arXiv subjects

Marc A. Suchard

Publications and source records attributed to Marc A. Suchard.

At least 19 recordsLinked to original sources

arXiv2026

An adaptive time-tree transition kernel for Bayesian phylogenetic inference

Bayesian phylogenetic and phylodynamic analyses can be very time-consuming, owing to the combination of complex models that are used to estimate key parameters from increasingly large genomic data sets and their associated metadata. The use of high-performance computer hardware can -- to a certain extent -- alleviate the computational burden and markedly decrease the time to results. Still, even converging to the posterior can be a lengthy endeavour, with the burn-in aspect of such analyses potentially taking days or even weeks for large data sets. One of the key aspects that hampers performance in Bayesian phylogenetic inference is the efficiency with which tree topology proposals explore tree space. We here propose a novel adaptive tree transition kernel, which we call `subTreeLeap' (STL), which involves modifying the phylogeny by walking along patristic distance paths in the tree according to an adaptable radius parameter. STL is a general proposal, which can be used with contemporaneous or time-calibrated sequence data, being particularly suited to the latter due to respecting temporal precedence constraints. We carefully assess its impact on convergence and statistical mixing of the exploration of posterior tree space, by comparison to replicate ``golden runs'' obtained from lengthy analyses of empirical data under standard tree transition kernels. We find that STL successfully explores the same posterior tree space as standard kernels, but often does so in a more efficient manner. We discuss limitations as well as future potential improvements to STL that could substantially increase the speed at which Bayesian phylogenetic inferences are obtained.

q-bio.PE↗

arXiv2026

Stable Matrix Parametrizations and Structured Adjoints for Ornstein-Uhlenbeck Processes

Ornstein-Uhlenbeck processes with flexible multivariate drift matrices are powerful models for capturing coupled, asymmetric, and damped-oscillatory mean reversion. However, likelihood-based inference is challenging because the drift matrix must remain Hurwitz stable, while likelihood and gradient evaluations require repeated, costly computation and differentiation of the drift matrix exponential and of solutions to the associated Lyapunov equation. We introduce the Hurwitz smooth spectral block parametrization (H-SSBP), which represents the drift as a change of basis applied to independent one- and two-dimensional stable blocks. Simple scalar constraints enforce Hurwitz stability, while the two-dimensional blocks vary smoothly between real- and complex-eigenvalue regimes, avoiding discrete model selection. The H-SSBP represents every real Hurwitz matrix diagonalizable over the complex numbers and has dense, full-measure support within the Hurwitz cone. Its block structure reduces the OU transition matrix, stationary and innovation covariances, and their reverse-mode derivatives to constant-size block or block-pair computations plus change-of-basis multiplications. Numerical experiments demonstrate dramatic speed-ups over alternatives, particularly for matrix-exponential adjoints and Lyapunov-equation kernels. Real-data analyses of asynchronous financial data and multivariate phylogenetic traits illustrate the proposed framework in practice.

stat.CO↗

arXiv2026

BEAGLE 4.1: A high-performance library for computation on phylogenetic trees across diverse parallel architectures

Efficient evaluation of sequence data likelihoods and their high-dimensional gradients on phylogenetic trees improves inference under both maximum-likelihood and Bayesian frameworks. Here, we present BEAGLE 4.1, a high-performance library for statistical phylogenetics that incorporates new algorithms to evaluate these gradients on phylogenetic trees. We also provide new hardware implementations for both likelihoods and gradients supporting ARM NEON intrinsics and optimized matrix multiplication units -- called tensor cores -- on NVIDIA graphics processing units (GPUs). We benchmark the performance scaling of the library across a number of patterns and taxa on multi-core CPUs and GPUs, and compare the speedup afforded by NVIDIA and AMD GPUs as well as performance scaling with an increasing number of GPUs. We show that multi-core CPU implementations provide up to a fourfold speedup over single-threaded CPU implementations and up to an tenfold speedup for nucleotide and codon models, respectively, with performance generally improving as the number of taxa and site patterns increases. GPUs outperform multi-threaded CPU implementations for a realistic number of patterns, even for nucleotide models with a small state-space size of 4, while for codon models they provide substantially higher performance gains even for a single pattern or four taxa. Tensor cores on GPUs provide up to 2-fold speedup relative to standard CUDA cores for codon models. Using NEON instructions on ARM CPUs affords up to a $\sim 1.3$-fold speedup over non-SIMD implementation with the speedup going down to 1.1-fold at 8 CPU threads. We provide these new algorithms to evaluate the gradient and efficient hardware implementations for both likelihood and gradient calculations through BEAGLE 4.1, such that they can be readily integrated into phylogenetic software packages.

