arXiv subjects

Tyler H. McCormick

Publications and source records attributed to Tyler H. McCormick.

At least 37 records · Page 2Linked to original sources

arXiv2024

Bayesian analysis of verbal autopsy data using factor models with age- and sex-dependent associations between symptoms

Verbal autopsies (VAs) are extensively used to investigate the population-level distributions of deaths by cause in low-resource settings without well-organized vital statistics systems. Computer-based methods are often adopted to assign causes of death to deceased individuals based on the interview responses of their family members or caregivers. In this article, we develop a new Bayesian approach that extracts information about cause-of-death distributions from VA data considering the age- and sex-related variation in the associations between symptoms. Its performance is compared with that of existing approaches using gold-standard data from the Population Health Metrics Research Consortium. In addition, we compute the relevance of predictors to causes of death based on information-theoretic measures.

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arXiv2024

Estimating spillovers using imprecisely measured networks

In many experimental contexts, whether and how network interactions impact the outcome of interest for both treated and untreated individuals are key concerns. Networks data is often assumed to perfectly represent these possible interactions. This paper considers the problem of estimating treatment effects when measured connections are, instead, a noisy representation of the true spillover pathways. We show that existing methods, using the potential outcomes framework, yield biased estimators in the presence of this mismeasurement. We develop a new method, using a class of mixture models, that can account for missing connections and discuss its estimation via the Expectation-Maximization algorithm. We check our method's performance by simulating experiments on real network data from 43 villages in India. Finally, we use data from a previously published study to show that estimates using our method are more robust to the choice of network measure.

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arXiv2024

Do We Really Even Need Data?

As artificial intelligence and machine learning tools become more accessible, and scientists face new obstacles to data collection (e.g. rising costs, declining survey response rates), researchers increasingly use predictions from pre-trained algorithms as outcome variables. Though appealing for financial and logistical reasons, using standard tools for inference can misrepresent the association between independent variables and the outcome of interest when the true, unobserved outcome is replaced by a predicted value. In this paper, we characterize the statistical challenges inherent to this so-called ``inference with predicted data'' problem and elucidate three potential sources of error: (i) the relationship between predicted outcomes and their true, unobserved counterparts, (ii) robustness of the machine learning model to resampling or uncertainty about the training data, and (iii) appropriately propagating not just bias but also uncertainty from predictions into the ultimate inference procedure.

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arXiv2024

Comparing the Robustness of Simple Network Scale-Up Method (NSUM) Estimators

The network scale-up method (NSUM) is a cost-effective approach to estimating the size or prevalence of a group of people that is hard to reach through a standard survey. The basic NSUM involves two steps: estimating respondents' degrees by one of various methods (in this paper we focus on the probe group method which uses the number of people a respondent knows in various groups of known size), and estimating the prevalence of the hard-to-reach population of interest using respondents' estimated degrees and the number of people they report knowing in the hard-to-reach group. Each of these two steps involves taking either an average of ratios or a ratio of averages. Using the ratio of averages for each step has so far been the most common approach. However, we present theoretical arguments that using the average of ratios at the second, prevalence-estimation step often has lower mean squared error when the random mixing assumption is violated, which seems likely in practice; this estimator which uses the ratio of averages for degree estimates and the average of ratios for prevalence was proposed early in NSUM development but has largely been unexplored and unused. Simulation results using an example network data set also support these findings. Based on this theoretical and empirical evidence, we suggest that future surveys that use a simple estimator may want to use this mixed estimator, and estimation methods based on this estimator may produce new improvements.

