变分推断的进步为贝叶斯估计问题提供了有前景的路径。这些进步使得变分系统发育推断成为马尔可夫链蒙特卡洛（Markov Chain Monte Carlo）方法的一种替代方案，用于近似系统发育后验。然而，此类方法的主要缺点之一是通过固定分布对先验进行建模，如果它们偏离当前数据分布，可能会使后验近似产生偏差。在本文中，我们提出了一种方法和实现框架，通过使用基于梯度的方法和基于神经网络的参数化来学习先验密度的参数，从而缓解先验密度的刚性。我们在几种马尔可夫链替换模型下，将该方法应用于分支长度和进化参数的估计。模拟结果表明，该方法在估计分支长度和进化模型参数方面非常有效。结果还表明，与预定义的先验模型相比，灵活的先验模型能提供更好的结果。最后，结果强调，使用神经网络能改善先验密度参数优化的初始化。
英文摘要：
The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the phylogenetic posterior. However, one of the main drawbacks of such approaches is modelling the prior through fixed distributions, which could bias the posterior approximation if they are distant from the current data distribution. In this paper, we propose an approach and an implementation framework to relax the rigidity of the prior densities by learning their parameters using a gradient-based method and a neural network-based parameterization. We applied this approach for branch lengths and evolutionary parameters estimation under several Markov chain substitution models. The results of performed simulations show that the approach is powerful in estimating branch lengths and evolutionary model parameters. They also show that a flexible prior model could provide better results than a predefined prior model. Finally, the results highlight that using neural networks improves the initialization of the optimization of the prior density parameters.
PhyloVAE: Unsupervised Learning of Phylogenetic Trees via Variational Autoencoders
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Center for Statistical Science, Peking University（北京大学统计科学中心）；Computational Biology Program, Fred Hutchinson Cancer Research Center（弗雷德·哈钦森癌症研究中心计算生物学项目）；Howard Hughes Medical Institute（霍华德·休斯医学研究所）
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 no…
We describe an "embarrassingly parallel" method for Bayesian phylogenetic inference, annealed Sequential Monte Carlo, based on recent advances in the Sequential Monte Carlo literature such as adaptive determination of annealing parameters. The algorithm provides an approximate posterior distribution over trees and evolutionary parameters as well as an unbiased estimator for the marginal likelihood. This unbiasedness property can be used for the purpose of testing the correctness of posterior simulation software. We evaluate the performance of phylogenetic annealed Sequential Monte Carlo by rev…
By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to increase in complexity to better capture micro and macroevolutionary processes. In a Bayesian framework, the marginal likelihood is how data update our prior beliefs about models, which gives us an intuitive measure of comparing model fit that is grounded in probability theory. Given the rapid increase in the number and complexity of phylogenetic models, methods f…
Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC) run explores the space of phylogenetic trees. In this paper, we investigate the Monte Carlo error of phylogenies, focusing on high-dimensional summaries of the posterior distribution, including variability in estimated edge/branch (known in phylogenetics as "split") probabilities and tree probabilities, and variability in the estimated summary tree. Specific…
Structural information of phylogenetic tree topologies plays an important role in phylogenetic inference. However, finding appropriate topological structures for specific phylogenetic inference tasks often requires significant design effort and domain expertise. In this paper, we propose a novel structural representation method for phylogenetic inference based on learnable topological features. By combining the raw node features that minimize the Dirichlet energy with modern graph representation learning techniques, our learnable topological features can provide efficient structural informatio…
Phylogenetic comparative methods correct for shared evolutionary history among a set of non-independent organisms by modeling sample traits as arising from a diffusion process along on the branches of a possibly unknown history. To incorporate such uncertainty, we present a scalable Bayesian inference framework under a general Gaussian trait evolution model that exploits Hamiltonian Monte Carlo (HMC). HMC enables efficient sampling of the constrained model parameters and takes advantage of the tree structure for fast likelihood and gradient computations, yielding algorithmic complexity linear …
The Bayesian method is noted to produce spuriously high posterior probabilities for phylogenetic trees in analysis of large datasets, but the precise reasons for this over-confidence are unknown. In general, the performance of Bayesian selection of misspecified models is poorly understood, even though this is of great scientific interest since models are never true in real data analysis. Here we characterize the asymptotic behavior of Bayesian model selection and show that when the competing models are equally wrong, Bayesian model selection exhibits surprising and polarized behaviors in large…
Given overlapping subsets of a set of taxa (e.g. species), and posterior distributions on phylogenetic tree topologies for each of these taxon sets, how can we infer a posterior distribution on phylogenetic tree topologies for the entire taxon set? Although the equivalent problem for in the non-Bayesian case has attracted substantial research, the Bayesian case has not attracted the attention it deserves. In this paper we develop a variational Bayes approach to this problem and demonstrate its effectiveness.
Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters, such as divergence times and population sizes, they form a generative process of molecular sequence evolution. Early work on computational methods for phylogenetic network inference focused exclusively on reticulations and sought networks with the fewest number of reticulations to fit the data. As processes such as incomplete lineage sorting (ILS) could be at …
Bayesian Markov chain Monte Carlo explores tree space slowly, in part because it frequently returns to the same tree topology. An alternative strategy would be to explore tree space systematically, and never return to the same topology. In this paper, we present an efficient parallelized method to map out the high likelihood set of phylogenetic tree topologies via systematic search, which we show to be a good approximation of the high posterior set of tree topologies. Here `likelihood' of a topology refers to the tree likelihood for the corresponding tree with optimized branch lengths. We call…
An adaptive time-tree transition kernel for Bayesian phylogenetic inference
KU Leuven（荷语鲁汶大学）；Fred Hutchinson Cancer Center（弗雷德·哈钦森癌症中心）；University of California, Los Angeles（加州大学洛杉矶分校）；David Geffen School of Medicine at UCLA（加州大学洛杉矶分校大卫格芬医学院）；University of Edinburgh（爱丁堡大学）；Getulio Vargas Foundation（热图利奥·瓦加斯基金会）
PhylaFlow: Hybrid Flow Matching in Billera-Holmes-Vogtmann Tree Space for Phylogenetic Inference
Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard（埃里克和wendy Schmidt中心，MIT和哈佛大学Broad研究所）；Department of Biomedical Informatics, Harvard Medical School（哈佛医学院生物医学信息学系）；Centennial High School（Centennial高中）；Infectious Disease and Microbiome Program, Broad Institute of MIT and Harvard（传染病与微生物组计划，MIT和哈佛大学Broad研究所）
One of the cornerstones in combating the HIV pandemic is being able to assess the current state and evolution of local HIV epidemics. This remains a complex problem, as many HIV infected individuals remain unaware of their infection status, leading to parts of HIV epidemics being undiagnosed and under-reported. To that end, we firstly present a method to learn epidemiological parameters from phylogenetic trees, using approximate Bayesian computation (ABC). The epidemiological parameters learned as a result of applying ABC are subsequently used in epidemiological models that aim to simulate a s…
Reconstructing pathogen dynamics from genetic data as they become available during an outbreak or epidemic represents an important statistical scenario in which observations arrive sequentially in time and one is interested in performing inference in an 'online' fashion. Widely-used Bayesian phylogenetic inference packages are not set up for this purpose, generally requiring one to recompute trees and evolutionary model parameters de novo when new data arrive. To accommodate increasing data flow in a Bayesian phylogenetic framework, we introduce a methodology to efficiently update the posterio…
KTH Royal Institute of Technology（KTH皇家理工学院）；Science for Life Laboratory（生命科学实验室）
Phylogenetics is a classical methodology in computational biology that today has become highly relevant for medical investigation of single-cell data, e.g., in the context of cancer development. The exponential size of the tree space is, unfortunately, a substantial obstacle for Bayesian phylogenetic inference using Markov chain Monte Carlo based methods since these rely on local operations. And although more recent variational inference (VI) based methods offer speed improvements, they rely on expensive auto-differentiation operations for learning the variational parameters. We propose VaiPhy…
BayesCAT: Bayesian Co-estimation of Alignment and Tree
传统上，同源性和序列比对是分开估计的：首先估计多个序列比对，然后基于在前一步骤中估计的序列比对来推断同源性。然而，在对齐估计的不确定性被忽略，导致，可能，在夸大的确定性，在遗传学估计。我们开发了一个联合模型，用于共同估计系统发育和序列比对，通过考虑系统发育推断中的比对不确定性，改进了传统方法的估计。我们的插入和缺失（indel）模型允许任意长度的重叠indel事件和indel片段大小的一般分布。我们采用贝叶斯方法，使用MCMC估计的联合后验分布的系统发育树和多序列比对。我们的方法有一个树和一个完整的历史的indel事件映射到树上的状态空间的马尔可夫链，而替代以前的方法有一个树和对齐。一个大的状态空间包含一个完整的历史的indel事件使我们的MCMC方法更具挑战性，但它使我们能够推断更多的信息indel过程。用模拟数据和实际数据比较了这种联合方法和传统的序贯方法的性能。名为BayesCAT（Bayesian Co-estimation of Alignment and Tree）的软件可在https://github.com/heejungshim/BayesCAT获得。
Inferring dependencies between complex biological traits while accounting for evolutionary relationships between specimens is of great scientific interest yet remains infeasible when trait and specimen counts grow large. The state-of-the-art approach uses a phylogenetic multivariate probit model to accommodate binary and continuous traits via a latent variable framework, and utilizes an efficient bouncy particle sampler (BPS) to tackle the computational bottleneck -- integrating many latent variables from a high-dimensional truncated normal distribution. This approach breaks down as the number…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees. Substitutions in sequences are modelled through a continuous-time Markov process, characterised by an instantaneous rate matrix, which standard models assume is time-reversible and stationary. These assumptions are biologically questionable and induce a likelihood function which is invariant to a tree's root position. This hampers inference because a tree's biological interpretation depends critically on where it is rooted. Relaxing both assumptions, we introduce a model whose likelihood can distinguish…
The rapid growth in genomic pathogen data spurs the need for efficient inference techniques, such as Hamiltonian Monte Carlo (HMC) in a Bayesian framework, to estimate parameters of these phylogenetic models where the dimensions of the parameters increase with the number of sequences $N$. HMC requires repeated calculation of the gradient of the data log-likelihood with respect to (wrt) all branch-length-specific (BLS) parameters that traditionally takes $\mathcal{O}(N^2)$ operations using the standard pruning algorithm. A recent study proposes an approach to calculate this gradient in $\mathca…
