cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.5787528.v1
title: Linear Non-Gaussian Component Analysis via Maximum Likelihood

description: Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) could be mixed in several principal components that are discarded and then these ICs cannot be recovered. We formulate a linear non-Gaussian component model with Gaussian noise components. To estimate the model parameters, we propose likelihood component analysis (LCA), in which dimension reduction and latent variable estimation are achieved simultaneously. Our method orders components by their marginal likelihood rather than ordering components by variance as in PCA. We present a parametric LCA using the logistic density and a semi-parametric LCA using tilted Gaussians with cubic B-splines. Our algorithm is scalable to datasets common in applications (e.g., hundreds of thousands of observations across hundreds of variables with dozens of latent components). In simulations, latent components are recovered that are discarded by PCA+ICA methods. We apply our method to multivariate data and demonstrate that LCA is a useful data visualization and dimension reduction tool that reveals features not apparent from PCA or PCA+ICA. We also apply our method to an fMRI experiment from the Human Connectome Project and identify artifacts missed by PCA+ICA. We present theoretical results on identifiability of the linear non-Gaussian component model and consistency of LCA.
DOI: 10.6084/m9.figshare.5787528.v3
title: Linear Non-Gaussian Component Analysis Via Maximum Likelihood

description: Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis (PCA) is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) could be mixed in several principal components that are discarded and then these ICs cannot be recovered. We formulate a linear non-Gaussian component model with Gaussian noise components. To estimate the model parameters, we propose likelihood component analysis (LCA), in which dimension reduction and latent variable estimation are achieved simultaneously. Our method orders components by their marginal likelihood rather than ordering components by variance as in PCA. We present a parametric LCA using the logistic density and a semiparametric LCA using tilted Gaussians with cubic B-splines. Our algorithm is scalable to datasets common in applications (e.g., hundreds of thousands of observations across hundreds of variables with dozens of latent components). In simulations, latent components are recovered that are discarded by PCA+ICA methods. We apply our method to multivariate data and demonstrate that LCA is a useful data visualization and dimension reduction tool that reveals features not apparent from PCA or PCA+ICA. We also apply our method to a functional magnetic resonance imaging experiment from the Human Connectome Project and identify artifacts missed by PCA+ICA. We present theoretical results on identifiability of the linear non-Gaussian component model and consistency of LCA. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.5787528.v2
title: Linear Non-Gaussian Component Analysis Via Maximum Likelihood

description: Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis (PCA) is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) could be mixed in several principal components that are discarded and then these ICs cannot be recovered. We formulate a linear non-Gaussian component model with Gaussian noise components. To estimate the model parameters, we propose likelihood component analysis (LCA), in which dimension reduction and latent variable estimation are achieved simultaneously. Our method orders components by their marginal likelihood rather than ordering components by variance as in PCA. We present a parametric LCA using the logistic density and a semiparametric LCA using tilted Gaussians with cubic B-splines. Our algorithm is scalable to datasets common in applications (e.g., hundreds of thousands of observations across hundreds of variables with dozens of latent components). In simulations, latent components are recovered that are discarded by PCA+ICA methods. We apply our method to multivariate data and demonstrate that LCA is a useful data visualization and dimension reduction tool that reveals features not apparent from PCA or PCA+ICA. We also apply our method to a functional magnetic resonance imaging experiment from the Human Connectome Project and identify artifacts missed by PCA+ICA. We present theoretical results on identifiability of the linear non-Gaussian component model and consistency of LCA. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.5787525.v1
title: Information-Based Optimal Subdata Selection for Big Data Linear Regression

description: Extraordinary amounts of data are being produced in many branches of science. Proven statistical methods are no longer applicable with extraordinary large data sets due to computational limitations. A critical step in big data analysis is data reduction. Existing investigations in the context of linear regression focus on subsampling-based methods. However, not only is this approach prone to sampling errors, it also leads to a covariance matrix of the estimators that is typically bounded from below by a term that is of the order of the inverse of the subdata size. We propose a novel approach, termed information-based optimal subdata selection (IBOSS). Compared to leading existing subdata methods, the IBOSS approach has the following advantages: (i) it is significantly faster; (ii) it is suitable for distributed parallel computing; (iii) the variances of the slope parameter estimators converge to 0 as the full data size increases even if the subdata size is fixed, i.e., the convergence rate depends on the full data size; (iv) data analysis for IBOSS subdata is straightforward and the sampling distribution of an IBOSS estimator is easy to assess. Theoretical results and extensive simulations demonstrate that the IBOSS approach is superior to subsampling-based methods, sometimes by orders of magnitude. The advantages of the new approach are also illustrated through analysis of real data.
DOI: 10.6084/m9.figshare.5787522
title: Group SLOPE – Adaptive Selection of Groups of Predictors

