arXiv subjects

Marc A. Suchard

Publications and source records attributed to Marc A. Suchard.

At least 37 records · Page 2Linked to original sources

arXiv2023

Random-effects substitution models for phylogenetics via scalable gradient approximations

Phylogenetic and discrete-trait evolutionary inference depend heavily on an appropriate characterization of the underlying character substitution process. In this paper, we present random-effects substitution models that extend common continuous-time Markov chain models into a richer class of processes capable of capturing a wider variety of substitution dynamics. As these random-effects substitution models often require many more parameters than their usual counterparts, inference can be both statistically and computationally challenging. Thus, we also propose an efficient approach to compute an approximation to the gradient of the data likelihood with respect to all unknown substitution model parameters. We demonstrate that this approximate gradient enables scaling of sampling-based inference, namely Bayesian inference via Hamiltonian Monte Carlo, under random-effects substitution models across large trees and state-spaces. Applied to a dataset of 583 SARS-CoV-2 sequences, an HKY model with random-effects shows strong signals of nonreversibility in the substitution process, and posterior predictive model checks clearly show that it is a more adequate model than a reversible model. When analyzing the pattern of phylogeographic spread of 1441 influenza A virus (H3N2) sequences between 14 regions, a random-effects phylogeographic substitution model infers that air travel volume adequately predicts almost all dispersal rates. A random-effects state-dependent substitution model reveals no evidence for an effect of arboreality on the swimming mode in the tree frog subfamily Hylinae. Simulations reveal that random-effects substitution models can accommodate both negligible and radical departures from the underlying base substitution model. We show that our gradient-based inference approach is over an order of magnitude more time efficient than conventional approaches.

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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

Quantitative bias analysis for outcome phenotype error correction in comparative effect estimation: an empirical and synthetic evaluation

Outcome phenotype measurement error is rarely corrected in comparative effect estimation studies in observational pharmacoepidemiology. Quantitative bias analysis (QBA) is a misclassification correction method that algebraically adjusts person counts in exposure-outcome contingency tables to reflect the magnitude of misclassification. The extent QBA minimizes bias is unclear because few systematic evaluations have been reported. We empirically evaluated QBA impact on odds ratios (OR) in several comparative effect estimation scenarios. We estimated non-differential and differential phenotype errors with internal validation studies using a probabilistic reference. Further, we synthesized an analytic space defined by outcome incidence, uncorrected ORs, and phenotype errors to identify which combinations produce invalid results indicative of input errors. We evaluated impact with relative bias [(OR-ORQBA)]/OR*100%]. Results were considered invalid if any contingency table cell was corrected to a negative number. Empirical bias correction was greatest in lower incidence scenarios where uncorrected ORs were larger. Similarly, synthetic bias correction was greater in lower incidence settings with larger uncorrected estimates. The invalid proportion of synthetic scenarios increased as uncorrected estimates increased. Results were invalid in common, low incidence scenarios indicating problematic inputs. This demonstrates the importance of accurately and precisely estimating phenotype errors before implementing QBA in comparative effect estimation studies.

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arXiv2023

Bayesian Safety Surveillance with Adaptive Bias Correction

Post-market safety surveillance is an integral part of mass vaccination programs. Typically relying on sequential analysis of real-world health data as they accrue, safety surveillance is challenged by the difficulty of sequential multiple testing and by biases induced by residual confounding. The current standard approach based on the maximized sequential probability ratio test (MaxSPRT) fails to satisfactorily address these practical challenges and it remains a rigid framework that requires pre-specification of the surveillance schedule. We develop an alternative Bayesian surveillance procedure that addresses both challenges using a more flexible framework. We adopt a joint statistical modeling approach to sequentially estimate the effect of vaccine exposure on the adverse event of interest and correct for estimation bias by simultaneously analyzing a large set of negative control outcomes through a Bayesian hierarchical model. We then compute a posterior probability of the alternative hypothesis via Markov chain Monte Carlo sampling and use it for sequential detection of safety signals. Through an empirical evaluation using six US observational healthcare databases covering more than 360 million patients, we benchmark the proposed procedure against MaxSPRT on testing errors and estimation accuracy, under two epidemiological designs, the historical comparator and the self-controlled case series. We demonstrate that our procedure substantially reduces Type 1 error rates, maintains high statistical power, delivers fast signal detection, and provides considerably more accurate estimation. As an effort to promote open science, we present all empirical results in an R ShinyApp and provide full implementation of our method in the R package EvidenceSynthesis.

