cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.8023382.v3
title: Penalized and Constrained Optimization: An Application to High-Dimensional Website Advertising

description: Firms are increasingly transitioning advertising budgets to Internet display campaigns, but this transition poses new challenges. These campaigns use numerous potential metrics for success (e.g., <i>reach</i> or <i>click rate</i>), and because each website represents a separate advertising opportunity, this is also an inherently high-dimensional problem. Further, advertisers often have constraints they wish to place on their campaign, such as targeting specific sub-populations or websites. These challenges require a method flexible enough to accommodate thousands of websites, as well as numerous metrics and campaign constraints. Motivated by this application, we consider the general constrained high-dimensional problem, where the parameters satisfy linear constraints. We develop the <i>Penalized and Constrained</i> optimization method (PaC) to compute the solution path for high-dimensional, linearly constrained criteria. PaC is extremely general; in addition to internet advertising, we show it encompasses many other potential applications, such as portfolio estimation, monotone curve estimation, and the generalized lasso. Computing the PaC coefficient path poses technical challenges, but we develop an efficient algorithm over a grid of tuning parameters. Through extensive simulations, we show PaC performs well. Finally, we apply PaC to a proprietary dataset in an exemplar Internet advertising case study and demonstrate its superiority over existing methods in this practical setting. 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.8028866.v3
title: Prediction and Inference With Missing Data in Patient Alert Systems

description: We describe the Bedside Patient Rescue (BPR) project, the goal of which is risk prediction of adverse events for non-intensive care unit patients using ∼100 variables (vitals, lab results, assessments, etc.). There are several missing predictor values for most patients, which in the health sciences is the norm, rather than the exception. A Bayesian approach is presented that addresses many of the shortcomings to standard approaches to missing predictors: (i) treatment of the uncertainty due to imputation is straight-forward in the Bayesian paradigm, (ii) the predictor distribution is flexibly modeled as an infinite normal mixture with latent variables to explicitly account for discrete predictors (i.e., as in multivariate probit regression models), and (iii) certain missing not at random situations can be handled effectively by allowing the indicator of missingness into the predictor distribution only to inform the distribution of the missing variables. The proposed approach also has the benefit of providing a distribution for the prediction, including the uncertainty inherent in the imputation. Therefore, we can ask questions such as: is it possible this individual is at high risk but we are missing too much information to know for sure? How much would we reduce the uncertainty in our risk prediction by obtaining a particular missing value? This approach is applied to the BPR problem resulting in excellent predictive capability to identify deteriorating patients. 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.8023376.v3
title: Quantile Function on Scalar Regression Analysis for Distributional Data

description: Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of summaries of the marginal distribution of pixel intensities, which leads to multiple testing problems and can miss out on insights not contained in the selected features. In this paper, we present methods to model the entire marginal distribution of pixel intensities via the quantile function as functional data, regressed on a set of demographic, clinical, and genetic predictors to investigate their effects of imaging-based cancer heterogeneity. We call this approach <i>quantile functional regression</i>, regressing subject-specific marginal distributions across repeated measurements on a set of covariates, allowing us to assess which covariates are associated with the distribution in a global sense, as well as to identify distributional features characterizing these differences, including mean, variance, skewness, heavy-tailedness, and various upper and lower quantiles. To account for smoothness in the quantile functions, account for intrafunctional correlation, and gain statistical power, we introduce custom basis functions we call <i>quantlets</i> that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given dataset and containing a Gaussian subspace so non-Gaussianness can be assessed. We fit this model using a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and provides fully Bayesian inference after fitting a Markov chain Monte Carlo. We demonstrate the benefit of the basis space modeling through simulation studies, and apply the method to Magnetic resonance imaging (MRI)-based radiomic dataset from Glioblastoma Multiforme to relate imaging-based quantile functions to various demographic, clinical, and genetic predictors, finding specific differences in tumor pixel intensity distribution between males and females and between tumors with and without DDIT3 mutations. 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.8023382.v2
title: Penalized and Constrained Optimization: An Application to High-Dimensional Website Advertising

description: Firms are increasingly transitioning advertising budgets to Internet display campaigns, but this transition poses new challenges. These campaigns use numerous potential metrics for success (e.g., <i>reach</i> or <i>click rate</i>), and because each website represents a separate advertising opportunity, this is also an inherently high-dimensional problem. Further, advertisers often have constraints they wish to place on their campaign, such as targeting specific sub-populations or websites. These challenges require a method flexible enough to accommodate thousands of websites, as well as numerous metrics and campaign constraints. Motivated by this application, we consider the general constrained high-dimensional problem, where the parameters satisfy linear constraints. We develop the <i>Penalized and Constrained</i> optimization method (PaC) to compute the solution path for high-dimensional, linearly constrained criteria. PaC is extremely general; in addition to internet advertising, we show it encompasses many other potential applications, such as portfolio estimation, monotone curve estimation, and the generalized lasso. Computing the PaC coefficient path poses technical challenges, but we develop an efficient algorithm over a grid of tuning parameters. Through extensive simulations, we show PaC performs well. Finally, we apply PaC to a proprietary dataset in an exemplar Internet advertising case study and demonstrate its superiority over existing methods in this practical setting. 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.7458809.v2
title: From Distance Correlation to Multiscale Graph Correlation

