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.

翻译：自回归模型能够从学习到的概率分布中进行可处理的采样，但其性能关键取决于分解过程中所使用的变量顺序，这会影响条件分布的复杂度。我们提出学习描述底层数据的马尔可夫随机场，并利用推断出的图模型结构来构建优化的变量顺序。我们在二维类图像模型上展示了该方法，其中结构感知的排序能够限制条件集，从而降低模型复杂度。在离散数据的伊辛模型上进行的数值实验表明，基于图信息的排序相比朴素变量排序能够生成保真度更高的样本。