# Learning Quasi-Kronecker Product Graphical Models

## TL;DR

This paper introduces a Bayesian hierarchical method for learning graphical models with support decomposable as a Kronecker product, effectively reducing hyperparameter complexity and avoiding overfitting.

## Contribution

It presents a novel approach leveraging the Kronecker structure and Bayesian hierarchy to improve model learning efficiency and robustness.

## Key findings

- Method successfully captures Kronecker-structured supports.
- Reduces hyperparameter count compared to traditional models.
- Demonstrates effectiveness through numerical experiments.

## Abstract

We consider the problem of learning graphical models where the support of the concentration matrix can be decomposed as a Kronecker product. We propose a method that uses the Bayesian hierarchical learning modeling approach. Thanks to the particular structure of the graph, we use a the number of hyperparameters which is small compared to the number of nodes in the graphical model. In this way, we avoid overfitting in the estimation of the hyperparameters. Finally, we test the effectiveness of the proposed method by a numerical example.