description: Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we establish a new framework that generalizes distance correlation (Dcorr)—a correlation measure that was recently proposed and shown to be universally consistent for dependence testing against all joint distributions of finite moments—to the multiscale graph correlation (MGC). By using the characteristic functions and incorporating the nearest neighbor machinery, we formalize the population version of local distance correlations, define the optimal scale in a given dependency, and name the optimal local correlation as MGC. The new theoretical framework motivates a theoretically sound sample MGC and allows a number of desirable properties to be proved, including the universal consistency, convergence, and almost unbiasedness of the sample version. The advantages of MGC are illustrated via a comprehensive set of simulations with linear, nonlinear, univariate, multivariate, and noisy dependencies, where it loses almost no power in monotone dependencies while achieving better performance in general dependencies, compared to Dcorr and other popular methods. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.8023385
title: Demand Models With Random Partitions

description: Many economic models of consumer demand require researchers to partition sets of products or attributes prior to the analysis. These models are common in applied problems when the product space is large or spans multiple categories. While the partition is traditionally fixed a priori, we let the partition be a model parameter and propose a Bayesian method for inference. The challenge is that demand systems are commonly multivariate models that are not conditionally conjugate with respect to partition indices, precluding the use of Gibbs sampling. We solve this problem by constructing a new location-scale partition distribution that can generate random-walk Metropolis–Hastings proposals and also serve as a prior. Our method is illustrated in the context of a store-level category demand model, where we find that allowing for partition uncertainty is important for preserving model flexibility, improving demand forecasts, and learning about the structure of demand. 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.8023376
title: Quantile Function on Scalar Regression Analysis for Distributional Data

description: Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of summaries of the marginal distribution of pixel intensities, which leads to multiple testing problems and can miss out on insights not contained in the selected features. In this paper, we present methods to model the entire marginal distribution of pixel intensities via the quantile function as functional data, regressed on a set of demographic, clinical, and genetic predictors to investigate their effects of imaging-based cancer heterogeneity. We call this approach <i>quantile functional regression</i>, regressing subject-specific marginal distributions across repeated measurements on a set of covariates, allowing us to assess which covariates are associated with the distribution in a global sense, as well as to identify distributional features characterizing these differences, including mean, variance, skewness, heavy-tailedness, and various upper and lower quantiles. To account for smoothness in the quantile functions, account for intrafunctional correlation, and gain statistical power, we introduce custom basis functions we call <i>quantlets</i> that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given dataset and containing a Gaussian subspace so non-Gaussianness can be assessed. We fit this model using a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and provides fully Bayesian inference after fitting a Markov chain Monte Carlo. We demonstrate the benefit of the basis space modeling through simulation studies, and apply the method to Magnetic resonance imaging (MRI)-based radiomic dataset from Glioblastoma Multiforme to relate imaging-based quantile functions to various demographic, clinical, and genetic predictors, finding specific differences in tumor pixel intensity distribution between males and females and between tumors with and without DDIT3 mutations. 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.8023376.v2
title: Quantile Function on Scalar Regression Analysis for Distributional Data

description: Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of summaries of the marginal distribution of pixel intensities, which leads to multiple testing problems and can miss out on insights not contained in the selected features. In this paper, we present methods to model the entire marginal distribution of pixel intensities via the quantile function as functional data, regressed on a set of demographic, clinical, and genetic predictors to investigate their effects of imaging-based cancer heterogeneity. We call this approach <i>quantile functional regression</i>, regressing subject-specific marginal distributions across repeated measurements on a set of covariates, allowing us to assess which covariates are associated with the distribution in a global sense, as well as to identify distributional features characterizing these differences, including mean, variance, skewness, heavy-tailedness, and various upper and lower quantiles. To account for smoothness in the quantile functions, account for intrafunctional correlation, and gain statistical power, we introduce custom basis functions we call <i>quantlets</i> that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given dataset and containing a Gaussian subspace so non-Gaussianness can be assessed. We fit this model using a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and provides fully Bayesian inference after fitting a Markov chain Monte Carlo. We demonstrate the benefit of the basis space modeling through simulation studies, and apply the method to Magnetic resonance imaging (MRI)-based radiomic dataset from Glioblastoma Multiforme to relate imaging-based quantile functions to various demographic, clinical, and genetic predictors, finding specific differences in tumor pixel intensity distribution between males and females and between tumors with and without DDIT3 mutations. 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.7590851
title: Nonparametric Imputation by Data Depth

