Exact Inference in High-order Structured Prediction

Chuyang Ke, Jean Honorio
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:16152-16167, 2023.

Abstract

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-ke23a, title = {Exact Inference in High-order Structured Prediction}, author = {Ke, Chuyang and Honorio, Jean}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {16152--16167}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/ke23a/ke23a.pdf}, url = {https://proceedings.mlr.press/v202/ke23a.html}, abstract = {In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.} }
Endnote
%0 Conference Paper %T Exact Inference in High-order Structured Prediction %A Chuyang Ke %A Jean Honorio %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-ke23a %I PMLR %P 16152--16167 %U https://proceedings.mlr.press/v202/ke23a.html %V 202 %X In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.
APA
Ke, C. & Honorio, J.. (2023). Exact Inference in High-order Structured Prediction. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:16152-16167 Available from https://proceedings.mlr.press/v202/ke23a.html.

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