高维聚类中的迁移学习：极小极大阈值及在单细胞数据中的应用
Transfer Learning in High-Dimensional Clustering: Minimax Thresholds and Applications in Single-Cell Data
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中文总结 AI 辅助
研究高维聚类中迁移学习问题，开发极小极大最优迁移辅助聚类方法，刻画一致目标聚类相变，可自适应选择聚类方式，扩展技术适应多社区多源数据集，模拟和实例分析验证方法有效性。
中文摘要 AI 辅助
聚类是统计学中的一个基本问题，在许多科学学科中都有应用。在许多涉及聚类的现代应用中，主要数据集（目标数据）伴随着相关数据集（源数据）。从这些源数据中转移信息可以提高目标聚类的准确性，这使得聚类的迁移学习具有实际重要性。尽管最近有进展，但在高维环境下，即使对于典型的高斯混合模型，源数据改善目标聚类的条件仍不清楚。本文研究了一个双社区高斯混合模型中的聚类问题，其中相关性通过目标和源聚类均值的几何对齐来体现。我们开发了一种极小极大最优的迁移辅助聚类方法，并在对数因子范围内，根据信噪比、样本大小、环境维度和数据集之间的对齐程度，刻画了一致目标聚类的相变。该技术还扩展到根据目标信号强度在仅目标聚类或源辅助聚类之间进行自适应选择。此外，我们还扩展技术以适应多个社区和多个源数据集。大量模拟以及对人类肺部单细胞RNA测序图谱的分析证明了我们方法的实际有效性。
英文摘要
Clustering is a fundamental problem in statistics, with applications across many scientific disciplines. In many modern applications involving clustering, the primary dataset (the target data) is accompanied by related datasets (the source data). Transferring information from such sources may improve clustering accuracy in the target, making transfer learning for clustering practically important. Despite recent progress, the conditions under which source data improve target clustering remain unclear in high-dimensional settings, even for the canonical Gaussian mixture model. In this paper, we study the clustering problem in a two-community Gaussian mixture model where relatedness is captured by the geometric alignment of the target and source cluster means. We develop a minimax-optimal transfer-assisted clustering procedure and characterize, up to logarithmic factors, the phase transition for consistent target clustering in terms of the signal-to-noise ratios, sample sizes, ambient dimension, and degree of alignment between the datasets. The technique is also extended to adaptively choose between the target-only or the source assisted clustering depending on the target signal strength. Furthermore, we also extend our techniques to accommodate multiple communities and and multiple source datasets. Extensive simulations and an analysis of a human lung single-cell RNA-sequencing atlas demonstrate the practical effectiveness of our methods.
