仅用每组中正例数量训练模型,实现无偏学习且效果稳定。
Learning from N-Tuple Data with M Positive Instances: Unbiased Risk Estimation and Theoretical Guarantees
- 基于每组正例数设计无偏风险估计器,链接组合生成与实例概率
- 理论保证泛化能力与统计一致性,支持不同组大小和正例数
- 适用于图像区域分类等弱监督场景,对类别不平衡鲁棒
弱监督学习常依赖粗粒度聚合信号而非个体标签。本文研究一种设置:每个训练样本为一个包含恰好 m 个正例的 n 元组,仅观测到每组的正例数量 m。该 NTMP(N-tuple with M positives)监督常见于带区域提议的图像分类和多实例测量。我们证明,通过将元组生成过程与潜在实例边际联系,元组计数可导出可训练的无偏风险估计器(URE)。从固定 (n,m) 出发,推导闭式解,并扩展至可变元组大小、可变正例数及其组合。只要有效混合率与类别先验分离,即可实现识别。利用 Rademacher 复杂度建立泛化界,在温和正则性假设下证明统计一致性并达到标准速率。为提升有限样本稳定性,引入简单的 ReLU 修正,保持渐近正确性。在转换为 NTMP 任务的多个基准上,该方法持续优于代表性弱监督基线,获得更优的精确率-召回率与 F1 平衡。在类别先验失衡及多种元组配置下仍表现稳健,表明仅凭计数监督亦可通过理论严谨且实用稳定的损失函数有效利用。
原文摘要 · Abstract (English)
Weakly supervised learning often operates with coarse aggregate signals rather than instance labels. We study a setting where each training example is an $n$-tuple containing exactly m positives, while only the count m per tuple is observed. This NTMP (N-tuple with M positives) supervision arises in, e.g., image classification with region proposals and multi-instance measurements. We show that tuple counts admit a trainable unbiased risk estimator (URE) by linking the tuple-generation process to latent instance marginals. Starting from fixed (n,m), we derive a closed-form URE and extend it to variable tuple sizes, variable counts, and their combination. Identification holds whenever the effective mixing rate is separated from the class prior. We establish generalization bounds via Rademacher complexity and prove statistical consistency with standard rates under mild regularity assumptions. To improve finite-sample stability, we introduce simple ReLU corrections to the URE that preserve asymptotic correctness. Across benchmarks converted to NTMP tasks, the approach consistently outperforms representative weak-supervision baselines and yields favorable precision-recall and F1 trade-offs. It remains robust under class-prior imbalance and across diverse tuple configurations, demonstrating that count-only supervision can be exploited effectively through a theoretically grounded and practically stable objective.
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