Learning Latent Partial Matchings with Gumbel-IPF Networks

Hedda Cohen Indelman, Tamir Hazan
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:1513-1521, 2024.

Abstract

Learning to match discrete objects has been a central task in machine learning, often facilitated by a continuous relaxation of the matching structure. However, practical problems entail partial matchings due to missing correspondences, which pose difficulties to the one-to-one matching learning techniques that dominate the state-of-the-art. This paper introduces Gumbel-IPF networks for learning latent partial matchings. At the core of our method is the differentiable Iterative Proportional Fitting (IPF) procedure that biproportionally projects onto the transportation polytope of target marginals. Our theoretical framework also allows drawing samples from the temperature-dependent partial matching distribution. We investigate the properties of common-practice relaxations through the lens of biproportional fitting and introduce a new metric, the empirical prediction shift. Our method’s advantages are demonstrated in experimental results on the semantic keypoints partial matching task on the Pascal VOC, IMC-PT-SparseGM, and CUB2001 datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-cohen-indelman24a, title = {Learning Latent Partial Matchings with {G}umbel-{IPF} Networks}, author = {Cohen Indelman, Hedda and Hazan, Tamir}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {1513--1521}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/cohen-indelman24a/cohen-indelman24a.pdf}, url = {https://proceedings.mlr.press/v238/cohen-indelman24a.html}, abstract = {Learning to match discrete objects has been a central task in machine learning, often facilitated by a continuous relaxation of the matching structure. However, practical problems entail partial matchings due to missing correspondences, which pose difficulties to the one-to-one matching learning techniques that dominate the state-of-the-art. This paper introduces Gumbel-IPF networks for learning latent partial matchings. At the core of our method is the differentiable Iterative Proportional Fitting (IPF) procedure that biproportionally projects onto the transportation polytope of target marginals. Our theoretical framework also allows drawing samples from the temperature-dependent partial matching distribution. We investigate the properties of common-practice relaxations through the lens of biproportional fitting and introduce a new metric, the empirical prediction shift. Our method’s advantages are demonstrated in experimental results on the semantic keypoints partial matching task on the Pascal VOC, IMC-PT-SparseGM, and CUB2001 datasets.} }
Endnote
%0 Conference Paper %T Learning Latent Partial Matchings with Gumbel-IPF Networks %A Hedda Cohen Indelman %A Tamir Hazan %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-cohen-indelman24a %I PMLR %P 1513--1521 %U https://proceedings.mlr.press/v238/cohen-indelman24a.html %V 238 %X Learning to match discrete objects has been a central task in machine learning, often facilitated by a continuous relaxation of the matching structure. However, practical problems entail partial matchings due to missing correspondences, which pose difficulties to the one-to-one matching learning techniques that dominate the state-of-the-art. This paper introduces Gumbel-IPF networks for learning latent partial matchings. At the core of our method is the differentiable Iterative Proportional Fitting (IPF) procedure that biproportionally projects onto the transportation polytope of target marginals. Our theoretical framework also allows drawing samples from the temperature-dependent partial matching distribution. We investigate the properties of common-practice relaxations through the lens of biproportional fitting and introduce a new metric, the empirical prediction shift. Our method’s advantages are demonstrated in experimental results on the semantic keypoints partial matching task on the Pascal VOC, IMC-PT-SparseGM, and CUB2001 datasets.
APA
Cohen Indelman, H. & Hazan, T.. (2024). Learning Latent Partial Matchings with Gumbel-IPF Networks. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:1513-1521 Available from https://proceedings.mlr.press/v238/cohen-indelman24a.html.

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