q-bio.PE↗

arXiv2026

Smoothly Time-Varying Continuous Time Markov Chains in Phylogenetics

The dependence of evolutionary rate estimates on the timeframe of sampling poses a fundamental challenge for reconstructing evolutionary histories from molecular sequence data, which is central to evolutionary biology and infectious disease research. We present a novel and flexible approach to accommodate time-varying evolutionary rates by modeling the sequence substitution process using inhomogeneous continuous-time Markov chains (ICTMCs) acting along the branches of the phylogeny, and parameterizing the log transformed rate as a smooth function of time using a cubic B-spline basis expansion. Following the parlance of phylogenetics that refers to rates of molecular substitutions as molecular clocks, we call this a spline clock model. Integrals of the rate function over all branches, required for likelihood evaluation, are approximated efficiently using Gauss-Legendre quadrature, and smoothness is enforced by assigning a Gaussian Markov random field prior to the spline coefficients. Through a simulation study, we demonstrate that the spline clock model recovers the true time-varying rates more accurately and with tighter credible intervals than competing clock models. We apply the spline clock model to examine the evolutionary rate of foamy virus and the rate of spatial diffusion of SARS-CoV-2 across Europe, recovering strong time-varying signal in both settings.

q-bio.PE↗

arXiv2026

Detecting Evolutionary Change-Points with Branch-Specific Substitution Models and Shrinkage Priors

Branch-specific substitution models are popular for detecting evolutionary change-points, such as shifts in selective pressure. However, applying such models typically requires prior knowledge of change-point locations on the phylogeny or faces scalability issues with large data sets. To address both limitations, we integrate branch-specific substitution models with shrinkage priors to automatically identify change-points without prior knowledge, while simultaneously estimating distinct substitution parameters for each branch. To enable tractable inference under this high-dimensional model, we develop an analytical gradient algorithm for the branch-specific substitution parameters where the computational time is linear in the number of parameters. We apply this gradient algorithm to infer selection pressure dynamics in the evolution of the BRCA1 gene in primates and mutational dynamics in viral sequences from the recent mpox epidemic. Our novel algorithm enhances inference efficiency, achieving up to a 126-fold speedup per iteration in maximum likelihood optimization when compared to central difference numerical gradient method and up to a 2026-fold improvement in computational performance within a Bayesian framework using Hamiltonian Monte Carlo sampler compared to conventional univariate random walk sampler.

q-bio.PE↗

arXiv2026

Non-Linear Drivers of Population Dynamics: a Nonparametric Coalescent Approach

Effective population size (Ne(t)) is a fundamental parameter in population genetics and phylodynamics that quantifies genetic diversity and reveals demographic history. Coalescent-based methods enable the inference of Ne(t) trajectories through time from phylogenies reconstructed from molecular sequence data. Understanding the ecological and environmental drivers of population dynamics requires linking Ne(t) to external covariates. Existing approaches typically impose log-linear relationships between covariates and Ne(t), which may fail to capture complex biological processes and can introduce bias when the true relationship is nonlinear. We present a flexible Bayesian framework that integrates covariates into coalescent models with piecewise-constant Ne(t) through a Gaussian process (GP) prior. The GP, a distribution over functions, naturally accommodates nonlinear covariate effects without restrictive parametric assumptions. This formulation improves estimation of covariate-Ne(t) relationships, mitigates bias under nonlinear associations, and yields interpretable uncertainty quantification that varies across the covariate space. To balance global covariate-driven patterns with local temporal dynamics, we couple the GP prior with a Gaussian Markov random field that enforces smoothness in Ne(t) trajectories. Through simulation studies and three empirical applications - yellow fever virus dynamics in Brazil (2016-2018), late-Quaternary musk ox demography, and HIV-1 CRF02-AG evolution in Cameroon - we demonstrate that our method both confirms linear relationships where appropriate and reveals nonlinear covariate effects that would otherwise be missed or mischaracterized. This framework advances phylodynamic inference by enabling more accurate and biologically realistic modeling of how environmental and epidemiological factors shape population size through time.

