cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.963486.v3
title: Robust Estimation for Generalized Additive Models

description: This article studies <i>M</i>-type estimators for fitting robust generalized additive models in the presence of anomalous data. A new theoretical construct is developed to connect the costly <i>M</i>-type estimation with least-squares type calculations. Its asymptotic properties are studied and used to motivate a computational algorithm. The main idea is to decompose the overall <i>M</i>-type estimation problem into a sequence of well-studied conventional additive model fittings. The resulting algorithm is fast and stable, can be paired with different nonparametric smoothers, and can also be applied to cases with multiple covariates. As another contribution of this article, automatic methods for smoothing parameter selection are proposed. These methods are designed to be resistant to outliers. The empirical performance of the proposed methodology is illustrated via both simulation experiments and real data analysis. Supplementary materials are available online.
DOI: 10.6084/m9.figshare.963483.v1
title: Generalized Isotonic Regression

description: We present a new computational and statistical approach for fitting isotonic models under convex differentiable loss functions through recursive partitioning. Models along the partitioning path are also isotonic and can be viewed as regularized solutions to the problem. Our approach generalizes and subsumes the well-known work of Barlow and Brunk on fitting isotonic regressions subject to specially structured loss functions, and expands the range of loss functions that can be used (e.g., adding Huber loss for robust regression). This is accomplished through an algorithmic adjustment to a recursive partitioning approach recently developed for solving large-scale ł<sub>2</sub>-loss isotonic regression problems. We prove that the new algorithm solves the generalized problem while maintaining the favorable computational and statistical properties of the <i>l</i><sub>2</sub> algorithm. The results are demonstrated on both real and synthetic data in two settings: fitting count data using negative Poisson log-likelihood loss, and fitting robust isotonic regressions using Huber loss. Proofs of theorems and a MATLAB-based software package implementing our algorithm are available in the online supplementary materials.
DOI: 10.6084/m9.figshare.963485.v3
title: Label Switching in Bayesian Mixture Models: Deterministic Relabeling Strategies

description: Label switching is a well-known problem in the Bayesian analysis of mixture models. On the one hand, it complicates inference, and on the other hand, it has been perceived as a prerequisite to justify Markov chain Monte Carlo (MCMC) convergence. As a result, nonstandard MCMC algorithms that traverse the symmetric copies of the posterior distribution, and possibly genuine modes, have been proposed. To perform component-specific inference, methods to undo the label switching and to recover the interpretation of the components need to be applied. If latent allocations for the design of the MCMC strategy are included, and the sampler has converged, then labels assigned to each component may change from iteration to iteration. However, observations being allocated together must remain similar, and we use this fundamental fact to derive an easy and efficient solution to the label switching problem. We compare our strategy with other relabeling algorithms on univariate and multivariate data examples and demonstrate improvements over alternative strategies. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.963481
title: Robust Parametric Classification and Variable Selection by a Minimum Distance Criterion

description: We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic regression, the bias due to outliers always causes the parameter vector to implode, that is, shrink toward the zero vector. Thus, using LASSO-like penalties to perform variable selection in the presence of outliers can result in missed detections of relevant covariates. We show that by choosing a minimum distance criterion together with an elastic net penalty, we can simultaneously find a parsimonious model and avoid estimation implosion even in the presence of many outliers in the important small <i>n</i> large <i>p</i> situation. Minimizing the penalized minimum distance criterion is a challenging problem due to its nonconvexity. To meet the challenge, we develop a simple and efficient MM (majorization–minimization) algorithm that can be adapted gracefully to the small <i>n</i> large <i>p</i> context. Performance of our algorithm is evaluated on simulated and real datasets. This article has supplementary materials available online.
DOI: 10.6084/m9.figshare.963482.v1
title: Modeling and Anomalous Cluster Detection for Point Processes Using Process Convolutions

description: We present a model using process convolutions, which describes spatial and temporal variations of the intensity of events that occur at random geographical locations. An inhomogeneous Poisson process is used to model the intensity over a spatial region with multiplicative spatial and temporal covariate effects. Temporal variation in the structure of the intensity is obtained by employing a time-varying process for the convolution. Use of a compactly supported kernel in the convolution improves the computational efficiency. Additionally, anomalous cluster detection in the event rates is developed based on exceedance probabilities. The methods are demonstrated on data of major crimes in Cincinnati during 2006. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.963483.v3
title: Generalized Isotonic Regression

