arXiv subjects

Seth Flaxman

Publications and source records attributed to Seth Flaxman.

At least 37 records · Page 2Linked to original sources

arXiv2022

Cox-Hawkes: doubly stochastic spatiotemporal Poisson processes

Hawkes processes are point process models that have been used to capture self-excitatory behavior in social interactions, neural activity, earthquakes and viral epidemics. They can model the occurrence of the times and locations of events. Here we develop a new class of spatiotemporal Hawkes processes that can capture both triggering and clustering behavior and we provide an efficient method for performing inference. We use a log-Gaussian Cox process (LGCP) as prior for the background rate of the Hawkes process which gives arbitrary flexibility to capture a wide range of underlying background effects (for infectious diseases these are called endemic effects). The Hawkes process and LGCP are computationally expensive due to the former having a likelihood with quadratic complexity in the number of observations and the latter involving inversion of the precision matrix which is cubic in observations. Here we propose a novel approach to perform MCMC sampling for our Hawkes process with LGCP background, using pre-trained Gaussian Process generators which provide direct and cheap access to samples during inference. We show the efficacy and flexibility of our approach in experiments on simulated data and use our methods to uncover the trends in a dataset of reported crimes in the US.

stat.ML↗

arXiv2022

$π$VAE: a stochastic process prior for Bayesian deep learning with MCMC

Stochastic processes provide a mathematically elegant way model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. In practice, however, efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($π$VAE). The $π$VAE is finitely exchangeable and Kolmogorov consistent, and thus is a continuous stochastic process. We use $π$VAE to learn low dimensional embeddings of function classes. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions to enable statistical inference (such as the integral of a log Gaussian process). For popular tasks, such as spatial interpolation, $π$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate that the low dimensional independently distributed latent space representation learnt provides an elegant and scalable means of performing Bayesian inference for stochastic processes within probabilistic programming languages such as Stan.

cs.LG↗

arXiv2022

PriorVAE: Encoding spatial priors with VAEs for small-area estimation

Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context they are used to encode correlation structures over space and can generalise well in interpolation tasks. Despite their flexibility, off-the-shelf GPs present serious computational challenges which limit their scalability and practical usefulness in applied settings. Here, we propose a novel, deep generative modelling approach to tackle this challenge, termed PriorVAE: for a particular spatial setting, we approximate a class of GP priors through prior sampling and subsequent fitting of a variational autoencoder (VAE). Given a trained VAE, the resultant decoder allows spatial inference to become incredibly efficient due to the low dimensional, independently distributed latent Gaussian space representation of the VAE. Once trained, inference using the VAE decoder replaces the GP within a Bayesian sampling framework. This approach provides tractable and easy-to-implement means of approximately encoding spatial priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two stage approach on Bayesian, small-area estimation tasks.

cs.LG↗

arXiv2022

Aggregated Gaussian Processes with Multiresolution Earth Observation Covariates

For many survey-based spatial modelling problems, responses are observed as spatially aggregated over survey regions due to limited resources. Covariates, from weather models and satellite imageries, can be observed at many different spatial resolutions, making the pre-processing of covariates a key challenge for any spatial modelling task. We propose a Gaussian process regression model to flexibly handle multiresolution covariates by employing an additive kernel that can efficiently aggregate features across resolutions. Compared to existing approaches that rely on resolution matching, our approach better maintains distributional information across resolutions, leading to better performance and interpretability. Our model yields stronger predictive performance and interpretability on both simulated and crop yield datasets.

stat.AP↗

arXiv2022

Bayesian Kernel Two-Sample Testing

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where applications are often restricted to univariate cases. Here, we propose a Bayesian kernel two-sample testing procedure based on modelling the difference between kernel mean embeddings in the reproducing kernel Hilbert space utilising the framework established by Flaxman et al (2016). The use of kernel methods enables its application to random variables in generic domains beyond the multivariate Euclidean spaces. The proposed procedure results in a posterior inference scheme that allows an automatic selection of the kernel parameters relevant to the problem at hand. In a series of synthetic experiments and two real data experiments (i.e. testing network heterogeneity from high-dimensional data and six-membered monocyclic ring conformation comparison), we illustrate the advantages of our approach.

