Estimating distributions and generating synthetic structured tensors

Determine how to estimate the underlying probability distribution of structured tensors and how to generate synthetic tensors that accurately follow a specified target distribution, enabling principled generative modeling for multi-way array data.

Background

The paper highlights that, despite extensive progress on statistical inference for tensor data (e.g., modeling correlations and factor structures), generative modeling for tensors remains underdeveloped. In particular, learning the full probability distribution of structured tensors and generating samples from it is not straightforward due to high dimensionality and multi-way dependencies.

The authors motivate addressing this gap by leveraging tensor structures (e.g., low Tucker rank) within diffusion models to achieve data efficiency and scalable generation, but they first pose the problem as an explicit open question to frame the need for such a framework.