description: Sorted L-One Penalized Estimation (SLOPE; Bogdan et al. 2013, 2015) is a relatively new convex optimization procedure, which allows for adaptive selection of regressors under sparse high-dimensional designs. Here, we extend the idea of SLOPE to deal with the situation when one aims at selecting whole groups of explanatory variables instead of single regressors. Such groups can be formed by clustering strongly correlated predictors or groups of dummy variables corresponding to different levels of the same qualitative predictor. We formulate the respective convex optimization problem, group SLOPE (gSLOPE), and propose an efficient algorithm for its solution. We also define a notion of the group false discovery rate (gFDR) and provide a choice of the sequence of tuning parameters for gSLOPE so that gFDR is provably controlled at a prespecified level if the groups of variables are orthogonal to each other. Moreover, we prove that the resulting procedure adapts to unknown sparsity and is asymptotically minimax with respect to the estimation of the proportions of variance of the response variable explained by regressors from different groups. We also provide a method for the choice of the regularizing sequence when variables in different groups are not orthogonal but statistically independent and illustrate its good properties with computer simulations. Finally, we illustrate the advantages of gSLOPE in the context of Genome Wide Association Studies. R package grpSLOPE with an implementation of our method is available on The Comprehensive R Archive Network.
DOI: 10.6084/m9.figshare.5787522.v2
title: Group SLOPE – Adaptive Selection of Groups of Predictors

description: Sorted L-One Penalized Estimation (SLOPE; Bogdan et al. 2013, 2015) is a relatively new convex optimization procedure, which allows for adaptive selection of regressors under sparse high-dimensional designs. Here, we extend the idea of SLOPE to deal with the situation when one aims at selecting whole groups of explanatory variables instead of single regressors. Such groups can be formed by clustering strongly correlated predictors or groups of dummy variables corresponding to different levels of the same qualitative predictor. We formulate the respective convex optimization problem, group SLOPE (gSLOPE), and propose an efficient algorithm for its solution. We also define a notion of the group false discovery rate (gFDR) and provide a choice of the sequence of tuning parameters for gSLOPE so that gFDR is provably controlled at a prespecified level if the groups of variables are orthogonal to each other. Moreover, we prove that the resulting procedure adapts to unknown sparsity and is asymptotically minimax with respect to the estimation of the proportions of variance of the response variable explained by regressors from different groups. We also provide a method for the choice of the regularizing sequence when variables in different groups are not orthogonal but statistically independent and illustrate its good properties with computer simulations. Finally, we illustrate the advantages of gSLOPE in the context of Genome Wide Association Studies. R package grpSLOPE with an implementation of our method is available on The Comprehensive R Archive Network.
DOI: 10.6084/m9.figshare.5787522.v1
title: Group SLOPE - adaptive selection of groups of predictors<sup>*</sup>

description: Sorted L-One Penalized Estimation (SLOPE, Bogdan et al., 2013, 2015) is a relatively new convex optimization procedure which allows for adaptive selection of regressors under sparse high dimensional designs. Here we extend the idea of SLOPE to deal with the situation when one aims at selecting whole groups of explanatory variables instead of single regressors. Such groups can be formed by clustering strongly correlated predictors or groups of dummy variables corresponding to different levels of the same qualitative predictor. We formulate the respective convex optimization problem, gSLOPE (group SLOPE), and propose an efficient algorithm for its solution. We also define a notion of the group false discovery rate (gFDR) and provide a choice of the sequence of tuning parameters for gSLOPE so that gFDR is provably controlled at a prespecified level if the groups of variables are orthogonal to each other. Moreover, we prove that the resulting procedure adapts to unknown sparsity and is asymptotically minimax with respect to the estimation of the proportions of variance of the response variable explained by regressors from different groups. We also provide a method for the choice of the regularizing sequence when variables in different groups are not orthogonal but statistically independent and illustrate its good properties with computer simulations. Finally, we illustrate the advantages of gSLOPE in the context of Genome Wide Association Studies. R package grpSLOPE with an implementation of our method is available on CRAN.
DOI: 10.6084/m9.figshare.5787513
title: Cross-Screening in Observational Studies That Test Many Hypotheses

