重新审视多标签分类中的F-measure优化：一种基于采样的方法
Revisiting F-measure Optimization in Multi-Label Classification: A Sampling-based Approach
对视觉多标签任务（如多标签图像识别、属性预测）而言，本文把F-measure最优预测规则中的q^3矩阵乘法改写为可用FFT加速的卷积（降至O(q^2 log q)），并用q个二分类器替代q个多分类器以缓解标签稀疏性，可直接替换现有多标签分类器的推理与训练流程。
原文依据 we first demonstrate that matrix multiplication can be reformulated as a series of convolutions by exploiting a special structure in the matrix
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论F-measure是多标签分类中广泛使用的指标，在该任务中需要为单个实例同时预测多个标签。F-measure的最优预测规则需要估计q^2+1个概率，其中q为标签数量。现有方法训练q个多项分布估计器（多类分类器）来直接估计这些概率，随后通过矩阵乘法进行预测。然而，该方法存在两个主要缺陷。首先，矩阵乘法的时间复杂度为O(q^3)，当q较大时计算代价高昂。其次，训练多项分布估计器十分困难，原因在于底层分布的稀疏性，这种稀疏性源于多标签数据集固有的不平衡，并被该方法自身所需的标签变换进一步加剧。本文首先证明，通过利用矩阵中的特殊结构，矩阵乘法可以被重新表述为一系列卷积。这些卷积随后可利用快速傅里叶变换（FFT）高效计算，从而将时间复杂度降至O(q^2 log q)。为避免多项分布标签变换，我们提出一种间接的“先采样后估计”方法来估计所需概率。该方法仅训练q个二分类估计器而非多项分布估计器，从而缓解稀疏性问题、简化训练过程并提升性能。我们为所提出的基于采样的方法的一致性提供了理论保证，并通过在多个数据集上的大量实验证明了其有效性。代码见：https://github.com/ZixunWang/MLC-F1-Sampling。
英文原文摘要 1746 字符
The F-measure is a widely used metric in multi-label classification, where multiple labels are predicted simultaneously for a single instance. The optimal prediction rule for F-measure requires estimating q^2+1 probabilities, where q is the number of labels. Existing approaches train q multinomial estimators (multi-class classifiers) to directly estimate these probabilities, followed by a matrix multiplication for making predictions. However, this method has two major drawbacks. First, the matrix multiplication incurs a time complexity of \mathcal O (q^3), which becomes computationally expensive for large q. Second, training multinomial estimators is challenging due to the sparsity of the underlying distributions, which results from the inherent imbalance in multi-label datasets and is further exacerbated by the label transformation required by the method itself. In this paper, we first demonstrate that matrix multiplication can be reformulated as a series of convolutions by exploiting a special structure in the matrix. These convolutions can then be efficiently computed using the Fast Fourier Transform (FFT), reducing the time complexity to \mathcal O (q^2\log q). To avoid multinomial label transformation, we propose an indirect sampling-then-estimation approach to estimate the required probabilities. This method trains only q binary estimators instead of multinomial ones, thereby alleviating the sparsity issue, simplifying the training process, and improving performance. We provide theoretical guarantees for the consistency of the proposed sampling-based method and demonstrate its effectiveness through extensive experiments on diverse datasets. The code is available in: https://github.com/ZixunWang/MLC-F1-Sampling.