stat.ME↗

arXiv2021

PCACE: A Statistical Approach to Ranking Neurons for CNN Interpretability

In this paper we introduce a new problem within the growing literature of interpretability for convolution neural networks (CNNs). While previous work has focused on the question of how to visually interpret CNNs, we ask what it is that we care to interpret, that is, which layers and neurons are worth our attention? Due to the vast size of modern deep learning network architectures, automated, quantitative methods are needed to rank the relative importance of neurons so as to provide an answer to this question. We present a new statistical method for ranking the hidden neurons in any convolutional layer of a network. We define importance as the maximal correlation between the activation maps and the class score. We provide different ways in which this method can be used for visualization purposes with MNIST and ImageNet, and show a real-world application of our method to air pollution prediction with street-level images.

cs.CV↗

arXiv2021

COVID-19-Associated Orphanhood and Caregiver Death in the United States

Background: Most COVID-19 deaths occur among adults, not children, and attention has focused on mitigating COVID-19 burden among adults. However, a tragic consequence of adult deaths is that high numbers of children might lose their parents and caregivers to COVID-19-associated deaths. Methods: We quantified COVID-19-associated caregiver loss and orphanhood in the US and for each state using fertility and excess and COVID-19 mortality data. We assessed burden and rates of COVID-19-associated orphanhood and deaths of custodial and co-residing grandparents, overall and by race/ethnicity. We further examined variations in COVID-19-associated orphanhood by race/ethnicity for each state. Results: We found that from April 1, 2020 through June 30, 2021, over 140,000 children in the US experienced the death of a parent or grandparent caregiver. The risk of such loss was 1.1 to 4.5 times higher among children of racial and ethnic minorities, compared to Non-Hispanic White children. The highest burden of COVID-19-associated death of parents and caregivers occurred in Southern border states for Hispanic children, Southeastern states for Black children, and in states with tribal areas for American Indian/Alaska Native populations. Conclusions: We found substantial disparities in distributions of COVID-19-associated death of parents and caregivers across racial and ethnic groups. Children losing caregivers to COVID-19 need care and safe, stable, and nurturing families with economic support, quality childcare and evidence-based parenting support programs. There is an urgent need to mount an evidence-based comprehensive response focused on those children at greatest risk, in the states most affected.

stat.AP↗

arXiv2021

Regularised B-splines projected Gaussian Process priors to estimate time-trends of age-specific COVID-19 deaths related to vaccine roll-out

The COVID-19 pandemic has caused severe public health consequences in the United States. In this study, we use a hierarchical Bayesian model to estimate the age-specific COVID-19 attributable deaths over time in the United States. The model is specified by a novel non-parametric spatial approach, a low-rank Gaussian Process (GP) projected by regularised B-splines. We show that this projection defines a new GP with attractive smoothness and computational efficiency properties, derive its kernel function, and discuss the penalty terms induced by the projected GP. Simulation analyses and benchmark results show that the spatial approach performs better than standard B-splines and Bayesian P-splines and equivalently well as a standard GP, for considerably lower runtimes. The B-splines projected GP priors that we develop are likely an appealing addition to the arsenal of Bayesian regularising priors. We apply the model to weekly, age-stratified COVID-19 attributable deaths reported by the US Centers for Disease Control, which are subject to censoring and reporting biases. Using the B-splines projected GP, we can estimate longitudinal trends in COVID-19 associated deaths across the US by 1-year age bands. These estimates are instrumental to calculate age-specific mortality rates, describe variation in age-specific deaths across the US, and for fitting epidemic models. Here, we couple the model with age-specific vaccination rates to show that lower vaccination rates in younger adults aged 18-64 are associated with significantly stronger resurgences in COVID-19 deaths, especially in Florida and Texas. These results underscore the critical importance of medically able individuals of all ages to be vaccinated against COVID-19 in order to limit fatal outcomes.

stat.AP↗

arXiv2021

Bayesian Probabilistic Numerical Integration with Tree-Based Models

Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP) approximation of the integrand. As a result, BQ is inherently limited to cases where GP approximations can be done in an efficient manner, thus often prohibiting very high-dimensional or non-smooth target functions. This paper proposes to tackle this issue with a new Bayesian numerical integration algorithm based on Bayesian Additive Regression Trees (BART) priors, which we call BART-Int. BART priors are easy to tune and well-suited for discontinuous functions. We demonstrate that they also lend themselves naturally to a sequential design setting and that explicit convergence rates can be obtained in a variety of settings. The advantages and disadvantages of this new methodology are highlighted on a set of benchmark tests including the Genz functions, and on a Bayesian survey design problem.