description: We discuss observational studies that test many causal hypotheses, either hypotheses about many outcomes or many treatments. To be credible an observational study that tests many causal hypotheses must demonstrate that its conclusions are neither artifacts of multiple testing nor of small biases from nonrandom treatment assignment. In a sense that needs to be defined carefully, hidden within a sensitivity analysis for nonrandom assignment is an enormous correction for multiple testing: In the absence of bias, it is extremely improbable that multiple testing alone would create an association insensitive to moderate biases. We propose a new strategy called “cross-screening,” different from but motivated by recent work of Bogomolov and Heller on replicability. Cross-screening splits the data in half at random, uses the first half to plan a study carried out on the second half, then uses the second half to plan a study carried out on the first half, and reports the more favorable conclusions of the two studies correcting using the Bonferroni inequality for having done two studies. If the two studies happen to concur, then they achieve Bogomolov–Heller replicability; however, importantly, replicability is not required for strong control of the family-wise error rate, and either study alone suffices for firm conclusions. In randomized studies with just a few null hypotheses, cross-screening is not an attractive method when compared with conventional methods of multiplicity control. However, cross-screening has substantially higher power when hundreds or thousands of hypotheses are subjected to sensitivity analyses in an observational study of moderate size. We illustrate the technique by comparing 46 biomarkers in individuals who consume large quantities of fish versus little or no fish. The R package CrossScreening on CRAN implements the cross-screening method. 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.5787513.v2
title: Cross-Screening in Observational Studies That Test Many Hypotheses

description: We discuss observational studies that test many causal hypotheses, either hypotheses about many outcomes or many treatments. To be credible an observational study that tests many causal hypotheses must demonstrate that its conclusions are neither artifacts of multiple testing nor of small biases from nonrandom treatment assignment. In a sense that needs to be defined carefully, hidden within a sensitivity analysis for nonrandom assignment is an enormous correction for multiple testing: In the absence of bias, it is extremely improbable that multiple testing alone would create an association insensitive to moderate biases. We propose a new strategy called “cross-screening,” different from but motivated by recent work of Bogomolov and Heller on replicability. Cross-screening splits the data in half at random, uses the first half to plan a study carried out on the second half, then uses the second half to plan a study carried out on the first half, and reports the more favorable conclusions of the two studies correcting using the Bonferroni inequality for having done two studies. If the two studies happen to concur, then they achieve Bogomolov–Heller replicability; however, importantly, replicability is not required for strong control of the family-wise error rate, and either study alone suffices for firm conclusions. In randomized studies with just a few null hypotheses, cross-screening is not an attractive method when compared with conventional methods of multiplicity control. However, cross-screening has substantially higher power when hundreds or thousands of hypotheses are subjected to sensitivity analyses in an observational study of moderate size. We illustrate the technique by comparing 46 biomarkers in individuals who consume large quantities of fish versus little or no fish. The R package CrossScreening on CRAN implements the cross-screening method. 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.5787513.v1
title: Cross-screening in observational studies that test many hypotheses

