Selecting Optimal Variable Order in Autoregressive Ising Models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915832145117184 |
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| author | Biswal, Shiba Vuffray, Marc Lokhov, Andrey Y. |
| author_facet | Biswal, Shiba Vuffray, Marc Lokhov, Andrey Y. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_20394 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Selecting Optimal Variable Order in Autoregressive Ising Models Biswal, Shiba Vuffray, Marc Lokhov, Andrey Y. Machine Learning Statistical Mechanics 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. |
| title | Selecting Optimal Variable Order in Autoregressive Ising Models |
| topic | Machine Learning Statistical Mechanics |
| url | https://arxiv.org/abs/2602.20394 |