stat.AP↗

arXiv2025

PDA in Action: Ten Principles for High-Quality Multi-Site Clinical Evidence Generation

Background: Distributed Research Networks (DRNs) offer significant opportunities for collaborative multi-site research and have significantly advanced healthcare research based on clinical observational data. However, generating high-quality real-world evidence using fit-for-use data from multi-site studies faces important challenges, including biases associated with various types of heterogeneity within and across sites and data sharing difficulties. Over the last ten years, Privacy-Preserving Distributed Algorithms (PDA) have been developed and utilized in numerous national and international real-world studies spanning diverse domains, from comparative effectiveness research, target trial emulation, to healthcare delivery, policy evaluation, and system performance assessment. Despite these advances, there remains a lack of comprehensive and clear guiding principles for generating high-quality real-world evidence through collaborative studies leveraging the methods under PDA. Objective: The paper aims to establish ten principles of best practice for conducting high-quality multi-site studies using PDA. These principles cover all phases of research, including study preparation, protocol development, analysis, and final reporting. Discussion: The ten principles for conducting a PDA study outline a principled, efficient, and transparent framework for employing distributed learning algorithms within DRNs to generate reliable and reproducible real-world evidence.

cs.CY↗

arXiv2025

Nonparametric Modeling of Continuous-Time Markov Chains

Inferring the infinitesimal rates of continuous-time Markov chains (CTMCs) is a central challenge in many scientific domains. This task is difficult because the number of rates grows quadratically with the state space, rates can be strongly dependent, and many transitions may be only partially observed. We introduce a Bayesian framework that models CTMC rates as flexible functions of covariates through Gaussian processes. This enables nonlinear covariate effects, improves inference by incorporating external information, and helps identify potential drivers of CTMC dynamics. For posterior inference, we use Hamiltonian Monte Carlo and develop scalable exact and approximate gradients for likelihoods involving repeated matrix exponentials. With $N$ observations and $K$ CTMC states, these gradients reduce the dominant cost of existing derivative calculations from $O(NK^3)$, with large constants, to $O(K^3+NK^2)$, with cheaper constants. We demonstrate the method in Bayesian phylogenetic and phylogeographic inference, where CTMCs are central, and show strong performance on synthetic and real datasets, including empirical quadratic scaling in $K$ even when $N<K$.

stat.ME↗

arXiv2025

Inhomogeneous continuous-time Markov chains to infer flexible time-varying evolutionary rates

Reconstructing evolutionary histories and estimating the rate of evolution from molecular sequence data is of central importance in evolutionary biology and infectious disease research. We introduce a flexible Bayesian phylogenetic inference framework that accommodates changing evolutionary rates over time by modeling sequence character substitution processes as inhomogeneous continuous-time Markov chains (ICTMCs) acting along the unknown phylogeny, where the rate remains as an unknown, positive and integrable function of time. The integral of the rate function appears in the finite-time transition probabilities of the ICTMCs that must be efficiently computed for all branches of the phylogeny to evaluate the observed data likelihood. Circumventing computational challenges that arise from a fully nonparametric function, we successfully parameterize the rate function as piecewise constant with a large number of epochs that we call the polyepoch clock model. This makes the transition probability computation relatively inexpensive and continues to flexibly capture rate change over time. We employ a Gaussian Markov random field prior to achieve temporal smoothing of the estimated rate function. Hamiltonian Monte Carlo sampling enabled by scalable gradient evaluation under this model makes our framework computationally efficient. We assess the performance of the polyepoch clock model in recovering the true timescales and rates through simulations under two different evolutionary scenarios. We then apply the polyepoch clock model to examine the rates of West Nile virus, Dengue virus and influenza A/H3N2 evolution, and estimate the time-varying rate of SARS-CoV-2 spread in Europe in 2020.

stat.ME↗

arXiv2025

Inhomogeneous branching trees with symmetric and asymmetric offspring and their genealogies

