Improving Deep Regression with Tightness
Keywords: regression representation, ordinality, tightness, depth estimation, age estimation
TL;DR: regression suffers from the weak ability to minimizing H(Z|Y), and preserving the ordinality of targets can reduce H(Z|Y).
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 fail to sufficiently reduce $H(Z|Y)$, despite its crucial role in 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
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Submission Number: 6321
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