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arXiv2023

Massive Parallelization of Massive Sample-size Survival Analysis

Large-scale observational health databases are increasingly popular for conducting comparative effectiveness and safety studies of medical products. However, increasing number of patients poses computational challenges when fitting survival regression models in such studies. In this paper, we use graphics processing units (GPUs) to parallelize the computational bottlenecks of massive sample-size survival analyses. Specifically, we develop and apply time- and memory-efficient single-pass parallel scan algorithms for Cox proportional hazards models and forward-backward parallel scan algorithms for Fine-Gray models for analysis with and without a competing risk using a cyclic coordinate descent optimization approach. We demonstrate that GPUs accelerate the computation of fitting these complex models in large databases by orders of magnitude as compared to traditional multi-core CPU parallelism. Our implementation enables efficient large-scale observational studies involving millions of patients and thousands of patient characteristics. The above implementation is available in the open-source R package Cyclops (Suchard et al., 2013).

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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

Sparse precision matrix estimation in phenotypic trait evolution models

Phylogenetic trait evolution models allow for the estimation of evolutionary correlations between a set of traits observed in a sample of related organisms. By directly modeling the evolution of the traits along an estimable phylogenetic tree, the model's structure effectively controls for shared evolutionary history. In these models, relevant correlations are usually assessed through the high posterior density interval of their marginal distributions. However, the selected correlations alone may not provide the full picture regarding trait relationships. Their association structure, expressed through a graph that encodes partial correlations, can in contrast highlight sparsity patterns featuring direct associations between traits. In order to develop a model-based method to identify this association structure we explore the use of Gaussian graphical models (GGM) for covariance selection. We model the precision matrix with a G-Wishart conjugate prior, which results in sparse precision estimates. Furthermore the model naturally allows for Bayes Factor tests of association between the traits, with no additional computation required. We evaluate our approach through Monte Carlo simulations and applications that examine the association structure and evolutionary correlations of phenotypic traits in Darwin's finches and genomic and phenotypic traits in prokaryotes. Our approach provides accurate graph estimates and lower errors for the precision and correlation parameter estimates, particularly for conditionally independent traits, which are the target for sparsity in GGMs.

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arXiv2022

hdtg: An R package for high-dimensional truncated normal simulation

Simulating from the multivariate truncated normal distribution (MTN) is required in various statistical applications yet remains challenging in high dimensions. Currently available algorithms and their implementations often fail when the number of parameters exceeds a few hundred. To provide a general computational tool to efficiently sample from high-dimensional MTNs, we introduce the hdtg package that implements two state-of-the-art simulation algorithms: harmonic Hamiltonian Monte Carlo (harmonic-HMC) and zigzag Hamiltonian Monte Carlo (Zigzag-HMC). Both algorithms exploit analytical solutions of the Hamiltonian dynamics under a quadratic potential energy with hard boundary constraints, leading to rejection-free methods. We compare their efficiencies against another state-of-the-art algorithm for MTN simulation, the minimax tilting accept-reject sampler (MET). The run-time of these three approaches heavily depends on the underlying multivariate normal correlation structure. Zigzag-HMC and harmonic-HMC both achieve 100 effective samples within 3,600 seconds across all tests with dimension ranging from 100 to 1,600, while MET has difficulty in several high-dimensional examples. We provide guidance on how to choose an appropriate method for a given situation and illustrate the usage of hdtg.

