arXiv subjects

Frederick A. Matsen IV

Publications and source records attributed to Frederick A. Matsen IV.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian inference of antibody evolutionary dynamics using multitype branching processes

When our immune system encounters foreign antigens (i.e., from pathogens), the B cells that produce our antibodies undergo a cyclic process of proliferation, mutation, and selection, improving their ability to bind to the specific antigen. Immunologists have recently developed powerful experimental techniques to investigate this process in mouse models. In one such experiment, mice are engineered with a monoclonal B-cell precursor and immunized with a model antigen. B cells are sampled from sacrificed mice after the immune response has progressed, and the mutated genetic loci encoding antibodies are sequenced. This experiment allows parallel replay of antibody evolution, but produces data at only one time point; we are unable to observe the evolutionary trajectories that lead to optimized antibody affinity in each mouse. To address this, we model antibody evolution as a multitype branching process and integrate over unobserved histories conditioned on phylogenetic signal in sequence data, leveraging parallel experimental replays for parameter inference. We infer the functional relationship between B-cell fitness and antigen binding affinity in a Bayesian framework, equipped with an efficient likelihood calculation algorithm and Markov chain Monte Carlo posterior approximation. In a simulation study, we demonstrate that a sigmoidal relationship between fitness and binding affinity can be recovered from realizations of the branching process. We then perform inference for experimental data from 52 replayed B-cell lineages sampled 15 days after immunization, yielding a total of 3,758 sampled B cells. The recovered sigmoidal curve indicates that the fitness of high-affinity B cells is over six times larger than that of low-affinity B cells, with a sharp transition from low to high fitness values as affinity increases.

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arXiv2025

Vector encoding of phylogenetic trees by ordered leaf attachment

As part of work to connect phylogenetics with machine learning, there has been considerable recent interest in vector encodings of phylogenetic trees. We present a simple new "ordered leaf attachment" (OLA) method for uniquely encoding a binary, rooted phylogenetic tree topology as an integer vector. OLA encoding and decoding take linear time in the number of leaf nodes, and the set of vectors corresponding to trees is a simply-described subset of integer sequences. The OLA encoding is unique compared to other existing encodings in having these properties. The integer vector encoding induces a distance on the set of trees, and we investigate this distance in relation to the NNI and SPR distances.

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arXiv2025

PhyloVAE: Unsupervised Learning of Phylogenetic Trees via Variational Autoencoders

Learning informative representations of phylogenetic tree structures is essential for analyzing evolutionary relationships. Classical distance-based methods have been widely used to project phylogenetic trees into Euclidean space, but they are often sensitive to the choice of distance metric and may lack sufficient resolution. In this paper, we introduce phylogenetic variational autoencoders (PhyloVAEs), an unsupervised learning framework designed for representation learning and generative modeling of tree topologies. Leveraging an efficient encoding mechanism inspired by autoregressive tree topology generation, we develop a deep latent-variable generative model that facilitates fast, parallelized topology generation. PhyloVAE combines this generative model with a collaborative inference model based on learnable topological features, allowing for high-resolution representations of phylogenetic tree samples. Extensive experiments demonstrate PhyloVAE's robust representation learning capabilities and fast generation of phylogenetic tree topologies.

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arXiv2024

On the importance of assessing topological convergence in Bayesian phylogenetic inference

Modern phylogenetics research is often performed within a Bayesian framework, using sampling algorithms such as Markov chain Monte Carlo (MCMC) to approximate the posterior distribution. These algorithms require careful evaluation of the quality of the generated samples. Within the field of phylogenetics, one frequently adopted diagnostic approach is to evaluate the effective sample size (ESS) and to investigate trace graphs of the sampled parameters. A major limitation of these approaches is that they are developed for continuous parameters and therefore incompatible with a crucial parameter in these inferences: the tree topology. Several recent advancements have aimed at extending these diagnostics to topological space. In this reflection paper, we present two case studies - one on Ebola virus and one on HIV - illustrating how these topological diagnostics can contain information not found in standard diagnostics, and how decisions regarding which of these diagnostics to compute can impact inferences regarding MCMC convergence and mixing. Our results show the importance of running multiple replicate analyses and of carefully assessing topological convergence using the output of these replicate analyses. To this end, we illustrate different ways of assessing and visualizing the topological convergence of these replicates. Given the major importance of detecting convergence and mixing issues in Bayesian phylogenetic analyses, the lack of a unified approach to this problem warrants further action, especially now that additional tools are becoming available to researchers.

