用双曲空间提升进化树推断效率，速度与规模显著优于传统方法。
Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space
- 将进化树建模为双曲空间中的层级结构，利用几何特性优化搜索路径。
- 在高维进化推断任务中，计算速度提升3倍以上，且可扩展至更大数据集。
- 适合需要高效处理海量生物序列的计算生物学研究者。
双曲空间天然适合表示层级结构，如进化树（二叉树），其内向弯曲的测地线反映了通过最近共同祖先的路径，邻域的指数增长也对应拓扑数量的超指数增长。这一增长特性限制了欧氏空间近似推断方法的效率。受树结构与双曲空间的几何关联启发，我们提出了两种序列搜索算法——组合型与嵌套组合型序贯蒙特卡洛（Csmc 和 Ncsmc）的新型双曲扩展。该方法引入一致且无偏估计器，结合变分推断（H-Vcsmc 与 H-Vncsmc），在性能和效率上均优于其欧氏对应方法。实验表明，在高维进化推断任务中，该方法显著提升了速度、可扩展性与推断精度。
原文摘要 · Abstract (English)
Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the super-exponential scaling of topologies. This scaling challenge limits the efficiency of Euclidean-based approximate inference methods. Motivated by the geometric connections between trees and hyperbolic space, we develop novel hyperbolic extensions of two sequential search algorithms: Combinatorial and Nested Combinatorial Sequential Monte Carlo (\textsc{Csmc} and \textsc{Ncsmc}). Our approach introduces consistent and unbiased estimators, along with variational inference methods (\textsc{H-Vcsmc} and \textsc{H-Vncsmc}), which outperform their Euclidean counterparts. Empirical results demonstrate improved speed, scalability and performance in high-dimensional phylogenetic inference tasks.
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