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arXiv2022

Accelerating Bayesian inference of dependency between complex biological traits

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 of specimens grows and fails to reliably characterize conditional dependencies between traits. Here, we propose an inference pipeline for phylogenetic probit models that greatly outperforms BPS. The novelty lies in 1) a combination of the recent Zigzag Hamiltonian Monte Carlo (Zigzag-HMC) with linear-time gradient evaluations and 2) a joint sampling scheme for highly correlated latent variables and correlation matrix elements. In an application exploring HIV-1 evolution from 535 viruses, the inference requires joint sampling from an 11,235-dimensional truncated normal and a 24-dimensional covariance matrix. Our method yields a 5-fold speedup compared to BPS and makes it possible to learn partial correlations between candidate viral mutations and virulence. Computational speedup now enables us to tackle even larger problems: we study the evolution of influenza H1N1 glycosylations on around 900 viruses. For broader applicability, we extend the phylogenetic probit model to incorporate categorical traits, and demonstrate its use to study Aquilegia flower and pollinator co-evolution.

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arXiv2022

Adjusting for both sequential testing and systematic error in safety surveillance using observational data: Empirical calibration and MaxSPRT

Post-approval safety surveillance of medical products using observational healthcare data can help identify safety issues beyond those found in pre-approval trials. When testing sequentially as data accrue, maximum sequential probability ratio testing (MaxSPRT) is a common approach to maintaining nominal type 1 error. However, the true type 1 error may still deviate from the specified one because of systematic error due to the observational nature of the analysis. This systematic error may persist even after controlling for known confounders. Here we propose to address this issue by combing MaxSPRT with empirical calibration. In empirical calibration, we assume uncertainty about the systematic error in our analysis, the source of uncertainty commonly overlooked in practice. We infer a probability distribution of systematic error by relying on a large set of negative controls: exposure-outcome where no causal effect is believed to exist. Integrating this distribution into our test statistics has previously been shown to restore type 1 error to nominal. Here we show how we can calibrate the critical value central to MaxSPRT. We evaluate this novel approach using simulations and real electronic health records, using H1N1 vaccinations during the 2009-2010 season as an example. Results show that combining empirical calibration with MaxSPRT restores nominal type 1 error. In our real-world example, adjusting for systematic error using empirical calibration has a larger impact than, and hence is just as essential as, adjusting for sequential testing using MaxSPRT. We recommend performing both, using the method described here.

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arXiv2022

Computational Statistics and Data Science in the Twenty-first Century

Data science has arrived, and computational statistics is its engine. As the scale and complexity of scientific and industrial data grow, the discipline of computational statistics assumes an increasingly central role among the statistical sciences. An explosion in the range of real-world applications means the development of more and more specialized computational methods, but five Core Challenges remain. We provide a high-level introduction to computational statistics by focusing on its central challenges, present recent model-specific advances and preach the ever-increasing role of non-sequential computational paradigms such as multi-core, many-core and quantum computing. Data science is bringing major changes to computational statistics, and these changes will shape the trajectory of the discipline in the 21st century.

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arXiv2022

Prior-preconditioned conjugate gradient method for accelerated Gibbs sampling in "large $n$ & large $p$" Bayesian sparse regression

In a modern observational study based on healthcare databases, the number of observations and of predictors typically range in the order of $10^5$ ~ $10^6$ and of $10^4$ ~ $10^5$. Despite the large sample size, data rarely provide sufficient information to reliably estimate such a large number of parameters. Sparse regression techniques provide potential solutions, one notable approach being the Bayesian methods based on shrinkage priors. In the "large n & large p" setting, however, posterior computation encounters a major bottleneck at repeated sampling from a high-dimensional Gaussian distribution, whose precision matrix $Φ$ is expensive to compute and factorize. In this article, we present a novel algorithm to speed up this bottleneck based on the following observation: we can cheaply generate a random vector $b$ such that the solution to the linear system $Φβ= b$ has the desired Gaussian distribution. We can then solve the linear system by the conjugate gradient (CG) algorithm through matrix-vector multiplications by $Φ$; this involves no explicit factorization or calculation of $Φ$ itself. Rapid convergence of CG in this context is guaranteed by the theory of prior-preconditioning we develop. We apply our algorithm to a clinically relevant large-scale observational study with n = 72,489 patients and p = 22,175 clinical covariates, designed to assess the relative risk of adverse events from two alternative blood anti-coagulants. Our algorithm demonstrates an order of magnitude speed-up in posterior inference, in our case cutting the computation time from two weeks to less than a day.

