Selecting Optimal Variable Order in Autoregressive Ising Models
This work addresses a specific bottleneck in autoregressive modeling for discrete data, offering an incremental improvement in sample quality.
The paper tackles the problem of variable ordering in autoregressive Ising models, showing that graph-informed orderings reduce model complexity and yield higher-fidelity generated samples compared to naive orderings.
Autoregressive models enable tractable sampling from learned probability distributions, but their performance critically depends on the variable ordering used in the factorization via complexities of the resulting conditional distributions. We propose to learn the Markov random field describing the underlying data, and use the inferred graphical model structure to construct optimized variable orderings. We illustrate our approach on two-dimensional image-like models where a structure-aware ordering leads to restricted conditioning sets, thereby reducing model complexity. Numerical experiments on Ising models with discrete data demonstrate that graph-informed orderings yield higher-fidelity generated samples compared to naive variable orderings.