Variational inference and density estimation with non-negative tensor of hierarchical tucker format
For researchers in high-dimensional probability and tensor compression, this work provides an efficient method to handle large-scale probability tensors, though it is an incremental improvement over existing hierarchical Tucker methods.
The paper introduces a two-stage method to compress high-dimensional discrete probability tensors into a non-negative hierarchical Tucker format, achieving linear computational complexity in the tensor order. Numerical experiments demonstrate successful compression of various high-dimensional probability tensors.
In this work, we present an efficient method to compress a high-dimensional discrete probability function, i.e., a probability tensor, into a non-negative hierarchical Tucker format. The methodology is a two-stage procedure. In the first stage, we take an existing interpolation method to compress the target tensor into a hierarchical Tucker (HT) in a manner similar to the CUR decomposition for low-rank matrix reconstruction. In the second stage, we fit the first-stage output against a non-negative hierarchical Tucker ansatz using a second-order method tailored specifically for this setting. When the tensor is of order \(d\), both stages admit an \(\mathcal{O}(d)\) computational complexity, and therefore the proposed methodology readily extends into high-dimensional settings. Numerical experiments show success in compressing various high-dimensional probability tensors.