description: We present a new computational and statistical approach for fitting isotonic models under convex differentiable loss functions through recursive partitioning. Models along the partitioning path are also isotonic and can be viewed as regularized solutions to the problem. Our approach generalizes and subsumes the well-known work of Barlow and Brunk on fitting isotonic regressions subject to specially structured loss functions, and expands the range of loss functions that can be used (e.g., adding Huber loss for robust regression). This is accomplished through an algorithmic adjustment to a recursive partitioning approach recently developed for solving large-scale ł<sub>2</sub>-loss isotonic regression problems. We prove that the new algorithm solves the generalized problem while maintaining the favorable computational and statistical properties of the <i>l</i><sub>2</sub> algorithm. The results are demonstrated on both real and synthetic data in two settings: fitting count data using negative Poisson log-likelihood loss, and fitting robust isotonic regressions using Huber loss. Proofs of theorems and a MATLAB-based software package implementing our algorithm are available in the online supplementary materials.
DOI: 10.6084/m9.figshare.963486.v2
title: Robust Estimation for Generalized Additive Models

description: This article studies <i>M</i>-type estimators for fitting robust generalized additive models in the presence of anomalous data. A new theoretical construct is developed to connect the costly <i>M</i>-type estimation with least-squares type calculations. Its asymptotic properties are studied and used to motivate a computational algorithm. The main idea is to decompose the overall <i>M</i>-type estimation problem into a sequence of well-studied conventional additive model fittings. The resulting algorithm is fast and stable, can be paired with different nonparametric smoothers, and can also be applied to cases with multiple covariates. As another contribution of this article, automatic methods for smoothing parameter selection are proposed. These methods are designed to be resistant to outliers. The empirical performance of the proposed methodology is illustrated via both simulation experiments and real data analysis. Supplementary materials are available online.
DOI: 10.6084/m9.figshare.963480
title: Functional Generalized Additive Models

description: We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to <i>t</i> of <i>F</i>{<i>X</i>(<i>t</i>), <i>t</i>} where <i>F</i>( ·, ·) is an unknown regression function and <i>X</i>(<i>t</i>) is a functional covariate. Rather than having an additive model in a finite number of principal components as by Müller and Yao (2008), our model incorporates the functional predictor directly and thus our model can be viewed as the natural functional extension of generalized additive models. We estimate <i>F</i>( ·, ·) using tensor-product B-splines with roughness penalties. A pointwise quantile transformation of the functional predictor is also considered to ensure each tensor-product B-spline has observed data on its support. The methods are evaluated using simulated data and their predictive performance is compared with other competing scalar-on-function regression alternatives. We illustrate the usefulness of our approach through an application to brain tractography, where <i>X</i>(<i>t</i>) is a signal from diffusion tensor imaging at position, <i>t</i>, along a tract in the brain. In one example, the response is disease-status (case or control) and in a second example, it is the score on a cognitive test. The FGAM is implemented in R in the refund package. There are additional supplementary materials available online.
DOI: 10.6084/m9.figshare.963482.v3
title: Modeling and Anomalous Cluster Detection for Point Processes Using Process Convolutions

description: We present a model using process convolutions, which describes spatial and temporal variations of the intensity of events that occur at random geographical locations. An inhomogeneous Poisson process is used to model the intensity over a spatial region with multiplicative spatial and temporal covariate effects. Temporal variation in the structure of the intensity is obtained by employing a time-varying process for the convolution. Use of a compactly supported kernel in the convolution improves the computational efficiency. Additionally, anomalous cluster detection in the event rates is developed based on exceedance probabilities. The methods are demonstrated on data of major crimes in Cincinnati during 2006. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.963483.v2
title: Generalized Isotonic Regression