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arXiv2023

Feasible contact tracing

Contact tracing is one of the most important tools for preventing the spread of infectious diseases, but as the experience of COVID-19 showed, it is also next-to-impossible to implement when the disease is spreading rapidly. We show how to substantially improve the efficiency of contact tracing by combining standard microeconomic tools that measure heterogeneity in how infectious a sick person is with ideas from machine learning about sequential optimization. Our contributions are twofold. First, we incorporate heterogeneity in individual infectiousness in a multi-armed bandit to establish optimal algorithms. At the heart of this strategy is a focus on learning. In the typical conceptualization of contact tracing, contacts of an infected person are tested to find more infections. Under a learning-first framework, however, contacts of infected persons are tested to ascertain whether the infected person is likely to be a "high infector" and to find additional infections only if it is likely to be highly fruitful. Second, we demonstrate using three administrative contact tracing datasets from India and Pakistan during COVID-19 that this strategy improves efficiency. Using our algorithm, we find 80% of infections with just 40% of contacts while current approaches test twice as many contacts to identify the same number of infections. We further show that a simple strategy that can be easily implemented in the field performs at nearly optimal levels, allowing for, what we call, feasible contact tracing. These results are immediately transferable to contact tracing in any epidemic.

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arXiv2023

Respondent-Driven Sampling: An Overview in the Context of Human Trafficking

Respondent-driven sampling (RDS) is both a sampling strategy and an estimation method. It is commonly used to study individuals that are difficult to access with standard sampling techniques. As with any sampling strategy, RDS has advantages and challenges. This article examines recent work using RDS in the context of human trafficking. We begin with an overview of the RDS process and methodology, then discuss RDS in the particular context of trafficking. We end with a description of recent work and potential future directions.

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arXiv2023

Bayesian Hyperbolic Multidimensional Scaling

Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold representing similarity. We propose a Bayesian approach to multidimensional scaling when the low-dimensional manifold is hyperbolic. Using hyperbolic space facilitates representing tree-like structures common in many settings (e.g. text or genetic data with hierarchical structure). A Bayesian approach provides regularization that minimizes the impact of measurement error in the observed data and assesses uncertainty. We also propose a case-control likelihood approximation that allows for efficient sampling from the posterior distribution in larger data settings, reducing computational complexity from approximately $O(n^2)$ to $O(n)$. We evaluate the proposed method against state-of-the-art alternatives using simulations, canonical reference datasets, Indian village network data, and human gene expression data.

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arXiv2023

Bayesian Age Category Reconciliation for Age- and Cause-specific Under-five Mortality Estimates

Age-disaggregated health data is crucial for effective public health planning and monitoring. Monitoring under-five mortality, for example, requires highly detailed age data since the distribution of potential causes of death varies substantially within the first few years of life. Comparative researchers often have to rely on multiple data sources yet, these sources often have ages aggregated at different levels, making it difficult to combine the data into a single, coherent picture. To address this challenge in the context of under-five cause-specific mortality, we propose a Bayesian approach, that calibrates data with different age structures to produce unified and accurate estimates of the standardized age group distributions. We consider age-disaggregated death counts as fully-classified multinomial data and show that by incorporating partially-classified aggregated data, we can construct an improved Bayes estimator of the multinomial parameters under the Kullback-Leibler (KL) loss. We illustrate the method using both synthetic and real data, demonstrating that the proposed method achieves adequate performance in imputing incomplete classification. Finally, we present the results of numerical studies examining the conditions necessary for obtaining improved estimators. These studies provide insights and interpretations that can be used to aid future research and inform guidance for practitioners on appropriate levels of age disaggregation, with the aim of improving the accuracy and reliability of under-five cause-specific mortality estimates.

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arXiv2022

Identifying the latent space geometry of network models through analysis of curvature

A common approach to modeling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter communities; negative curvature induces repulsion. We consistently estimate manifold type, dimension, and curvature from simply connected, complete Riemannian manifolds of constant curvature. We represent the graph as a noisy distance matrix based on the ties between cliques, then develop hypothesis tests to determine whether the observed distances could plausibly be embedded isometrically in each of the candidate geometries. We apply our approach to data-sets from economics and neuroscience.