We define symmetric and asymmetric branching trees, a class of processes particularly suited for modeling genealogies of inhomogeneous populations where individuals may reproduce throughout life. In this framework, a broad class of Crump-Mode-Jagers processes can be constructed as (a)symmetric Sevast'yanov processes, which count the branches of the tree. Analogous definitions yield reduced (a)symmetric Sevast'yanov processes, which restrict attention to branches that lead to extant progeny. We characterize their laws through generating functions. The genealogy obtained by pruning away branches without extant progeny at a fixed time is shown to satisfy a branching property, which provides distributional characterizations of the genealogy.

math.PR↗

arXiv2025

Quantum Speedups for Multiproposal MCMC

Multiproposal Markov chain Monte Carlo (MCMC) algorithms choose from multiple proposals to generate their next chain step in order to sample from challenging target distributions more efficiently. However, on classical machines, these algorithms require $\mathcal{O}(P)$ target evaluations for each Markov chain step when choosing from $P$ proposals. Recent work demonstrates the possibility of quadratic quantum speedups for one such multiproposal MCMC algorithm. After generating $P$ proposals, this quantum parallel MCMC (QPMCMC) algorithm requires only $\mathcal{O}(\sqrt{P})$ target evaluations at each step, outperforming its classical counterpart. However, generating $P$ proposals using classical computers still requires $\mathcal{O}(P)$ time complexity, resulting in the overall complexity of QPMCMC remaining $\mathcal{O}(P)$. Here, we present a new, faster quantum multiproposal MCMC strategy, QPMCMC2. With a specially designed Tjelmeland distribution that generates proposals close to the input state, QPMCMC2 requires only $\mathcal{O}(1)$ target evaluations and $\mathcal{O}(\log P)$ qubits when computing over a large number of proposals $P$. Unlike its slower predecessor, the QPMCMC2 Markov kernel (1) maintains detailed balance exactly and (2) is fully explicit for a large class of graphical models. We demonstrate this flexibility by applying QPMCMC2 to novel Ising-type models built on bacterial evolutionary networks and obtain significant speedups for Bayesian ancestral trait reconstruction for 248 observed salmonella bacteria.

quant-ph↗

arXiv2024

Infinite Mixture Models for Improved Modeling of Across-Site Evolutionary Variation

Scientific studies in many areas of biology routinely employ evolutionary analyses based on the probabilistic inference of phylogenetic trees from molecular sequence data. Evolutionary processes that act at the molecular level are highly variable, and properly accounting for heterogeneity in evolutionary processes is crucial for more accurate phylogenetic inference. Nucleotide substitution rates and patterns are known to vary among sites in multiple sequence alignments, and such variation can be modeled by partitioning alignments into categories corresponding to different substitution models. Determining $\textit{a priori}$ appropriate partitions can be difficult, however, and better model fit can be achieved through flexible Bayesian infinite mixture models that simultaneously infer the number of partitions, the partition that each site belongs to, and the evolutionary parameters corresponding to each partition. Here, we consider several different types of infinite mixture models, including classic Dirichlet process mixtures, as well as novel approaches for modeling across-site evolutionary variation: hierarchical models for data with a natural group structure, and infinite hidden Markov models that account for spatial patterns in alignments. In analyses of several viral data sets, we find that different types of infinite mixture models emerge as the best choices in different scenarios. To enable these models to scale efficiently to large data sets, we adapt efficient Markov chain Monte Carlo algorithms and exploit opportunities for parallel computing. We implement this infinite mixture modeling framework in BEAST X, a widely-used software package for Bayesian phylogenetic inference.

q-bio.PE↗

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.

q-bio.PE↗

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.

stat.ML↗

arXiv2024

Zigzag path connects two Monte Carlo samplers: Hamiltonian counterpart to a piecewise deterministic Markov process

