Gradient Aligned Regression via Pairwise Losses

Dixian Zhu, Tianbao Yang, Livnat Jerby
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:80259-80281, 2025.

Abstract

Regression is a fundamental task in machine learning that has garnered extensive attention over the past decades. The conventional approach for regression involves employing loss functions that primarily concentrate on aligning model prediction with the ground truth for each individual data sample. Recent research endeavors have introduced novel perspectives by incorporating label similarity into regression through the imposition of additional pairwise regularization or contrastive learning on the latent feature space, demonstrating their effectiveness. However, there are two drawbacks to these approaches: (i) their pairwise operations in the latent feature space are computationally more expensive than conventional regression losses; (ii) they lack theoretical insights behind these methods. In this work, we propose GAR (Gradient Aligned Regression) as a competitive alternative method in label space, which is constituted by a conventional regression loss and two pairwise label difference losses for gradient alignment including magnitude and direction. GAR enjoys: i) the same level efficiency as conventional regression loss because the quadratic complexity for the proposed pairwise losses can be reduced to linear complexity; ii) theoretical insights from learning the pairwise label difference to learning the gradient of the ground truth function. We limit our current scope as regression on the clean data setting without noises, outliers or distributional shifts, etc. We demonstrate the effectiveness of the proposed method practically on two synthetic datasets and on eight extensive real-world tasks from six benchmark datasets with other eight competitive baselines. Running time experiments demonstrate the superior efficiency of the proposed GAR compared to existing methods with pairwise regularization or contrastive learning in the latent feature space. Additionally, ablation studies confirm the effectiveness of each component of GAR. The code is open sourced at https://github.com/DixianZhu/GAR.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhu25x, title = {Gradient Aligned Regression via Pairwise Losses}, author = {Zhu, Dixian and Yang, Tianbao and Jerby, Livnat}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {80259--80281}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhu25x/zhu25x.pdf}, url = {https://proceedings.mlr.press/v267/zhu25x.html}, abstract = {Regression is a fundamental task in machine learning that has garnered extensive attention over the past decades. The conventional approach for regression involves employing loss functions that primarily concentrate on aligning model prediction with the ground truth for each individual data sample. Recent research endeavors have introduced novel perspectives by incorporating label similarity into regression through the imposition of additional pairwise regularization or contrastive learning on the latent feature space, demonstrating their effectiveness. However, there are two drawbacks to these approaches: (i) their pairwise operations in the latent feature space are computationally more expensive than conventional regression losses; (ii) they lack theoretical insights behind these methods. In this work, we propose GAR (Gradient Aligned Regression) as a competitive alternative method in label space, which is constituted by a conventional regression loss and two pairwise label difference losses for gradient alignment including magnitude and direction. GAR enjoys: i) the same level efficiency as conventional regression loss because the quadratic complexity for the proposed pairwise losses can be reduced to linear complexity; ii) theoretical insights from learning the pairwise label difference to learning the gradient of the ground truth function. We limit our current scope as regression on the clean data setting without noises, outliers or distributional shifts, etc. We demonstrate the effectiveness of the proposed method practically on two synthetic datasets and on eight extensive real-world tasks from six benchmark datasets with other eight competitive baselines. Running time experiments demonstrate the superior efficiency of the proposed GAR compared to existing methods with pairwise regularization or contrastive learning in the latent feature space. Additionally, ablation studies confirm the effectiveness of each component of GAR. The code is open sourced at https://github.com/DixianZhu/GAR.} }
Endnote
%0 Conference Paper %T Gradient Aligned Regression via Pairwise Losses %A Dixian Zhu %A Tianbao Yang %A Livnat Jerby %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhu25x %I PMLR %P 80259--80281 %U https://proceedings.mlr.press/v267/zhu25x.html %V 267 %X Regression is a fundamental task in machine learning that has garnered extensive attention over the past decades. The conventional approach for regression involves employing loss functions that primarily concentrate on aligning model prediction with the ground truth for each individual data sample. Recent research endeavors have introduced novel perspectives by incorporating label similarity into regression through the imposition of additional pairwise regularization or contrastive learning on the latent feature space, demonstrating their effectiveness. However, there are two drawbacks to these approaches: (i) their pairwise operations in the latent feature space are computationally more expensive than conventional regression losses; (ii) they lack theoretical insights behind these methods. In this work, we propose GAR (Gradient Aligned Regression) as a competitive alternative method in label space, which is constituted by a conventional regression loss and two pairwise label difference losses for gradient alignment including magnitude and direction. GAR enjoys: i) the same level efficiency as conventional regression loss because the quadratic complexity for the proposed pairwise losses can be reduced to linear complexity; ii) theoretical insights from learning the pairwise label difference to learning the gradient of the ground truth function. We limit our current scope as regression on the clean data setting without noises, outliers or distributional shifts, etc. We demonstrate the effectiveness of the proposed method practically on two synthetic datasets and on eight extensive real-world tasks from six benchmark datasets with other eight competitive baselines. Running time experiments demonstrate the superior efficiency of the proposed GAR compared to existing methods with pairwise regularization or contrastive learning in the latent feature space. Additionally, ablation studies confirm the effectiveness of each component of GAR. The code is open sourced at https://github.com/DixianZhu/GAR.
APA
Zhu, D., Yang, T. & Jerby, L.. (2025). Gradient Aligned Regression via Pairwise Losses. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:80259-80281 Available from https://proceedings.mlr.press/v267/zhu25x.html.

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