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arXiv2022

Consistently estimating network statistics using Aggregated Relational Data

Collecting complete network data is expensive, time-consuming, and often infeasible. Aggregated Relational Data (ARD), which capture information about a social network by asking a respondent questions of the form ``How many people with trait X do you know?'' provide a low-cost option when collecting complete network data is not possible. Rather than asking about connections between each pair of individuals directly, ARD collects the number of contacts the respondent knows with a given trait. Despite widespread use and a growing literature on ARD methodology, there is still no systematic understanding of when and why ARD should accurately recover features of the unobserved network. This paper provides such a characterization by deriving conditions under which statistics about the unobserved network (or functions of these statistics like regression coefficients) can be consistently estimated using ARD. We do this by first providing consistent estimates of network model parameters for three commonly used probabilistic models: the beta-model with node-specific unobserved effects, the stochastic block model with unobserved community structure, and latent geometric space models with unobserved latent locations. A key observation behind these results is that cross-group link probabilities for a collection of (possibly unobserved) groups identifies the model parameters, meaning ARD is sufficient for parameter estimation. With these estimated parameters, it is possible to simulate graphs from the fitted distribution and analyze the distribution of network statistics. We can then characterize conditions under which the simulated networks based on ARD will allow for consistent estimation of the unobserved network statistics, such as eigenvector centrality or response functions by or of the unobserved network, such as regression coefficients.

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arXiv2022

The openVA Toolkit for Verbal Autopsies

Verbal autopsy (VA) is a survey-based tool widely used to infer cause of death (COD) in regions without complete-coverage civil registration and vital statistics systems. In such settings, many deaths happen outside of medical facilities and are not officially documented by a medical professional. VA surveys, consisting of signs and symptoms reported by a person close to the decedent, are used to infer the cause of death for an individual, and to estimate and monitor the cause of death distribution in the population. Several classification algorithms have been developed and widely used to assign cause of death using VA data. However, The incompatibility between different idiosyncratic model implementations and required data structure makes it difficult to systematically apply and compare different methods. The openVA package provides the first standardized framework for analyzing VA data that is compatible with all openly available methods and data structure. It provides an open-sourced, R implementation of several most widely used VA methods. It supports different data input and output formats, and customizable information about the associations between causes and symptoms. The paper discusses the relevant algorithms, their implementations in R packages under the openVA suite, and demonstrates the pipeline of model fitting, summary, comparison, and visualization in the R environment.

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arXiv2022

Regression of exchangeable relational arrays

Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms, and dynamic protein-protein interactions are all examples of relational arrays. Elements of a relational array are often modeled as a linear function of observable covariates. Uncertainty estimates for regression coefficient estimators -- and ideally the coefficient estimators themselves -- must account for dependence between elements of the array (e.g. relations involving the same actor) and existing estimators of standard errors that recognize such relational dependence rely on estimating extremely complex, heterogeneous structure across actors. This paper develops a new class of parsimonious coefficient and standard error estimators for regressions of relational arrays. We leverage an exchangeability assumption to derive standard error estimators that pool information across actors and are substantially more accurate than existing estimators in a variety of settings. This exchangeability assumption is pervasive in network and array models in the statistics literature, but not previously considered when adjusting for dependence in a regression setting with relational data. We demonstrate improvements in inference theoretically, via a simulation study, and by analysis of a data set involving international trade.

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arXiv2021

Spectral goodness-of-fit tests for complete and partial network data

Networks describe the, often complex, relationships between individual actors. In this work, we address the question of how to determine whether a parametric model, such as a stochastic block model or latent space model, fits a dataset well and will extrapolate to similar data. We use recent results in random matrix theory to derive a general goodness-of-fit test for dyadic data. We show that our method, when applied to a specific model of interest, provides an straightforward, computationally fast way of selecting parameters in a number of commonly used network models. For example, we show how to select the dimension of the latent space in latent space models. Unlike other network goodness-of-fit methods, our general approach does not require simulating from a candidate parametric model, which can be cumbersome with large graphs, and eliminates the need to choose a particular set of statistics on the graph for comparison. It also allows us to perform goodness-of-fit tests on partial network data, such as Aggregated Relational Data. We show with simulations that our method performs well in many situations of interest. We analyze several empirically relevant networks and show that our method leads to improved community detection algorithms. R code to implement our method is available on Github.

