# A New Family of Tractable Ising Models

arXiv: https://arxiv.org/abs/1906.06431 · HTML: https://mlsanity.com/paper/1906.06431/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2019.

## Built on by (most cited first, 1 of 1)

- [Inference and Optimization for Engineering and Physical Systems](https://mlsanity.com/paper/2208.13880/) (2022)

## Abstract (arXiv)

We present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive "gluing" of planar and O(1)-sized components along with subsets of at most three vertices into a tree. The polynomial time algorithm of the dynamic programming type for solving exact inference (partition function computation) and sampling consists of a sequential application of an efficient (for planar) or brute-force (for O(1)-sized) inference and sampling to the components as a black box. To illustrate the utility of the new family of tractable graphical models, we first build an O(N3/2) algorithm for inference and sampling of the K5-minor-free zero-field Ising models - an extension of the planar zero-field Ising models - which is neither genus- nor treewidth-bounded. Second, we demonstrate empirically an improvement in the approximation quality of the NP-hard problem of the square-grid Ising model (with non-zero field) inference.