description: We present a new computational and statistical approach for fitting isotonic models under convex differentiable loss functions through recursive partitioning. Models along the partitioning path are also isotonic and can be viewed as regularized solutions to the problem. Our approach generalizes and subsumes the well-known work of Barlow and Brunk on fitting isotonic regressions subject to specially structured loss functions, and expands the range of loss functions that can be used (e.g., adding Huber loss for robust regression). This is accomplished through an algorithmic adjustment to a recursive partitioning approach recently developed for solving large-scale ł<sub>2</sub>-loss isotonic regression problems. We prove that the new algorithm solves the generalized problem while maintaining the favorable computational and statistical properties of the <i>l</i><sub>2</sub> algorithm. The results are demonstrated on both real and synthetic data in two settings: fitting count data using negative Poisson log-likelihood loss, and fitting robust isotonic regressions using Huber loss. Proofs of theorems and a MATLAB-based software package implementing our algorithm are available in the online supplementary materials.
DOI: 10.6084/m9.figshare.963485.v2
title: Label Switching in Bayesian Mixture Models: Deterministic Relabeling Strategies

description: Label switching is a well-known problem in the Bayesian analysis of mixture models. On the one hand, it complicates inference, and on the other hand, it has been perceived as a prerequisite to justify Markov chain Monte Carlo (MCMC) convergence. As a result, nonstandard MCMC algorithms that traverse the symmetric copies of the posterior distribution, and possibly genuine modes, have been proposed. To perform component-specific inference, methods to undo the label switching and to recover the interpretation of the components need to be applied. If latent allocations for the design of the MCMC strategy are included, and the sampler has converged, then labels assigned to each component may change from iteration to iteration. However, observations being allocated together must remain similar, and we use this fundamental fact to derive an easy and efficient solution to the label switching problem. We compare our strategy with other relabeling algorithms on univariate and multivariate data examples and demonstrate improvements over alternative strategies. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.963478
title: Approximate Bayesian Computation and Bayes’ Linear Analysis: Toward High-Dimensional ABC

description: Bayes’ linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article, we connect these ideas by demonstrating that regression-adjustment ABC algorithms produce samples for which first- and second-order moment summaries approximate adjusted expectation and variance for a Bayes’ linear analysis. This gives regression-adjustment methods a useful interpretation and role in exploratory analysis in high-dimensional problems. As a result, we propose a new method for combining high-dimensional, regression-adjustment ABC with lower-dimensional approaches (such as using Markov chain Monte Carlo for ABC). This method first obtains a rough estimate of the joint posterior via regression-adjustment ABC, and then estimates each univariate marginal posterior distribution separately in a lower-dimensional analysis. The marginal distributions of the initial estimate are then modified to equal the separately estimated marginals, thereby providing an improved estimate of the joint posterior. We illustrate this method with several examples. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.963479
title: On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments

description: Kriging is commonly used for developing emulators as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix, which can lead to large variability and poor performance of the kriging predictor. First, we study some causes of ill-conditioning in kriging. We then study the use of nugget in kriging to overcome the numerical instability. Some asymptotic results on its interpolation bias and mean squared prediction errors are presented. Finally, we study the choice of the nugget parameter based on some algebraic lower bounds and use of a regularizing trace. A simulation study is performed to show the differences between kriging with and without nugget and to demonstrate the advantages of the former. This article has supplementary materials online.
DOI: 10.6084/m9.figshare.963482.v2
title: Modeling and Anomalous Cluster Detection for Point Processes Using Process Convolutions

description: We present a model using process convolutions, which describes spatial and temporal variations of the intensity of events that occur at random geographical locations. An inhomogeneous Poisson process is used to model the intensity over a spatial region with multiplicative spatial and temporal covariate effects. Temporal variation in the structure of the intensity is obtained by employing a time-varying process for the convolution. Use of a compactly supported kernel in the convolution improves the computational efficiency. Additionally, anomalous cluster detection in the event rates is developed based on exceedance probabilities. The methods are demonstrated on data of major crimes in Cincinnati during 2006. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.963479.v1
title: On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments

description: Kriging is commonly used for developing emulators as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix, which can lead to large variability and poor performance of the kriging predictor. First, we study some causes of ill-conditioning in kriging. We then study the use of nugget in kriging to overcome the numerical instability. Some asymptotic results on its interpolation bias and mean squared prediction errors are presented. Finally, we study the choice of the nugget parameter based on some algebraic lower bounds and use of a regularizing trace. A simulation study is performed to show the differences between kriging with and without nugget and to demonstrate the advantages of the former. This article has supplementary materials online.
DOI: 10.6084/m9.figshare.963480.v1
title: Functional Generalized Additive Models