description: We present single imputation method for missing values which borrows the idea of data depth—a measure of centrality defined for an arbitrary point of a space with respect to a probability distribution or data cloud. This consists in iterative maximization of the depth of each observation with missing values, and can be employed with any properly defined statistical depth function. For each single iteration, imputation reverts to optimization of quadratic, linear, or quasiconcave functions that are solved analytically by linear programming or the Nelder–Mead method. As it accounts for the underlying data topology, the procedure is distribution free, allows imputation close to the data geometry, can make prediction in situations where local imputation (<i>k</i>-nearest neighbors, random forest) cannot, and has attractive robustness and asymptotic properties under elliptical symmetry. It is shown that a special case—when using the Mahalanobis depth—has direct connection to well-known methods for the multivariate normal model, such as iterated regression and regularized PCA. The methodology is extended to multiple imputation for data stemming from an elliptically symmetric distribution. Simulation and real data studies show good results compared with existing popular alternatives. The method has been implemented as an R-package. Supplementary materials for the article are available online.
DOI: 10.6084/m9.figshare.7461701
title: Quantile Co-Movement in Financial Markets: A Panel Quantile Model With Unobserved Heterogeneity

description: This article introduces a new procedure for analyzing the quantile co-movement of a large number of financial time series based on a large-scale panel data model with factor structures. The proposed method attempts to capture the unobservable heterogeneity of each of the financial time series based on sensitivity to explanatory variables and to the unobservable factor structure. In our model, the dimension of the common factor structure varies across quantiles, and the explanatory variables is allowed to depend on the factor structure. The proposed method allows for both cross-sectional and serial dependence, and heteroscedasticity, which are common in financial markets. We propose new estimation procedures for both frequentist and Bayesian frameworks. Consistency and asymptotic normality of the proposed estimator are established. We also propose a new model selection criterion for determining the number of common factors together with theoretical support. We apply the method to analyze the returns for over 6000 international stocks from over 60 countries during the subprime crisis, European sovereign debt crisis, and subsequent period. The empirical analysis indicates that the common factor structure varies across quantiles. We find that the common factors for the quantiles and the common factors for the mean are different. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7461701.v3
title: Quantile Co-Movement in Financial Markets: A Panel Quantile Model With Unobserved Heterogeneity

description: This article introduces a new procedure for analyzing the quantile co-movement of a large number of financial time series based on a large-scale panel data model with factor structures. The proposed method attempts to capture the unobservable heterogeneity of each of the financial time series based on sensitivity to explanatory variables and to the unobservable factor structure. In our model, the dimension of the common factor structure varies across quantiles, and the explanatory variables is allowed to depend on the factor structure. The proposed method allows for both cross-sectional and serial dependence, and heteroscedasticity, which are common in financial markets. We propose new estimation procedures for both frequentist and Bayesian frameworks. Consistency and asymptotic normality of the proposed estimator are established. We also propose a new model selection criterion for determining the number of common factors together with theoretical support. We apply the method to analyze the returns for over 6000 international stocks from over 60 countries during the subprime crisis, European sovereign debt crisis, and subsequent period. The empirical analysis indicates that the common factor structure varies across quantiles. We find that the common factors for the quantiles and the common factors for the mean are different. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7590851.v3
title: Nonparametric Imputation by Data Depth

description: We present single imputation method for missing values which borrows the idea of data depth—a measure of centrality defined for an arbitrary point of a space with respect to a probability distribution or data cloud. This consists in iterative maximization of the depth of each observation with missing values, and can be employed with any properly defined statistical depth function. For each single iteration, imputation reverts to optimization of quadratic, linear, or quasiconcave functions that are solved analytically by linear programming or the Nelder–Mead method. As it accounts for the underlying data topology, the procedure is distribution free, allows imputation close to the data geometry, can make prediction in situations where local imputation (<i>k</i>-nearest neighbors, random forest) cannot, and has attractive robustness and asymptotic properties under elliptical symmetry. It is shown that a special case—when using the Mahalanobis depth—has direct connection to well-known methods for the multivariate normal model, such as iterated regression and regularized PCA. The methodology is extended to multiple imputation for data stemming from an elliptically symmetric distribution. Simulation and real data studies show good results compared with existing popular alternatives. The method has been implemented as an R-package. Supplementary materials for the article are available online.
DOI: 10.6084/m9.figshare.7461701.v2
title: Quantile Co-Movement in Financial Markets: A Panel Quantile Model With Unobserved Heterogeneity

description: This article introduces a new procedure for analyzing the quantile co-movement of a large number of financial time series based on a large-scale panel data model with factor structures. The proposed method attempts to capture the unobservable heterogeneity of each of the financial time series based on sensitivity to explanatory variables and to the unobservable factor structure. In our model, the dimension of the common factor structure varies across quantiles, and the explanatory variables is allowed to depend on the factor structure. The proposed method allows for both cross-sectional and serial dependence, and heteroscedasticity, which are common in financial markets. We propose new estimation procedures for both frequentist and Bayesian frameworks. Consistency and asymptotic normality of the proposed estimator are established. We also propose a new model selection criterion for determining the number of common factors together with theoretical support. We apply the method to analyze the returns for over 6000 international stocks from over 60 countries during the subprime crisis, European sovereign debt crisis, and subsequent period. The empirical analysis indicates that the common factor structure varies across quantiles. We find that the common factors for the quantiles and the common factors for the mean are different. Supplementary materials for this article are available online.