cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.7874177.v3
title: Smoothing With Couplings of Conditional Particle Filters

description: In state–space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has methodological benefits: independent estimators can be generated in parallel, and CI can be constructed from the central limit theorem to quantify the approximation error. To design unbiased estimators, we combine a generic debiasing technique for Markov chains, with a Markov chain Monte Carlo algorithm for smoothing. The resulting procedure is widely applicable and we show in numerical experiments that the removal of the bias comes at a manageable increase in variance. We establish the validity of the proposed estimators under mild assumptions. Numerical experiments are provided on toy models, including a setting of highly informative observations, and for a realistic Lotka–Volterra model with an intractable transition density. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7869365.v3
title: Ensemble Kalman Methods for High-Dimensional Hierarchical Dynamic Space-Time Models

description: We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the geophysics literature, with state-space algorithms from the statistics literature. Our algorithms address a variety of estimation scenarios, including online and off-line state and parameter estimation. We take a Bayesian perspective, for which the goal is to generate samples from the joint posterior distribution of states and parameters. The key benefit of our approach is the use of ensemble Kalman methods for dimension reduction, which allows inference for high-dimensional state vectors. We compare our methods to existing ones, including ensemble Kalman filters, particle filters, and particle MCMC. Using a real data example of cloud motion and data simulated under a number of nonlinear and non-Gaussian scenarios, we show that our approaches outperform these existing methods. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7999325.v1
title: Functional Censored Quantile Regression

description: We propose a functional censored quantile regression model to describe the time-varying relationship between time-to-event outcomes and corresponding functional covariates. The time-varying effect is modeled as an unspecified function that is approximated via B-splines. A generalized approximate cross-validation method is developed to select the number of knots by minimizing the expected loss. We establish asymptotic properties of the method and the knot selection procedure. Furthermore, we conduct extensive simulation studies to evaluate the finite sample performance of our method. Finally, we analyze the functional relationship between ambulatory blood pressure trajectories and clinical outcome in stroke patients. The results reinforce the importance of the morning blood pressure surge phenomenon, whose effect has caught attention but remains controversial in the medical literature. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7874159.v2
title: Nonnegative Matrix Factorization Via Archetypal Analysis

description: Given a collection of data points, nonnegative matrix factorization (NMF) suggests expressing them as convex combinations of a small set of “archetypes” with nonnegative entries. This decomposition is unique only if the true archetypes are nonnegative and sufficiently sparse (or the weights are sufficiently sparse), a regime that is captured by the separability condition and its generalizations. In this article, we study an approach to NMF that can be traced back to the work of Cutler and Breiman [(1994), “Archetypal Analysis,” <i>Technometrics</i>, 36, 338–347] and does not require the data to be separable, while providing a generally unique decomposition. We optimize a trade-off between two objectives: we minimize the distance of the data points from the convex envelope of the archetypes (which can be interpreted as an empirical risk), while also minimizing the distance of the archetypes from the convex envelope of the data (which can be interpreted as a data-dependent regularization). The archetypal analysis method of Cutler and Breiman is recovered as the limiting case in which the last term is given infinite weight. We introduce a “uniqueness condition” on the data which is necessary for identifiability. We prove that, under uniqueness (plus additional regularity conditions on the geometry of the archetypes), our estimator is robust. While our approach requires solving a nonconvex optimization problem, we find that standard optimization methods succeed in finding good solutions for both real and synthetic data. Supplementary materials for this article are available online
DOI: 10.6084/m9.figshare.8069495.v3
title: A Bayesian General Linear Modeling Approach to Cortical Surface fMRI Data Analysis

description: Cortical surface functional magnetic resonance imaging (cs-fMRI) has recently grown in popularity versus traditional volumetric fMRI. In addition to offering better whole-brain visualization, dimension reduction, removal of extraneous tissue types, and improved alignment of cortical areas across subjects, it is also more compatible with common assumptions of Bayesian spatial models. However, as no spatial Bayesian model has been proposed for cs-fMRI data, most analyses continue to employ the classical general linear model (GLM), a “massive univariate” approach. Here, we propose a spatial Bayesian GLM for cs-fMRI, which employs a class of sophisticated spatial processes to model latent activation fields. We make several advances compared with existing spatial Bayesian models for volumetric fMRI. First, we use integrated nested Laplacian approximations, a highly accurate and efficient Bayesian computation technique, rather than variational Bayes. To identify regions of activation, we utilize an excursions set method based on the joint posterior distribution of the latent fields, rather than the marginal distribution at each location. Finally, we propose the first multi-subject spatial Bayesian modeling approach, which addresses a major gap in the existing literature. The methods are very computationally advantageous and are validated through simulation studies and two task fMRI studies from the Human Connectome Project. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.7881014.v2
title: Individualized Multilayer Tensor Learning With an Application in Imaging Analysis