Zigzag and other piecewise deterministic Markov process samplers have attracted significant interest for their non-reversibility and other appealing properties for Bayesian posterior computation. Hamiltonian Monte Carlo is another state-of-the-art sampler, exploiting fictitious momentum to guide Markov chains through complex target distributions. We establish an important connection between the zigzag sampler and a variant of Hamiltonian Monte Carlo based on Laplace-distributed momentum. The position and velocity component of the corresponding Hamiltonian dynamics travels along a zigzag path paralleling the Markovian zigzag process; however, the dynamics is non-Markovian in this position-velocity space as the momentum component encodes non-immediate pasts. This information is partially lost during a momentum refreshment step, in which we preserve its direction but re-sample magnitude. In the limit of increasingly frequent momentum refreshments, we prove that Hamiltonian zigzag converges strongly to its Markovian counterpart. This theoretical insight suggests that, when retaining full momentum information, Hamiltonian zigzag can better explore target distributions with highly correlated parameters by suppressing the diffusive behavior of Markovian zigzag. We corroborate this intuition by comparing performance of the two zigzag cousins on high-dimensional truncated multivariate Gaussians, including a 11,235-dimensional target arising from a Bayesian phylogenetic multivariate probit modeling of HIV virus data.

stat.CO↗

arXiv2024

Scaling Hawkes processes to one million COVID-19 cases

Hawkes stochastic point process models have emerged as valuable statistical tools for analyzing viral contagion. The spatiotemporal Hawkes process characterizes the speeds at which viruses spread within human populations. Unfortunately, likelihood-based inference using these models requires $O(N^2)$ floating-point operations, for $N$ the number of observed cases. Recent work responds to the Hawkes likelihood's computational burden by developing efficient graphics processing unit (GPU)-based routines that enable Bayesian analysis of tens-of-thousands of observations. We build on this work and develop a high-performance computing (HPC) strategy that divides 30 Markov chains between 4 GPU nodes, each of which uses multiple GPUs to accelerate its chain's likelihood computations. We use this framework to apply two spatiotemporal Hawkes models to the analysis of one million COVID-19 cases in the United States between March 2020 and June 2023. In addition to brute-force HPC, we advocate for two simple strategies as scalable alternatives to successful approaches proposed for small data settings. First, we use known county-specific population densities to build a spatially varying triggering kernel in a manner that avoids computationally costly nearest neighbors search. Second, we use a cut-posterior inference routine that accounts for infections' spatial location uncertainty by iteratively sampling latent locations uniformly within their respective counties of occurrence, thereby avoiding full-blown latent variable inference for 1,000,000 infection locations.

stat.CO↗

arXiv2023

On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2

The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC's infinitesimal generator (rate) matrix. Motivated by the derivative's extreme computational complexity as a function of state space cardinality, recent work demonstrates the surprising effectiveness of a naive, first-order approximation for a host of problems in computational biology. In response to this empirical success, we obtain rigorous deterministic and probabilistic bounds for the error accrued by the naive approximation and establish a "blessing of dimensionality" result that is universal for a large class of rate matrices with random entries. Finally, we apply the first-order approximation within surrogate-trajectory Hamiltonian Monte Carlo for the analysis of the early spread of SARS-CoV-2 across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology.

stat.CO↗

arXiv2023

Efficient GPU-accelerated fitting of observational health-scaled stratified and time-varying Cox models

The Cox proportional hazards model stands as a widely-used semi-parametric approach for survival analysis in medical research and many other fields. Numerous extensions of the Cox model have further expanded its versatility. Statistical computing challenges arise, however, when applying many of these extensions with the increasing complexity and volume of modern observational health datasets. To address these challenges, we demonstrate how to employ massive parallelization through graphics processing units (GPU) to enhance the scalability of the stratified Cox model, the Cox model with time-varying covariates, and the Cox model with time-varying coefficients. First we establish how the Cox model with time-varying coefficients can be transformed into the Cox model with time-varying covariates when using discrete time-to-event data. We then demonstrate how to recast both of these into a stratified Cox model and identify their shared computational bottleneck that results when evaluating the now segmented partial likelihood and its gradient with respect to regression coefficients at scale. These computations mirror a highly transformed segmented scan operation. While this bottleneck is not an immediately obvious target for multi-core parallelization, we convert it into an un-segmented operation to leverage the efficient many-core parallel scan algorithm. Our massively parallel implementation significantly accelerates model fitting on large-scale and high-dimensional Cox models with stratification or time-varying effect, delivering an order of magnitude speedup over traditional central processing unit-based implementations.

stat.CO↗