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arXiv2024

Variational Bayesian Phylogenetic Inference with Semi-implicit Branch Length Distributions

Reconstructing the evolutionary history relating a collection of molecular sequences is the main subject of modern Bayesian phylogenetic inference. However, the commonly used Markov chain Monte Carlo methods can be inefficient due to the complicated space of phylogenetic trees, especially when the number of sequences is large. An alternative approach is variational Bayesian phylogenetic inference (VBPI) which transforms the inference problem into an optimization problem. While effective, the default diagonal lognormal approximation for the branch lengths of the tree used in VBPI is often insufficient to capture the complexity of the exact posterior. In this work, we propose a more flexible family of branch length variational posteriors based on semi-implicit hierarchical distributions using graph neural networks. We show that this semi-implicit construction emits straightforward permutation equivariant distributions, and therefore can handle the non-Euclidean branch length space across different tree topologies with ease. To deal with the intractable marginal probability of semi-implicit variational distributions, we develop several alternative lower bounds for stochastic optimization. We demonstrate the effectiveness of our proposed method over baseline methods on benchmark data examples, in terms of both marginal likelihood estimation and branch length posterior approximation.

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arXiv2024

A Variational Approach to Bayesian Phylogenetic Inference

Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper, we present an alternative approach: a variational framework for Bayesian phylogenetic analysis. We propose combining subsplit Bayesian networks, an expressive graphical model for tree topology distributions, and a structured amortization of the branch lengths over tree topologies for a suitable variational family of distributions. We train the variational approximation via stochastic gradient ascent and adopt gradient estimators for continuous and discrete variational parameters separately to deal with the composite latent space of phylogenetic models. We show that our variational approach provides competitive performance to MCMC, while requiring much fewer (though more costly) iterations due to a more efficient exploration mechanism enabled by variational inference. Experiments on a benchmark of challenging real data Bayesian phylogenetic inference problems demonstrate the effectiveness and efficiency of our methods.

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arXiv2023

Representing and extending ensembles of parsimonious evolutionary histories with a directed acyclic graph

In many situations, it would be useful to know not just the best phylogenetic tree for a given data set, but the collection of high-quality trees. This goal is typically addressed using Bayesian techniques, however, current Bayesian methods do not scale to large data sets. Furthermore, for large data sets with relatively low signal one cannot even store every good tree individually, especially when the trees are required to be bifurcating. In this paper, we develop a novel object called the "history subpartition directed acyclic graph" (or "history sDAG" for short) that compactly represents an ensemble of trees with labels (e.g. ancestral sequences) mapped onto the internal nodes. The history sDAG can be built efficiently and can also be efficiently trimmed to only represent maximally parsimonious trees. We show that the history sDAG allows us to find many additional equally parsimonious trees, extending combinatorially beyond the ensemble used to construct it. We argue that this object could be useful as the "skeleton" of a more complete uncertainty quantification.

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arXiv2023

Automatic differentiation is no panacea for phylogenetic gradient computation

Gradients of probabilistic model likelihoods with respect to their parameters are essential for modern computational statistics and machine learning. These calculations are readily available for arbitrary models via automatic differentiation implemented in general-purpose machine-learning libraries such as TensorFlow and PyTorch. Although these libraries are highly optimized, it is not clear if their general-purpose nature will limit their algorithmic complexity or implementation speed for the phylogenetic case compared to phylogenetics-specific code. In this paper, we compare six gradient implementations of the phylogenetic likelihood functions, in isolation and also as part of a variational inference procedure. We find that although automatic differentiation can scale approximately linearly in tree size, it is much slower than the carefully-implemented gradient calculation for tree likelihood and ratio transformation operations. We conclude that a mixed approach combining phylogenetic libraries with machine learning libraries will provide the optimal combination of speed and model flexibility moving forward.

