Deep convolutional neural networks (CNNs) trained with logistic and softmax losses have made significant advancement in visual recognition tasks in computer vision. When training data exhibit class imbalances, the class-wise reweighted version of logistic and softmax losses are often used to boost performance of the unweighted version. In this paper, motivated to explain the reweighting mechanism, we explicate the learning property of those two loss functions by analyzing the necessary condition (e.g., gradient equals to zero) after training CNNs to converge to a local minimum. The analysis immediately provides us explanations for understanding (1) quantitative effects of the class-wise reweighting mechanism: deterministic effectiveness for binary classification using logistic loss yet indeterministic for multi-class classification using softmax loss; (2) disadvantage of logistic loss for single-label multi-class classification via one-vs.-all approach, which is due to the averaging effect on predicted probabilities for the negative class (e.g., non-target classes) in the learning process. With the disadvantage and advantage of logistic loss disentangled, we thereafter propose a novel reweighted logistic loss for multi-class classification. Our simple yet effective formulation improves ordinary logistic loss by focusing on learning hard non-target classes (target vs. non-target class in one-vs.-all) and turned out to be competitive with softmax loss. We evaluate our method on several benchmark datasets to demonstrate its effectiveness.
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This content will become publicly available on March 1, 2025
Approximately Optimal Domain Adaptation with Fisher’s Linear Discriminant
We propose and study a data-driven method that can interpolate between a classical and a modern approach to classification for a class of linear models. The class is the convex combinations of an average of the source task classifiers and a classifier trained on the limited data available for the target task. We derive the expected loss of an element in the class with respect to the target distribution for a specific generative model, propose a computable approximation of the loss, and demonstrate that the element of the proposed class that minimizes the approximated risk is able to exploit a natural bias–variance trade-off in task space in both simulated and real-data settings. We conclude by discussing further applications, limitations, and potential future research directions.
more » « less- Award ID(s):
- 2031985
- PAR ID:
- 10537985
- Publisher / Repository:
- Mathematics
- Date Published:
- Journal Name:
- Mathematics
- Volume:
- 12
- Issue:
- 5
- ISSN:
- 2227-7390
- Page Range / eLocation ID:
- 746
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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