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arXiv2021

Inference for Network Regression Models with Community Structure

Network regression models, where the outcome comprises the valued edge in a network and the predictors are actor or dyad-level covariates, are used extensively in the social and biological sciences. Valid inference relies on accurately modeling the residual dependencies among the relations. Frequently homogeneity assumptions are placed on the errors which are commonly incorrect and ignore critical, natural clustering of the actors. In this work, we present a novel regression modeling framework that models the errors as resulting from a community-based dependence structure and exploits the subsequent exchangeability properties of the error distribution to obtain parsimonious standard errors for regression parameters.

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arXiv2021

Anomaly Detection in Large Scale Networks with Latent Space Models

We develop a real-time anomaly detection algorithm for directed activity on large, sparse networks. We model the propensity for future activity using a dynamic logistic model with interaction terms for sender- and receiver-specific latent factors in addition to sender- and receiver-specific popularity scores; deviations from this underlying model constitute potential anomalies. Latent nodal attributes are estimated via a variational Bayesian approach and may change over time, representing natural shifts in network activity. Estimation is augmented with a case-control approximation to take advantage of the sparsity of the network and reduces computational complexity from $O(N^2)$ to $O(E)$, where $N$ is the number of nodes and $E$ is the number of observed edges. We run our algorithm on network event records collected from an enterprise network of over 25,000 computers and are able to identify a red team attack with half the detection rate required of the model without latent interaction terms.

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arXiv2020

Modeling the social media relationships of Irish politicians using a generalized latent space stochastic blockmodel

Dáil Éireann is the principal chamber of the Irish parliament. The 31st Dáil Éireann is the principal chamber of the Irish parliament. The 31st Dáil was in session from March 11th, 2011 to February 6th, 2016. Many of the members of the Dáil were active on social media and many were Twitter users who followed other members of the Dáil. The pattern of following amongst these politicians provides insights into political alignment within the Dáil. We propose a new model, called the generalized latent space stochastic blockmodel, which extends and generalizes both the latent space model and the stochastic blockmodel to study social media connections between members of the Dáil. The probability of an edge between two nodes in a network depends on their respective class labels as well as latent positions in an unobserved latent space. The proposed model is capable of representing transitivity, clustering, as well as disassortative mixing. A Bayesian method with Markov chain Monte Carlo sampling is proposed for estimation of model parameters. Model selection is performed using the WAIC criterion and models of different number of classes or dimensions of latent space are compared. We use the model to study Twitter following relationships of members of the Dáil and interpret structure found in these relationships. We find that the following relationships amongst politicians is mainly driven by past and present political party membership. We also find that the modeling outputs are informative when studying voting within the Dáil.

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arXiv2019

Using Bayesian latent Gaussian graphical models to infer symptom associations in verbal autopsies

Learning dependence relationships among variables of mixed types provides insights in a variety of scientific settings and is a well-studied problem in statistics. Existing methods, however, typically rely on copious, high quality data to accurately learn associations. In this paper, we develop a method for scientific settings where learning dependence structure is essential, but data are sparse and have a high fraction of missing values. Specifically, our work is motivated by survey-based cause of death assessments known as verbal autopsies (VAs). We propose a Bayesian approach to characterize dependence relationships using a latent Gaussian graphical model that incorporates informative priors on the marginal distributions of the variables. We demonstrate such information can improve estimation of the dependence structure, especially in settings with little training data. We show that our method can be integrated into existing probabilistic cause-of-death assignment algorithms and improves model performance while recovering dependence patterns between symptoms that can inform efficient questionnaire design in future data collection.

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arXiv2019

Bayesian Joint Spike-and-Slab Graphical Lasso

In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce fully Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shrinkage and model selection simultaneously. We develop an EM algorithm that performs fast and dynamic explorations of posterior modes. Our approach selects sparse models efficiently with substantially smaller bias than would be induced by alternative regularization procedures. The performance of the proposed methods are demonstrated through simulation and two real data examples.

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