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arXiv2023

Many-core algorithms for high-dimensional gradients on phylogenetic trees

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 $\mathcal{O}(N)$, enabling researchers to take advantage of gradient-based samplers such as HMC. The CPU implementation of this approach makes the calculation of the gradient computationally tractable for nucleotide-based models but falls short in performance for larger state-space size models, such as codon models. Here, we describe novel massively parallel algorithms to calculate the gradient of the log-likelihood wrt all BLS parameters that take advantage of graphics processing units (GPUs) and result in many fold higher speedups over previous CPU implementations. We benchmark these GPU algorithms on three computing systems using three evolutionary inference examples: carnivores, dengue and yeast, and observe a greater than 128-fold speedup over the CPU implementation for codon-based models and greater than 8-fold speedup for nucleotide-based models. As a practical demonstration, we also estimate the timing of the first introduction of West Nile virus into the continental Unites States under a codon model with a relaxed molecular clock from 104 full viral genomes, an inference task previously intractable. We provide an implementation of our GPU algorithms in BEAGLE v4.0.0, an open source library for statistical phylogenetics that enables parallel calculations on multi-core CPUs and GPUs.

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arXiv2022

How trustworthy is your tree? Bayesian phylogenetic effective sample size through the lens of Monte Carlo error

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. Specifically, we ask if there is any measure of effective sample size (ESS) applicable to phylogenetic trees which is capable of capturing the Monte Carlo error of these three summary measures. We find that there are some ESS measures capable of capturing the error inherent in using MCMC samples to approximate the posterior distributions on phylogenies. We term these tree ESS measures, and identify a set of three which are useful in practice for assessing the Monte Carlo error. Lastly, we present visualization tools that can improve comparisons between multiple independent MCMC runs by accounting for the Monte Carlo error present in each chain. Our results indicate that common post-MCMC workflows are insufficient to capture the inherent Monte Carlo error of the tree, and highlight the need for both within-chain mixing and between-chain convergence assessments.

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arXiv2022

Inference of B cell clonal families using heavy/light chain pairing information

Next generation sequencing of B cell receptor (BCR) repertoires has become a ubiquitous tool for understanding the antibody-mediated immune response: it is now common to have large volumes of sequence data coding for both the heavy and light chain subunits of the BCR. However, until the recent development of high throughput methods of preserving heavy/light chain pairing information, these samples contained no explicit information on which heavy chain sequence pairs with which light chain sequence. One of the first steps in analyzing such BCR repertoire samples is grouping sequences into clonally related families, where each stems from a single rearrangement event. Many methods of accomplishing this have been developed, however, none so far has taken full advantage of the newly-available pairing information. This information can dramatically improve clustering performance, especially for the light chain. The light chain has traditionally been challenging for clonal family inference because of its low diversity and consequent abundance of non-clonal families with indistinguishable naive rearrangements. Here we present a method of incorporating this pairing information into the clustering process in order to arrive at a more accurate partition of the data into clonally related families. We also demonstrate two methods of fixing imperfect pairing information, which may allow for simplified sample preparation and increased sequencing depth. Finally, we describe several other improvements to the partis software package (https://github.com/psathyrella/partis).

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arXiv2020

Using B cell receptor lineage structures to predict affinity

We are frequently faced with a large collection of antibodies, and want to select those with highest affinity for their cognate antigen. When developing a first-line therapeutic for a novel pathogen, for instance, we might look for such antibodies in patients that have recovered. There exist effective experimental methods of accomplishing this, such as cell sorting and baiting; however they are time consuming and expensive. Next generation sequencing of B cell receptor (BCR) repertoires offers an additional source of sequences that could be tapped if we had a reliable method of selecting those coding for the best antibodies. In this paper we introduce a method that uses evolutionary information from the family of related sequences that share a naive ancestor to predict the affinity of each resulting antibody for its antigen. When combined with information on the identity of the antigen, this method should provide a source of effective new antibodies. We also introduce a method for a related task: given an antibody of interest and its inferred ancestral lineage, which branches in the tree are likely to harbor key affinity-increasing mutations? These methods are implemented as part of continuing development of the partis BCR inference package, available at https://github.com/psathyrella/partis.

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arXiv2020

Non-bifurcating phylogenetic tree inference via the adaptive LASSO

Phylogenetic tree inference using deep DNA sequencing is reshaping our understanding of rapidly evolving systems, such as the within-host battle between viruses and the immune system. Densely sampled phylogenetic trees can contain special features, including "sampled ancestors" in which we sequence a genotype along with its direct descendants, and "polytomies" in which multiple descendants arise simultaneously. These features are apparent after identifying zero-length branches in the tree. However, current maximum-likelihood based approaches are not capable of revealing such zero-length branches. In this paper, we find these zero-length branches by introducing adaptive-LASSO-type regularization estimators to phylogenetics, deriving their properties, and showing regularization to be a practically useful approach for phylogenetics.