stat.ME↗

arXiv2021

Unrepresentative Big Surveys Significantly Overestimate US Vaccine Uptake

Surveys are a crucial tool for understanding public opinion and behavior, and their accuracy depends on maintaining statistical representativeness of their target populations by minimizing biases from all sources. Increasing data size shrinks confidence intervals but magnifies the impact of survey bias, an instance of the Big Data Paradox (Meng 2018). Here we demonstrate this paradox in estimates of first-dose COVID-19 vaccine uptake in US adults: Delphi-Facebook (about 250,000 responses per week) and Census Household Pulse (about 75,000 per week). By May 2021, Delphi-Facebook overestimated uptake by 17 percentage points and Census Household Pulse by 14, compared to a benchmark from the Centers for Disease Control and Prevention (CDC). Moreover, their large data sizes led to minuscule margins of error on the incorrect estimates. In contrast, an Axios-Ipsos online panel with about 1,000 responses following survey research best practices (AAPOR) provided reliable estimates and uncertainty. We decompose observed error using a recent analytic framework to explain the inaccuracy in the three surveys. We then analyze the implications for vaccine hesitancy and willingness. We show how a survey of 250,000 respondents can produce an estimate of the population mean that is no more accurate than an estimate from a simple random sample of size 10. Our central message is that data quality matters far more than data quantity, and compensating the former with the latter is a mathematically provable losing proposition.

stat.AP↗

arXiv2021

Epidemia: An R Package for Semi-Mechanistic Bayesian Modelling of Infectious Diseases using Point Processes

This article introduces epidemia, an R package for Bayesian, regression-oriented modeling of infectious diseases. The implemented models define a likelihood for all observed data while also explicitly modeling transmission dynamics: an approach often termed as semi-mechanistic. Infections are propagated over time using renewal equations. This approach is inspired by self-exciting, continuous-time point processes such as the Hawkes process. A variety of inferential tasks can be performed using the package. Key epidemiological quantities, including reproduction numbers and latent infections, may be estimated within the framework. The models may be used to evaluate the determinants of changes in transmission rates, including the effects of control measures. Epidemic dynamics may be simulated either from a fitted model or a prior model; allowing for prior/posterior predictive checks, experimentation, and forecasting.

stat.CO↗

arXiv2021

Gaussian Process Nowcasting: Application to COVID-19 Mortality Reporting

Updating observations of a signal due to the delays in the measurement process is a common problem in signal processing, with prominent examples in a wide range of fields. An important example of this problem is the nowcasting of COVID-19 mortality: given a stream of reported counts of daily deaths, can we correct for the delays in reporting to paint an accurate picture of the present, with uncertainty? Without this correction, raw data will often mislead by suggesting an improving situation. We present a flexible approach using a latent Gaussian process that is capable of describing the changing auto-correlation structure present in the reporting time-delay surface. This approach also yields robust estimates of uncertainty for the estimated nowcasted numbers of deaths. We test assumptions in model specification such as the choice of kernel or hyper priors, and evaluate model performance on a challenging real dataset from Brazil. Our experiments show that Gaussian process nowcasting performs favourably against both comparable methods, and against a small sample of expert human predictions. Our approach has substantial practical utility in disease modelling -- by applying our approach to COVID-19 mortality data from Brazil, where reporting delays are large, we can make informative predictions on important epidemiological quantities such as the current effective reproduction number.

stat.AP↗

arXiv2021

Improving axial resolution in SIM using deep learning

Structured Illumination Microscopy is a widespread methodology to image live and fixed biological structures smaller than the diffraction limits of conventional optical microscopy. Using recent advances in image up-scaling through deep learning models, we demonstrate a method to reconstruct 3D SIM image stacks with twice the axial resolution attainable through conventional SIM reconstructions. We further evaluate our method for robustness to noise & generalisability to varying observed specimens, and discuss potential adaptions of the method to further improvements in resolution.

eess.IV↗

arXiv2021

Understanding the 2016 US Presidential Election using ecological inference and distribution regression with census microdata