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arXiv2021

Scalable Bayesian divergence time estimation with ratio transformations

Divergence time estimation is crucial to provide temporal signals for dating biologically important events, from species divergence to viral transmissions in space and time. With the advent of high-throughput sequencing, recent Bayesian phylogenetic studies have analyzed hundreds to thousands of sequences. Such large-scale analyses challenge divergence time reconstruction by requiring inference on highly-correlated internal node heights that often become computationally infeasible. To overcome this limitation, we explore a ratio transformation that maps the original N - 1 internal node heights into a space of one height parameter and N - 2 ratio parameters. To make analyses scalable, we develop a collection of linear-time algorithms to compute the gradient and Jacobian-associated terms of the log-likelihood with respect to these ratios. We then apply Hamiltonian Monte Carlo sampling with the ratio transform in a Bayesian framework to learn the divergence times in four pathogenic virus phylogenies: West Nile virus, rabies virus, Lassa virus and Ebola virus. Our method both resolves a mixing issue in the West Nile virus example and improves inference efficiency by at least 5-fold for the Lassa and rabies virus examples. Our method also makes it now computationally feasible to incorporate mixed-effects molecular clock models for the Ebola virus example, confirms the findings from the original study and reveals clearer multimodal distributions of the divergence times of some clades of interest.

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arXiv2021

Shrinkage with shrunken shoulders: Gibbs sampling shrinkage model posteriors with guaranteed convergence rates

Use of continuous shrinkage priors -- with a "spike" near zero and heavy-tails towards infinity -- is an increasingly popular approach to induce sparsity in parameter estimates. When the parameters are only weakly identified by the likelihood, however, the posterior may end up with tails as heavy as the prior, jeopardizing robustness of inference. A natural solution is to "shrink the shoulders" of a shrinkage prior by lightening up its tails beyond a reasonable parameter range, yielding a regularized version of the prior. We develop a regularization approach which, unlike previous proposals, preserves computationally attractive structures of original shrinkage priors. We study theoretical properties of the Gibbs sampler on resulting posterior distributions, with emphasis on convergence rates of the P{ó}lya-Gamma Gibbs sampler for sparse logistic regression. Our analysis shows that the proposed regularization leads to geometric ergodicity under a broad range of global-local shrinkage priors. Essentially, the only requirement is for the prior $π_{\rm local}$ on the local scale $λ$ to satisfy $π_{\rm local}(0) < \infty$. If $π_{\rm local}(\cdot)$ further satisfies $\lim_{λ\to 0} π_{\rm local}(λ) / λ^a < \infty$ for $a > 0$, as in the case of Bayesian bridge priors, we show the sampler to be uniformly ergodic.

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arXiv2021

From viral evolution to spatial contagion: a biologically modulated Hawkes model

Mutations sometimes increase contagiousness for evolving pathogens. During an epidemic, scientists use viral genome data to infer a shared evolutionary history and connect this history to geographic spread. We propose a model that directly relates a pathogen's evolution to its spatial contagion dynamics -- effectively combining the two epidemiological paradigms of phylogenetic inference and self-exciting process modeling -- and apply this \emph{phylogenetic Hawkes process} to a Bayesian analysis of 23,422 viral cases from the 2014-2016 Ebola outbreak in West Africa. The proposed model is able to detect individual viruses with significantly elevated rates of spatiotemporal propagation for a subset of 1,610 samples that provide genome data. Finally, to facilitate model application in big data settings, we develop massively parallel implementations for the gradient and Hessian of the log-likelihood and apply our high performance computing framework within an adaptively preconditioned Hamiltonian Monte Carlo routine.

