Bayesian Distilled Clustering for High-Dimensional Mixture Models
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高维混合模型的贝叶斯蒸馏聚类
- 研究问题
- 高维混合模型中，如何识别真正区分潜在群体的变量，避免无关维度掩盖群体结构，并使聚类子空间符合研究目标？
- 方法与思路
- 作者用贝叶斯变量选择获得后验纳入概率，通过控制期望错误发现比例提取变量子集，再聚类并进行条件独立性诊断。
- 材料陈述的贡献
- 摘要提出与混合结构和响应模型相联系的子空间选择框架，使变量筛选针对群体分离及响应行为，而非一般降维标准。
- 阅读关注点
- 应核对纳入概率的定义、错误发现比例控制的具体含义、混合模型的可识别性，以及筛选后的聚类与诊断如何处理不确定性。
- 阅读边界
- 仅据 arXiv v1 预印本摘要，不能声称已同行评审或期刊接收；摘要未提供定理条件、数值验证或比较结果。
原文摘要
Latent subgroup analysis is central to fields such as genomics, precision medicine, and social science, where the goal is to identify heterogeneous populations with distinct covariate structures or response behaviors. Mixture models provide a natural probabilistic framework for this task, representing the data-generating distribution as a weighted combination of subgroup-specific laws with unobserved labels. In high-dimensional regimes, these analyses face significant challenges. Often, only a small subset of covariates drives meaningful subgroup separation; the remaining variables may introduce noise or redundancy. Standard clustering methods typically treat all dimensions as equal, but in high-dimensional spaces, irrelevant coordinates can distort distances and obscure the low-dimensional structures defining latent classes. This paper introduces a Bayesian distilled clustering framework for high-dimensional mixture models. We propose that clustering should occur within a statistically justified subspace rather than the full ambient space. Our method utilizes a Bayesian variable selection model to estimate posterior inclusion probabilities, quantifying the evidence that each covariate contributes to subgroup separation or response behavior. A "distilled" covariate set is then identified by controlling the expected false-discovery proportion. Clustering is performed on this reduced subspace, followed by conditional independence diagnostics to examine subgroup-specific dependencies among selected variables. Critically, this framework is model-based: the distillation step is tied directly to the mixture structure and response model rather than a generic dimension-reduction criterion. This ensures the resulting subspace remains aligned with the scientific objective: identifying latent subgroups that differ in both distributional structure and behavior.