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arXiv 2410.03052cs.LG
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通过快速最优传输嵌入类别层次结构来学习结构化表示

Learning Structured Representations by Embedding Class Hierarchy with Fast Optimal Transport

University of Illinois, Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校);Stanford University(斯坦福大学);Okinawa Institute of Science and Technology(冲绳科学技术研究所)

Siqi Zeng, Sixian Du, Makoto Yamada, Han Zhao

AI总结:

针对现有CPCC正则化依赖类别均值导致多模态分布表征不佳的问题,提出基于EMD距离的OT-CPCC方法,并设计线性时间复杂度的Fast FlowTree算法,在保持性能的同时提升效率。

摘要:

为了将标签中的结构化知识嵌入到特征表示中,先前的工作[Zeng等人,2022]提出在监督学习过程中使用共表型相关系数(CPCC)作为正则化项。该正则化器计算类别均值的成对欧氏距离,并将其与从标签层次树导出的相应最短路径距离对齐。然而,类别均值可能不是类别条件分布的良好代表,尤其是当这些分布本质上呈现多模态时。为了解决这一局限性,在CPCC框架下,我们提出使用推土机距离(EMD)来度量特征空间中类别之间的成对距离。我们证明了我们的精确EMD方法推广了先前的工作,并在类别条件分布为高斯分布时恢复了现有算法。为了进一步提高我们方法的计算效率,我们通过探索四种EMD近似变体引入了最优传输-CPCC(OT-CPCC)家族。我们最高效的OT-CPCC变体,即所提出的快速FlowTree算法,其运行时间与数据集大小呈线性关系,同时在多个数据集和任务上保持有竞争力的性能。代码可在https://github.com/uiuctml/OTCPCC获取。

英文摘要:

To embed structured knowledge within labels into feature representations, prior work [Zeng et al., 2022] proposed to use the Cophenetic Correlation Coefficient (CPCC) as a regularizer during supervised learning. This regularizer calculates pairwise Euclidean distances of class means and aligns them with the corresponding shortest path distances derived from the label hierarchy tree. However, class means may not be good representatives of the class conditional distributions, especially when they are multi-mode in nature. To address this limitation, under the CPCC framework, we propose to use the Earth Mover's Distance (EMD) to measure the pairwise distances among classes in the feature space. We show that our exact EMD method generalizes previous work, and recovers the existing algorithm when class-conditional distributions are Gaussian. To further improve the computational efficiency of our method, we introduce the Optimal Transport-CPCC family by exploring four EMD approximation variants. Our most efficient OT-CPCC variant, the proposed Fast FlowTree algorithm, runs in linear time in the size of the dataset, while maintaining competitive performance across datasets and tasks. The code is available at https://github.com/uiuctml/OTCPCC.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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