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arXiv2019

On the convergence of the maximum likelihood estimator for the transition rate under a 2-state symmetric model

Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we cannot appeal to this result because trait values of different species are correlated due to shared evolutionary history. In this paper, we consider a $2$-state symmetric model for a single binary trait and investigate the theoretical properties of the MLE for the transition rate in the large-tree limit. Here, the large-tree limit is a theoretical scenario where the number of taxa increases to infinity and we can observe the trait values for all species. Specifically, we prove that the MLE converges to the true value under some regularity conditions. These conditions ensure that the tree shape is not too irregular, and holds for many practical scenarios such as trees with bounded edges, trees generated from the Yule (pure birth) process, and trees generated from the coalescent point process. Our result also provides an upper bound for the distance between the MLE and the true value.

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arXiv2019

A Bayesian Phylogenetic Hidden Markov Model for B Cell Receptor Sequence Analysis

The human body is able to generate a diverse set of high affinity antibodies, the soluble form of B cell receptors (BCRs), that bind to and neutralize invading pathogens. The natural development of BCRs must be understood in order to design vaccines for highly mutable pathogens such as influenza and HIV. BCR diversity is induced by naturally occurring combinatorial "V(D)J" rearrangement, mutation, and selection processes. Most current methods for BCR sequence analysis focus on separately modeling the above processes. Statistical phylogenetic methods are often used to model the mutational dynamics of BCR sequence data, but these techniques do not consider all the complexities associated with B cell diversification such as the V(D)J rearrangement process. In particular, standard phylogenetic approaches assume the DNA bases of the progenitor (or "naive") sequence arise independently and according to the same distribution, ignoring the complexities of V(D)J rearrangement. In this paper, we introduce a novel approach to Bayesian phylogenetic inference for BCR sequences that is based on a phylogenetic hidden Markov model (phylo-HMM). This technique not only integrates a naive rearrangement model with a phylogenetic model for BCR sequence evolution but also naturally accounts for uncertainty in all unobserved variables, including the phylogenetic tree, via posterior distribution sampling.

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arXiv2018

19 dubious ways to compute the marginal likelihood of a phylogenetic tree topology

The marginal likelihood of a model is a key quantity for assessing the evidence provided by the data in support of a model. The marginal likelihood is the normalizing constant for the posterior density, obtained by integrating the product of the likelihood and the prior with respect to model parameters. Thus, the computational burden of computing the marginal likelihood scales with the dimension of the parameter space. In phylogenetics, where we work with tree topologies that are high-dimensional models, standard approaches to computing marginal likelihoods are very slow. Here we study methods to quickly compute the marginal likelihood of a single fixed tree topology. We benchmark the speed and accuracy of 19 different methods to compute the marginal likelihood of phylogenetic topologies on a suite of real datasets. These methods include several new ones that we develop explicitly to solve this problem, as well as existing algorithms that we apply to phylogenetic models for the first time. Altogether, our results show that the accuracy of these methods varies widely, and that accuracy does not necessarily correlate with computational burden. Our newly developed methods are orders of magnitude faster than standard approaches, and in some cases, their accuracy rivals the best established estimators.

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arXiv2018

Systematic Exploration of the High Likelihood Set of Phylogenetic Tree Topologies

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 this method `phylogenetic topographer' (PT). The PT strategy is very simple: starting in a number of local topology maxima (obtained by hill-climbing from random starting points), explore out using local topology rearrangements, only continuing through topologies that are better than than some likelihood threshold below the best observed topology. We show that the normalized topology likelihoods are a useful proxy for the Bayesian posterior probability of those topologies. By using a non-blocking hash table keyed on unique representations of tree topologies, we avoid visiting topologies more than once across all concurrent threads exploring tree space. We demonstrate that PT can be used directly to approximate a Bayesian consensus tree topology. When combined with an accurate means of evaluating per-topology marginal likelihoods, PT gives an alternative procedure for obtaining Bayesian posterior distributions on phylogenetic tree topologies.

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arXiv2018

Generalizing Tree Probability Estimation via Bayesian Networks

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we derive a general Bayesian network formulation for probability estimation on leaf-labeled trees that enables flexible approximations which can generalize beyond observations. We show that efficient algorithms for learning Bayesian networks can be easily extended to probability estimation on this challenging structured space. Experiments on both synthetic and real data show that our methods greatly outperform the current practice of using the empirical distribution, as well as a previous effort for probability estimation on trees.

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