We combine fine-grained spatially referenced census data with the vote outcomes from the 2016 US presidential election. Using this dataset, we perform ecological inference using distribution regression (Flaxman et al, KDD 2015) with a multinomial-logit regression so as to model the vote outcome Trump, Clinton, Other / Didn't vote as a function of demographic and socioeconomic features. Ecological inference allows us to estimate "exit poll" style results like what was Trump's support among white women, but for entirely novel categories. We also perform exploratory data analysis to understand which census variables are predictive of voting for Trump, voting for Clinton, or not voting for either. All of our methods are implemented in Python and R, and are available online for replication.

stat.AP↗

arXiv2021

Bayesian Approaches to Distribution Regression

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not propagate the uncertainty in observations due to sampling variability in the groups. This effectively assumes that small and large groups are estimated equally well, and should have equal weight in the final regression. We account for this uncertainty with a Bayesian distribution regression formalism, improving the robustness and performance of the model when group sizes vary. We frame our models in a neural network style, allowing for simple MAP inference using backpropagation to learn the parameters, as well as MCMC-based inference which can fully propagate uncertainty. We demonstrate our approach on illustrative toy datasets, as well as on a challenging problem of predicting age from images.

stat.ML↗

arXiv2021

Referenced Thermodynamic Integration for Bayesian Model Selection: Application to COVID-19 Model Selection

Model selection is a fundamental part of the applied Bayesian statistical methodology. Metrics such as the Akaike Information Criterion are commonly used in practice to select models but do not incorporate the uncertainty of the models' parameters and can give misleading choices. One approach that uses the full posterior distribution is to compute the ratio of two models' normalising constants, known as the Bayes factor. Often in realistic problems, this involves the integration of analytically intractable, high-dimensional distributions, and therefore requires the use of stochastic methods such as thermodynamic integration (TI). In this paper we apply a variation of the TI method, referred to as referenced TI, which computes a single model's normalising constant in an efficient way by using a judiciously chosen reference density. The advantages of the approach and theoretical considerations are set out, along with explicit pedagogical 1 and 2D examples. Benchmarking is presented with comparable methods and we find favourable convergence performance. The approach is shown to be useful in practice when applied to a real problem - to perform model selection for a semi-mechanistic hierarchical Bayesian model of COVID-19 transmission in South Korea involving the integration of a 200D density.

stat.AP↗

arXiv2020

Semi-Mechanistic Bayesian Modeling of COVID-19 with Renewal Processes

We propose a general Bayesian approach to modeling epidemics such as COVID-19. The approach grew out of specific analyses conducted during the pandemic, in particular an analysis concerning the effects of non-pharmaceutical interventions (NPIs) in reducing COVID-19 transmission in 11 European countries. The model parameterizes the time varying reproduction number $R_t$ through a regression framework in which covariates can e.g be governmental interventions or changes in mobility patterns. This allows a joint fit across regions and partial pooling to share strength. This innovation was critical to our timely estimates of the impact of lockdown and other NPIs in the European epidemics, whose validity was borne out by the subsequent course of the epidemic. Our framework provides a fully generative model for latent infections and observations deriving from them, including deaths, cases, hospitalizations, ICU admissions and seroprevalence surveys. One issue surrounding our model's use during the COVID-19 pandemic is the confounded nature of NPIs and mobility. We use our framework to explore this issue. We have open sourced an R package epidemia implementing our approach in Stan. Versions of the model are used by New York State, Tennessee and Scotland to estimate the current situation and make policy decisions.

stat.AP↗

arXiv2020

Inference of COVID-19 epidemiological distributions from Brazilian hospital data

Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalised with COVID-19 using a large dataset ($N=21{,}000-157{,}000$) from the Brazilian Sistema de Informação de Vigilância Epidemiológica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and shows significant variation in the mean of the symptom-onset-to-death time, with ranges between 11.2-17.8 days across the different states, and a mean of 15.2 days for Brazil. We find strong evidence in favour of specific probability density function choices: for example, the gamma distribution gives the best fit for onset-to-death and the generalised log-normal for onset-to-hospital-admission. Our results show that epidemiological distributions have considerable geographical variation, and provide the first estimates of these distributions in a low and middle-income setting. At the subnational level, variation in COVID-19 outcome timings are found to be correlated with poverty, deprivation and segregation levels, and weaker correlation is observed for mean age, wealth and urbanicity.

q-bio.PE↗