  With the advent of quantum and quantum-inspired machine learning, adapting
the structure of learning models to match the structure of target datasets has
been shown to be crucial for obtaining high performance. Probabilistic models
based on tensor networks (TNs) are prime candidates to benefit from
data-dependent design considerations, owing to their bias towards correlations
which are local with respect to the topology of the model. In this work, we use
methods from spectral graph theory to search for optimal permutations of model
sites which are adapted to the structure of an input dataset. Our method uses
pairwise mutual information estimates from the target dataset to ensure that
strongly correlated bits are placed closer to each other relative to the
model's topology. We demonstrate the effectiveness of such preprocessing for
probabilistic modeling tasks, finding substantial improvements in the
performance of generative models based on matrix product states (MPS) across a
variety of datasets. We also show how spectral embedding, a dimensionality
reduction technique from spectral graph theory, can be used to gain further
insights into the structure of datasets of interest.
