发育分叉附近RNA速度的图正则化统计理论
A statistical theory of graph regularization for RNA velocity near developmental bifurcations
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中文总结 AI 辅助
该研究建立发育分叉附近RNA速度图正则化的统计理论，推导偏差-方差分解，提出分支敏感风险，揭示邻近图正则化的几何局限性，为RNA速度估计提供数学基础。
中文摘要 AI 辅助
基于图的正则化被广泛用于稳定含噪的RNA速度估计，通过鼓励转录相似的细胞共享相似的速度向量。然而，在发育分叉附近，基于邻近性的图可能连接来自不同子谱系的细胞，在降低估计方差的同时，会削弱具有生物学意义的谱系特异性动态。我们将图正则化的RNA速度公式化为潜在误设的细胞状态图上的统计估计问题，并开发了分析该权衡的理论框架。我们推导了精确的图谱偏差-方差分解，其刻画了拉普拉斯正则化如何抑制估计噪声，同时引入系统性平滑偏差。为量化谱系保留，我们引入了分支敏感风险，将谱系内去噪与跨谱系信息泄漏分离开来。我们进一步表明，持续的跨分支连接可诱导非零的分支偏差，这意味着标准邻近图正则化在发育分叉附近可能仍保持渐近不一致。这些结果为理解RNA速度估计中图正则化的统计益处和几何局限性提供了数学基础。
英文摘要
Graph-based regularization is widely used to stabilize noisy RNA-velocity estimates by encouraging transcriptionally similar cells to share similar velocity vectors. Near developmental bifurcations, however, proximity-based graphs may connect cells from distinct daughter lineages, reducing estimation variance at the cost of attenuating biologically meaningful lineage-specific dynamics. We formulate graph-regularized RNA velocity as a statistical estimation problem on a potentially misspecified cell-state graph and develop a theoretical framework for analyzing this trade-off. We derive an exact graph-spectral bias--variance decomposition that characterizes how Laplacian regularization suppresses estimation noise while introducing systematic smoothing bias. To quantify lineage preservation, we introduce a branch-sensitive risk that separates within-lineage denoising from cross-lineage information leakage. We further show that persistent cross-branch connectivity can induce nonvanishing branch bias, implying that standard proximity-graph regularization may remain asymptotically inconsistent near developmental bifurcations. These results provide a mathematical foundation for understanding both the statistical benefits and the geometric limitations of graph regularization for RNA-velocity estimation.
