Keywords: regression, classification, entropy, depth estimation, counting, age estimation
TL;DR: We observe that many regression problems are preferably formulated as classification tasks, and we provide a theoretical analysis to explain this phenomenon then we propose an ordinal entropy loss to improve the performance of regression.
Abstract: In computer vision, it is often observed that formulating regression problems as a classification task yields better performance. We investigate this curious phenomenon and provide a derivation to show that classification, with the cross-entropy loss, outperforms regression with a mean squared error loss in its ability to learn high-entropy feature representations. Based on the analysis, we propose an ordinal entropy loss to encourage higher-entropy feature spaces while maintaining ordinal relationships to improve the performance of regression tasks. Experiments on synthetic and real-world regression tasks demonstrate the importance and benefits of increasing entropy for regression.
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