不依赖插补，用概率质量核处理异构缺失数据
HI-PMK: A Data-Dependent Kernel for Incomplete Heterogeneous Data Representation
- 基于概率质量设计适配异构特征的相似性度量
- 对三类缺失机制均采用保守策略，提升鲁棒性
- 适合隐私敏感、缺失模式复杂的实际场景
真实世界机器学习中，处理缺失且异构的数据仍是核心挑战，缺失可能遵循复杂机制（MCAR、MAR、MNAR），特征类型也混杂（数值型与类别型）。现有方法常依赖插补，可能引入偏差或隐私风险，或无法同时应对异构性与结构化缺失。我们提出新型数据依赖表示学习方法——异构不完整概率质量核（HI-PMK），无需插补。其关键创新：(1) 基于概率质量的局部分布自适应相似性度量，适用于数值、序数、名义型特征；(2) 缺失感知不确定性策略（MaxU），通过为未观测项分配最大合理相似性，保守处理三类缺失机制。该方法具备隐私保护性、可扩展性，并可直接用于分类、聚类等下游任务。在超过15个基准数据集上的实验表明，HI-PMK在各类缺失设置下持续优于传统插补流水线和核方法。
原文摘要 · Abstract (English)
Handling incomplete and heterogeneous data remains a central challenge in real-world machine learning, where missing values may follow complex mechanisms (MCAR, MAR, MNAR) and features can be of mixed types (numerical and categorical). Existing methods often rely on imputation, which may introduce bias or privacy risks, or fail to jointly address data heterogeneity and structured missingness. We propose the \textbf{H}eterogeneous \textbf{I}ncomplete \textbf{P}robability \textbf{M}ass \textbf{K}ernel (\textbf{HI-PMK}), a novel data-dependent representation learning approach that eliminates the need for imputation. HI-PMK introduces two key innovations: (1) a probability mass-based dissimilarity measure that adapts to local data distributions across heterogeneous features (numerical, ordinal, nominal), and (2) a missingness-aware uncertainty strategy (MaxU) that conservatively handles all three missingness mechanisms by assigning maximal plausible dissimilarity to unobserved entries. Our approach is privacy-preserving, scalable, and readily applicable to downstream tasks such as classification and clustering. Extensive experiments on over 15 benchmark datasets demonstrate that HI-PMK consistently outperforms traditional imputation-based pipelines and kernel methods across a wide range of missing data settings. Code is available at: https://github.com/echoid/Incomplete-Heter-Kernel
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