Learning Constrained Structured Spaces with Application to Multi-Graph Matching

Hedda Cohen Indelman, Tamir Hazan
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:2589-2602, 2023.

Abstract

Multi-graph matching is a prominent structured prediction task, in which the predicted label is constrained to the space of cycle-consistent matchings. While direct loss minimization is an effective method for learning predictors over structured label spaces, it cannot be applied efficiently to the problem at hand, since executing a specialized solver across sets of matching predictions is computationally prohibitive. Moreover, there’s no supervision on the ground-truth matchings over cycle-consistent prediction sets. Our key insight is to strictly enforce the matching constraints in pairwise matching predictions and softly enforce the cycle-consistency constraints by casting them as weighted loss terms, such that the severity of inconsistency with global predictions is tuned by a penalty parameter. Inspired by the classic penalty method, we prove that our method theoretically recovers the optimal multi-graph matching constrained solution. Our method’s advantages are brought to light in experimental results on the popular keypoint matching task on the Pascal VOC and the Willow ObjectClass datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-indelman23a, title = {Learning Constrained Structured Spaces with Application to Multi-Graph Matching}, author = {Indelman, Hedda Cohen and Hazan, Tamir}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {2589--2602}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/indelman23a/indelman23a.pdf}, url = {https://proceedings.mlr.press/v206/indelman23a.html}, abstract = {Multi-graph matching is a prominent structured prediction task, in which the predicted label is constrained to the space of cycle-consistent matchings. While direct loss minimization is an effective method for learning predictors over structured label spaces, it cannot be applied efficiently to the problem at hand, since executing a specialized solver across sets of matching predictions is computationally prohibitive. Moreover, there’s no supervision on the ground-truth matchings over cycle-consistent prediction sets. Our key insight is to strictly enforce the matching constraints in pairwise matching predictions and softly enforce the cycle-consistency constraints by casting them as weighted loss terms, such that the severity of inconsistency with global predictions is tuned by a penalty parameter. Inspired by the classic penalty method, we prove that our method theoretically recovers the optimal multi-graph matching constrained solution. Our method’s advantages are brought to light in experimental results on the popular keypoint matching task on the Pascal VOC and the Willow ObjectClass datasets.} }
Endnote
%0 Conference Paper %T Learning Constrained Structured Spaces with Application to Multi-Graph Matching %A Hedda Cohen Indelman %A Tamir Hazan %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-indelman23a %I PMLR %P 2589--2602 %U https://proceedings.mlr.press/v206/indelman23a.html %V 206 %X Multi-graph matching is a prominent structured prediction task, in which the predicted label is constrained to the space of cycle-consistent matchings. While direct loss minimization is an effective method for learning predictors over structured label spaces, it cannot be applied efficiently to the problem at hand, since executing a specialized solver across sets of matching predictions is computationally prohibitive. Moreover, there’s no supervision on the ground-truth matchings over cycle-consistent prediction sets. Our key insight is to strictly enforce the matching constraints in pairwise matching predictions and softly enforce the cycle-consistency constraints by casting them as weighted loss terms, such that the severity of inconsistency with global predictions is tuned by a penalty parameter. Inspired by the classic penalty method, we prove that our method theoretically recovers the optimal multi-graph matching constrained solution. Our method’s advantages are brought to light in experimental results on the popular keypoint matching task on the Pascal VOC and the Willow ObjectClass datasets.
APA
Indelman, H.C. & Hazan, T.. (2023). Learning Constrained Structured Spaces with Application to Multi-Graph Matching. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:2589-2602 Available from https://proceedings.mlr.press/v206/indelman23a.html.

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