose a hierarchical tensor-network approach for approximating high-dimensional
probability density via empirical distribution. This leverages randomized singular value …

We show how to construct nonnegative low-rank approximations of nonnegative tensors in
Tucker and tensor train formats. We use alternating projections between the nonnegative …

This work is concerned with solving high-dimensional Fokker-Planck equations with the
novel perspective that solving the PDE can be reduced to independent instances of density …

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 …

Physics is living an era of unprecedented cross-fertilization among the different areas of
science. In this perspective review, we discuss the manifold impact that state-of-the-art cold …

In this paper, we present a density estimation framework based on tree tensor-network
states. The proposed method consists of determining the tree topology with Chow-Liu …

We present a tensorization algorithm for constructing tensor train representations of
functions, drawing on sketching and cross interpolation ideas. The method only requires …

Tensor networks (TNs) have seen an increase in applications in recent years. While they
were originally developed to model many-body quantum systems, their usage has …

Nonparametric models are of great interest in various scientific and engineering disciplines.
Classical kernel methods, while numerically robust and statistically sound in low …

The numerical representation of high-dimensional Gibbs distributions is challenging due to
the curse of dimensionality manifesting through the intractable normalization constant …