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arXiv2021

Bayesian mitigation of spatial coarsening for a Hawkes model applied to gunfire, wildfire and viral contagion

Self-exciting spatiotemporal Hawkes processes have found increasing use in the study of large-scale public health threats ranging from gun violence and earthquakes to wildfires and viral contagion. Whereas many such applications feature locational uncertainty, i.e., the exact spatial positions of individual events are unknown, most Hawkes model analyses to date have ignored spatial coarsening present in the data. Three particular 21st century public health crises -- urban gun violence, rural wildfires and global viral spread -- present qualitatively and quantitatively varying uncertainty regimes that exhibit (a) different collective magnitudes of spatial coarsening, (b) uniform and mixed magnitude coarsening, (c) differently shaped uncertainty regions and -- less orthodox -- (d) locational data distributed within the `wrong' effective space. We explicitly model such uncertainties in a Bayesian manner and jointly infer unknown locations together with all parameters of a reasonably flexible Hawkes model, obtaining results that are practically and statistically distinct from those obtained while ignoring spatial coarsening. This work also features two different secondary contributions: first, to facilitate Bayesian inference of locations and background rate parameters, we make a subtle yet crucial change to an established kernel-based rate model; and second, to facilitate the same Bayesian inference at scale, we develop a massively parallel implementation of the model's log-likelihood gradient with respect to locations and thus avoid its quadratic computational cost in the context of Hamiltonian Monte Carlo. Our examples involve thousands of observations and allow us to demonstrate practicality at moderate scales.

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arXiv2021

Principled, practical, flexible, fast: a new approach to phylogenetic factor analysis

Biological phenotypes are products of complex evolutionary processes in which selective forces influence multiple biological trait measurements in unknown ways. Phylogenetic factor analysis disentangles these relationships across the evolutionary history of a group of organisms. Scientists seeking to employ this modeling framework confront numerous modeling and implementation decisions, the details of which pose computational and replicability challenges. General and impactful community employment requires a data scientific analysis plan that balances flexibility, speed and ease of use, while minimizing model and algorithm tuning. Even in the presence of non-trivial phylogenetic model constraints, we show that one may analytically address latent factor uncertainty in a way that (a) aids model flexibility, (b) accelerates computation (by as much as 500-fold) and (c) decreases required tuning. We further present practical guidance on inference and modeling decisions as well as diagnosing and solving common problems in these analyses. We codify this analysis plan in an automated pipeline that distills the potentially overwhelming array of modeling decisions into a small handful of (typically binary) choices. We demonstrate the utility of these methods and analysis plan in four real-world problems of varying scales.

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arXiv2021

Shrinkage-based random local clocks with scalable inference

Local clock models propose that the rate of molecular evolution is constant within phylogenetic sub-trees. Current local clock inference procedures scale poorly to large taxa problems, impose model misspecification, or require a priori knowledge of the existence and location of clocks. To overcome these challenges, we present an autocorrelated, Bayesian model of heritable clock rate evolution that leverages heavy-tailed priors with mean zero to shrink increments of change between branch-specific clocks. We further develop an efficient Hamiltonian Monte Carlo sampler that exploits closed form gradient computations to scale our model to large trees. Inference under our shrinkage-clock exhibits an over 3-fold speed increase compared to the popular random local clock when estimating branch-specific clock rates on a simulated dataset. We further show our shrinkage-clock recovers known local clocks within a rodent and mammalian phylogeny. Finally, in a problem that once appeared computationally impractical, we investigate the heritable clock structure of various surface glycoproteins of influenza A virus in the absence of prior knowledge about clock placement.

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