# Local Perturb-and-MAP for Structured Prediction

arXiv: https://arxiv.org/abs/1605.07686 · HTML: https://mlsanity.com/paper/1605.07686/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2016.

## Built on by (most cited first, 2 of 2)

- [Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approach](https://mlsanity.com/paper/2106.03188/) (2021)
- [Regularized Large Neighborhood Search](https://mlsanity.com/paper/2606.02294/) (2026)

## Abstract (arXiv)

Conditional random fields (CRFs) provide a powerful tool for structured prediction, but cast significant challenges in both the learning and inference steps. Approximation techniques are widely used in both steps, which should be considered jointly to guarantee good performance (a.k.a. "inferning"). Perturb-and-MAP models provide a promising alternative to CRFs, but require global combinatorial optimization and hence they are usable only on specific models. In this work, we present a new Local Perturb-and-MAP (locPMAP) framework that replaces the global optimization with a local optimization by exploiting our observed connection between locPMAP and the pseudolikelihood of the original CRF model. We test our approach on three different vision tasks and show that our method achieves consistently improved performance over other approximate inference techniques optimized to a pseudolikelihood objective. Additionally, we demonstrate that we can integrate our method in the fully convolutional network framework to increase our model's complexity. Finally, our observed connection between locPMAP and the pseudolikelihood leads to a novel perspective for understanding and using pseudolikelihood.