description: We discuss observational studies that test many causal hypotheses, either hypotheses about many outcomes or many treatments. To be credible an observational study that tests many causal hypotheses must demonstrate that its conclusions are neither artifacts of multiple testing nor of small biases from nonrandom treatment assignment. In a sense that needs to be defined carefully, hidden within a sensitivity analysis for nonrandom assignment is an enormous correction for multiple testing: in the absence of bias, it is extremely improbable that multiple testing alone would create an association insensitive to moderate biases. We propose a new strategy called “cross-screening,” different from but motivated by recent work of Bogomolov and Heller on replicability. Cross-screening splits the data in half at random, uses the first half to plan a study carried out on the second half, then uses the second half to plan a study carried out on the first half, and reports the more favorable conclusions of the two studies correcting using the Bonferroni inequality for having done two studies. If the two studies happen to concur, then they achieve Bogomolov-Heller replicability; however, importantly, replicability is not required for strong control of the family-wise error rate, and either study alone suffices for firm conclusions. In randomized studies with just a few null hypotheses, cross-screening is not an attractive method when compared with conventional methods of multiplicity control. However, cross-screening has substantially higher power when hundreds or thousands of hypotheses are subjected to sensitivity analyses in an observational study of moderate size. We illustrate the technique by comparing 46 biomarkers in individuals who consume large quantities of fish versus little or no fish.
DOI: 10.6084/m9.figshare.5787501
title: Partially Linear Functional Additive Models for Multivariate Functional Data

description: We investigate a class of partially linear functional additive models (PLFAM) that predicts a scalar response by both parametric effects of a multivariate predictor and nonparametric effects of a multivariate functional predictor. We jointly model multiple functional predictors that are cross-correlated using multivariate functional principal component analysis (mFPCA), and model the nonparametric effects of the principal component scores as additive components in the PLFAM. To address the high-dimensional nature of functional data, we let the number of mFPCA components diverge to infinity with the sample size, and adopt the component selection and smoothing operator (COSSO) penalty to select relevant components and regularize the fitting. A fundamental difference between our framework and the existing high-dimensional additive models is that the mFPCA scores are estimated with error, and the magnitude of measurement error increases with the order of mFPCA. We establish the asymptotic convergence rate for our estimator, while allowing the number of components diverge. When the number of additive components is fixed, we also establish the asymptotic distribution for the partially linear coefficients. The practical performance of the proposed methods is illustrated via simulation studies and a crop yield prediction application. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.5787501.v1
title: Partially Linear Functional Additive Models for Multivariate Functional Data

description: We investigate a class of partially linear functional additive models (PLFAM) that predicts a scalar response by both parametric effects of a multivariate predictor and nonparametric effects of a multivariate functional predictor. We jointly model multiple functional predictors that are cross-correlated using multivariate functional principal component analysis (mFPCA), and model the nonparametric effects of the principal component scores as additive components in the PLFAM. To address the high-dimensional nature of functional data, we let the number of mFPCA components diverge to infinity with the sample size, and adopt the component selection and smoothing operator (COSSO) penalty to select relevant components and regularize the fitting. A fundamental difference between our framework and the existing high-dimensional additive models is that the mFPCA scores are estimated with error, and the magnitude of measurement error increases with the order of mFPCA. We establish the asymptotic convergence rate for our estimator, while allowing the number of components diverge. When the number of additive components is fixed, we also establish the asymptotic distribution for the partially linear coefficients. The practical performance of the proposed methods is illustrated via simulation studies and a crop yield prediction application. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.5787495
title: Modeling Random Effects Using Global–Local Shrinkage Priors in Small Area Estimation

description: Small area estimation is becoming increasingly popular for survey statisticians. One very important program is Small Area Income and Poverty Estimation undertaken by the United States Bureau of the Census, which aims at providing estimates related to income and poverty based on American Community Survey data at the state level and even at lower levels of geography. This article introduces global–local (GL) shrinkage priors for random effects in small area estimation to capture wide area level variation when the number of small areas is very large. These priors employ two levels of parameters, global and local parameters, to express variances of area-specific random effects so that both small and large random effects can be captured properly. We show via simulations and data analysis that use of the GL priors can improve estimation results in most cases. 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.5787495.v2
title: Modeling Random Effects Using Global–Local Shrinkage Priors in Small Area Estimation

description: Small area estimation is becoming increasingly popular for survey statisticians. One very important program is Small Area Income and Poverty Estimation undertaken by the United States Bureau of the Census, which aims at providing estimates related to income and poverty based on American Community Survey data at the state level and even at lower levels of geography. This article introduces global–local (GL) shrinkage priors for random effects in small area estimation to capture wide area level variation when the number of small areas is very large. These priors employ two levels of parameters, global and local parameters, to express variances of area-specific random effects so that both small and large random effects can be captured properly. We show via simulations and data analysis that use of the GL priors can improve estimation results in most cases. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.