description: We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to <i>t</i> of <i>F</i>{<i>X</i>(<i>t</i>), <i>t</i>} where <i>F</i>(·, ·) is an unknown regression function and <i>X</i>(<i>t</i>) is a functional covariate. Rather than having an additive model in a finite number of principal components as by Müller and Yao (2008), our model incorporates the functional predictor directly and thus our model can be viewed as the natural functional extension of generalized additive models. We estimate <i>F</i>(·, ·) using tensor-product B-splines with roughness penalties. A pointwise quantile transformation of the functional predictor is also considered to ensure each tensor-product B-spline has observed data on its support. The methods are evaluated using simulated data and their predictive performance is compared with other competing scalar-on-function regression alternatives. We illustrate the usefulness of our approach through an application to brain tractography, where <i>X</i>(<i>t</i>) is a signal from diffusion tensor imaging at position, <i>t</i>, along a tract in the brain. In one example, the response is disease-status (case or control) and in a second example, it is the score on a cognitive test. The FGAM is implemented in R in the refund package. There are additional supplementary materials available online.
DOI: 10.6084/m9.figshare.963481.v1
title: Robust Parametric Classification and Variable Selection by a Minimum Distance Criterion

description: We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic regression, the bias due to outliers always causes the parameter vector to implode, that is, shrink toward the zero vector. Thus, using LASSO-like penalties to perform variable selection in the presence of outliers can result in missed detections of relevant covariates. We show that by choosing a minimum distance criterion together with an elastic net penalty, we can simultaneously find a parsimonious model and avoid estimation implosion even in the presence of many outliers in the important small <i>n</i> large <i>p</i> situation. Minimizing the penalized minimum distance criterion is a challenging problem due to its nonconvexity. To meet the challenge, we develop a simple and efficient MM (majorization–minimization) algorithm that can be adapted gracefully to the small <i>n</i> large <i>p</i> context. Performance of our algorithm is evaluated on simulated and real datasets. This article has supplementary materials available online.
DOI: 10.6084/m9.figshare.963478.v1
title: Approximate Bayesian Computation and Bayes’ Linear Analysis: Toward High-Dimensional ABC

description: Bayes’ linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article, we connect these ideas by demonstrating that regression-adjustment ABC algorithms produce samples for which first- and second-order moment summaries approximate adjusted expectation and variance for a Bayes’ linear analysis. This gives regression-adjustment methods a useful interpretation and role in exploratory analysis in high-dimensional problems. As a result, we propose a new method for combining high-dimensional, regression-adjustment ABC with lower-dimensional approaches (such as using Markov chain Monte Carlo for ABC). This method first obtains a rough estimate of the joint posterior via regression-adjustment ABC, and then estimates each univariate marginal posterior distribution separately in a lower-dimensional analysis. The marginal distributions of the initial estimate are then modified to equal the separately estimated marginals, thereby providing an improved estimate of the joint posterior. We illustrate this method with several examples. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.963480.v3
title: Functional Generalized Additive Models

description: We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to <i>t</i> of <i>F</i>{<i>X</i>(<i>t</i>), <i>t</i>} where <i>F</i>( ·, ·) is an unknown regression function and <i>X</i>(<i>t</i>) is a functional covariate. Rather than having an additive model in a finite number of principal components as by Müller and Yao (2008), our model incorporates the functional predictor directly and thus our model can be viewed as the natural functional extension of generalized additive models. We estimate <i>F</i>( ·, ·) using tensor-product B-splines with roughness penalties. A pointwise quantile transformation of the functional predictor is also considered to ensure each tensor-product B-spline has observed data on its support. The methods are evaluated using simulated data and their predictive performance is compared with other competing scalar-on-function regression alternatives. We illustrate the usefulness of our approach through an application to brain tractography, where <i>X</i>(<i>t</i>) is a signal from diffusion tensor imaging at position, <i>t</i>, along a tract in the brain. In one example, the response is disease-status (case or control) and in a second example, it is the score on a cognitive test. The FGAM is implemented in R in the refund package. There are additional supplementary materials available online.