Variational Bayesian phylogenetic inference (VBPI) provides a promising
general variational framework for efficient estimation of phylogenetic
posteriors. However, the current diagonal Lognormal branch length approximation
would significantly restrict the quality of the approximating distributions. In
this paper, we propose a new type of VBPI, VBPI-NF, as a first step to empower
phylogenetic posterior estimation with deep learning techniques. By handling
the non-Euclidean branch length space of phylogenetic models with carefully
designed permutation equivariant transformations, VBPI-NF uses normalizing
flows to provide a rich family of flexible branch length distributions that
generalize across different tree topologies. We show that VBPI-NF significantly
improves upon the vanilla VBPI on a benchmark of challenging real data Bayesian
phylogenetic inference problems. Further investigation also reveals that the
structured parameterization in those permutation equivariant transformations
can provide additional amortization benefit.

本文提出一种名为 VBPI-NF 的变分贝叶斯方法，通过谨慎设计的置换等变变换来处理系统发育模型的非欧几里得分支长度空间，利用正则流提供丰富灵活的分支长度分布，从而显著改进了贝叶斯系统发育推断的实际数据表现。

基于规范流的改进变分贝叶斯系统演化推断

Improved Variational Bayesian Phylogenetic Inference with Normalizing  Flows

In order to gain an understanding of the effectiveness of phylogenetic Markov
chain Monte Carlo (MCMC), it is important to understand how quickly the
empirical distribution of the MCMC converges to the posterior distribution. In
this paper we investigate this problem on phylogenetic tree topologies with a
metric that is especially well suited to the task: the subtree
prune-and-regraft (SPR) metric. This metric directly corresponds to the minimum
number of MCMC rearrangements required to move between trees in common
phylogenetic MCMC implementations. We develop a novel graph-based approach to
analyze tree posteriors and find that the SPR metric is much more informative
than simpler metrics that are unrelated to MCMC moves. In doing so we show
conclusively that topological peaks do occur in Bayesian phylogenetic
posteriors from real data sets as sampled with standard MCMC approaches,
investigate the efficiency of Metropolis-coupled MCMC (MCMCMC) in traversing
the valleys between peaks, and show that conditional clade distribution (CCD)
can have systematic problems when there are multiple peaks.

通过使用适合该任务的子树钳剪与再接（SPR）度量标准，研究了贝叶斯系统发育后分布中的拓扑峰值，并提出了一种基于图形的方法，评价了 MCMC 下的树拓扑结构，并发现在实际数据集中，存在拓扑峰值和连续多峰问题。