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arXiv · 2502.09122

Improving Deep Regression with Tightness

Shihao Zhang·Yuguang Yan·Angela Yao
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Abstract

For deep regression, preserving the ordinality of the targets with respect to the feature representation improves performance across various tasks. However, a theoretical explanation for the benefits of ordinality is still lacking. This work reveals that preserving ordinality reduces the conditional entropy $H(Z|Y)$ of representation $Z$ conditional on the target $Y$. However, our findings reveal that typical regression losses do little to reduce $H(Z|Y)$, even though it is vital for generalization performance. With this motivation, we introduce an optimal transport-based regularizer to preserve the similarity relationships of targets in the feature space to reduce $H(Z|Y)$. Additionally, we introduce a simple yet efficient strategy of duplicating the regressor targets, also with the aim of reducing $H(Z|Y)$. Experiments on three real-world regression tasks verify the effectiveness of our strategies to improve deep regression. Code: https://github.com/needylove/Regression_tightness.

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Shihao Zhang, Yuguang Yan, Angela Yao. 2025-02-13. Improving Deep Regression with Tightness. https://arxiv.org/abs/2502.09122

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