description: This work is motivated by multimodality breast cancer imaging data, which is quite challenging in that the signals of discrete tumor-associated microvesicles are randomly distributed with heterogeneous patterns. This imposes a significant challenge for conventional imaging regression and dimension reduction models assuming a homogeneous feature structure. We develop an innovative multilayer tensor learning method to incorporate heterogeneity to a higher-order tensor decomposition and predict disease status effectively through utilizing subject-wise imaging features and multimodality information. Specifically, we construct a multilayer decomposition which leverages an individualized imaging layer in addition to a modality-specific tensor structure. One major advantage of our approach is that we are able to efficiently capture the heterogeneous spatial features of signals that are not characterized by a population structure as well as integrating multimodality information simultaneously. To achieve scalable computing, we develop a new bi-level block improvement algorithm. In theory, we investigate both the algorithm convergence property, tensor signal recovery error bound and asymptotic consistency for prediction model estimation. We also apply the proposed method for simulated and human breast cancer imaging data. Numerical results demonstrate that the proposed method outperforms other existing competing methods. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.8014586.v1
title: Expected Conditional Characteristic Function-based Measures for Testing Independence

description: We propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. The relation between our index and other similar measures is studied, which indicates that they all belong to a large framework of reproducing kernel Hilbert space. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. In addition, our index is also applicable when both variables are continuous. We develop two empirical estimates and obtain their respective asymptotic distributions. We illustrate the advantages of our approach by numerical studies across a variety of settings including a real data example. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7819544.v2
title: Category-Adaptive Variable Screening for Ultra-High Dimensional Heterogeneous Categorical Data

description: The populations of interest in modern studies are very often heterogeneous. The population heterogeneity, the qualitative nature of the outcome variable and the high dimensionality of the predictors pose significant challenge in statistical analysis. In this article, we introduce a category-adaptive screening procedure with high-dimensional heterogeneous data, which is to detect category-specific important covariates. The proposal is a model-free approach without any specification of a regression model and an adaptive procedure in the sense that the set of active variables is allowed to vary across different categories, thus making it more flexible to accommodate heterogeneity. For response-selective sampling data, another main discovery of this article is that the proposed method works directly without any modification. Under mild regularity conditions, the newly procedure is shown to possess the sure screening and ranking consistency properties. Simulation studies contain supportive evidence that the proposed method performs well under various settings and it is effective to extract category-specific information. Applications are illustrated with two real datasets. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.8069315.v3
title: A Large-Scale Constrained Joint Modeling Approach for Predicting User Activity, Engagement, and Churn With Application to Freemium Mobile Games

description: We develop a <i>constrained extremely zero inflated joint</i> (CEZIJ) modeling framework for simultaneously analyzing player activity, engagement, and dropouts (churns) in app-based mobile freemium games. Our proposed framework addresses the complex interdependencies between a player’s decision to use a freemium product, the extent of her direct and indirect engagement with the product and her decision to permanently drop its usage. CEZIJ extends the existing class of joint models for longitudinal and survival data in several ways. It not only accommodates extremely zero-inflated responses in a joint model setting but also incorporates domain-specific, convex structural constraints on the model parameters. Longitudinal data from app-based mobile games usually exhibit a large set of potential predictors and choosing the relevant set of predictors is highly desirable for various purposes including improved predictability. To achieve this goal, CEZIJ conducts simultaneous, coordinated selection of fixed and random effects in high-dimensional penalized generalized linear mixed models. For analyzing such large-scale datasets, variable selection and estimation are conducted via a distributed computing based split-and-conquer approach that massively increases scalability and provides better predictive performance over competing predictive methods. Our results reveal codependencies between varied player characteristics that promote player activity and engagement. Furthermore, the predicted churn probabilities exhibit idiosyncratic clusters of player profiles over time based on which marketers and game managers can segment the playing population for improved monetization of app-based freemium games. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.7895756.v2
title: On Prediction Properties of Kriging: Uniform Error Bounds and Robustness

description: Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict for a range of untried points simultaneously. In this work, we obtain some error bounds for the simple and universal kriging predictor under the uniform metric. It works for a scattered set of input points in an arbitrary dimension, and also covers the case where the covariance function of the Gaussian process is misspecified. These results lead to a better understanding of the rate of convergence of kriging under the Gaussian or the Matérn correlation functions, the relationship between space-filling designs and kriging models, and the robustness of the Matérn correlation functions. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7869362.v2
title: Multiresolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

description: The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multiresolution functional ANOVA (MRFA) model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input nonlinear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed MRFA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, in terms of both sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.8069309.v3
title: Robust Clustering With Subpopulation-Specific Deviations

description: The National Birth Defects Prevention Study (NBDPS) is a case-control study of birth defects conducted across 10 U.S. states. Researchers are interested in characterizing the etiologic role of maternal diet, collected using a food frequency questionnaire. Because diet is multidimensional, dimension reduction methods such as cluster analysis are often used to summarize dietary patterns. In a large, heterogeneous population, traditional clustering methods, such as latent class analysis, used to estimate dietary patterns can produce a large number of clusters due to a variety of factors, including study size and regional diversity. These factors result in a loss of interpretability of patterns that may differ due to minor consumption changes. Based on adaptation of the local partition process, we propose a new method, robust profile clustering, to handle these data complexities. Here, participants may be clustered at two levels: (1) globally, where women are assigned to an overall population-level cluster via an overfitted finite mixture model, and (2) locally, where regional variations in diet are accommodated via a beta-Bernoulli process dependent on subpopulation differences. We use our method to analyze the NBDPS data, deriving prepregnancy dietary patterns for women in the NBDPS while accounting for regional variability. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.7999331.v3
title: A Generalized Gaussian Process Model for Computer Experiments With Binary Time Series

description: Non-Gaussian observations such as binary responses are common in some computer experiments. Motivated by the analysis of a class of cell adhesion experiments, we introduce a generalized Gaussian process model for binary responses, which shares some common features with standard GP models. In addition, the proposed model incorporates a flexible mean function that can capture different types of time series structures. Asymptotic properties of the estimators are derived, and an optimal predictor as well as its predictive distribution are constructed. Their performance is examined via two simulation studies. The methodology is applied to study computer simulations for cell adhesion experiments. The fitted model reveals important biological information in repeated cell bindings, which is not directly observable in lab experiments. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.8145704.v3
title: Bayesian Optimal Design for Ordinary Differential Equation Models With Application in Biological Science

description: Bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of nonlinear ordinary differential equations. The motivation is an experiment to estimate parameters in the equations governing the transport of amino acids through cell membranes in human placentas. Decision-theoretic Bayesian design of experiments for such nonlinear models is conceptually very attractive, allowing the formal incorporation of prior knowledge to overcome the parameter dependence of frequentist design and being less reliant on asymptotic approximations. However, the necessary approximation and maximization of the, typically analytically intractable, expected utility results in a computationally challenging problem. These issues are further exacerbated if the solution to the differential equations is not available in closed-form. This article proposes a new combination of a probabilistic solution to the equations embedded within a Monte Carlo approximation to the expected utility with cyclic descent of a smooth approximation to find the optimal design. A novel precomputation algorithm reduces the computational burden, making the search for an optimal design feasible for bigger problems. The methods are demonstrated by finding new designs for a number of common models derived from differential equations, and by providing optimal designs for the placenta experiment. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.7792106.v2
title: Informed Proposals for Local MCMC in Discrete Spaces

description: <b>There is a lack of methodological results to design efficient Markov chain Monte Carlo (</b><b>MCMC</b><b>) algorithms for statistical models with discrete-valued high-dimensional parameters. Motivated by this consideration, we propose a simple framework for the design of informed</b><b>MCMC</b><b>proposals (i.e., Metropolis–Hastings proposal distributions that appropriately incorporate local information about the target) which is naturally applicable to discrete spaces. Using Peskun-type comparisons of Markov kernels, we explicitly characterize the class of asymptotically optimal proposal distributions under this framework, which we refer to as <i>locally balanced</i> proposals. The resulting algorithms are straightforward to implement in discrete spaces and provide orders of magnitude improvements in efficiency compared to alternative</b><b>MCMC</b><b>schemes, including discrete versions of Hamiltonian Monte Carlo. Simulations are performed with both simulated and real datasets, including a detailed application to Bayesian record linkage. A direct connection with gradient-based</b><b>MCMC</b><b>suggests that locally balanced proposals can be seen as a natural way to extend the latter to discrete spaces. Supplementary materials for this article are available online.</b>
DOI: 10.6084/m9.figshare.9103811.v3
title: Statistical Topology and the Random Interstellar Medium

description: We use topological methods to investigate the small-scale variation and local spatial characteristics of the interstellar medium (ISM) in three regions of the southern sky. We demonstrate that there are circumstances where topological methods can identify differences in distributions when conventional marginal or correlation analyses may not. We propose a nonparametric method for comparing two fields based on the counts of topological features and the geometry of the associated persistence diagrams. We investigate the expected distribution of topological structures quantified through Betti numbers under Gaussian random field (GRF) assumptions, which underlie many astrophysical models of the ISM. When we apply the methods to the astrophysical data, we find strong evidence that one of the three regions is both topologically dissimilar to the other two and not consistent with an underlying GRF model. This region is proximal to a region of recent star formation whereas the others are more distant. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.