cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.27604536
title: Coefficient Shape Alignment in Multiple Functional Linear Regression

description: In multivariate functional data analysis, different functional covariates often exhibit homogeneity. The covariates with pronounced homogeneity can be analyzed jointly within the same group, offering a parsimonious approach to modeling multivariate functional data. In this article, a novel grouped multiple functional regression model with a new regularization approach termed “coefficient shape alignment” is developed to tackle functional covariates homogeneity. The modeling procedure includes two steps: first aggregate covariates into disjoint groups using the new regularization approach; then the grouped multiple functional regression model is established based on the detected grouping structure. In this grouped model, the coefficient functions of covariates in the same group share the same shape, invariant to scaling. The new regularization approach works by penalizing coefficient shape discrepancy. We establish the conditions under which the true grouping structure can be accurately identified and derive the asymptotic properties of the model estimates. Extensive simulation studies are conducted to assess the finite-sample performance of the proposed methods. The practical applicability of the model is demonstrated through real data analysis in the context of sugar quality evaluation. This work offers a novel framework for analyzing the homogeneity of functional covariates and constructing parsimonious models for multivariate functional data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
DOI: 10.6084/m9.figshare.27233654
title: Robust Permutation Tests in Linear Instrumental Variables Regression

description: This article develops permutation versions of identification-robust tests in linear instrumental variables regression. Unlike the existing randomization and rank-based tests in which independence between the instruments and the error terms is assumed, the permutation Anderson-Rubin (AR), Lagrange Multiplier (LM) and Conditional Likelihood Ratio (CLR) tests are asymptotically similar and robust to conditional heteroscedasticity under standard exclusion restriction, that is, the orthogonality between the instruments and the error terms. Moreover, when the instruments are independent of the structural error term, the permutation AR tests are exact, hence, robust to heavy tails. As such, these tests share the strengths of the rank-based tests and the wild bootstrap AR tests. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
DOI: 10.6084/m9.figshare.27233654.v1
title: Robust Permutation Tests in Linear Instrumental Variables Regression

description: This article develops permutation versions of identification-robust tests in linear instrumental variables regression. Unlike the existing randomization and rank-based tests in which independence between the instruments and the error terms is assumed, the permutation Anderson-Rubin (AR), Lagrange Multiplier (LM) and Conditional Likelihood Ratio (CLR) tests are asymptotically similar and robust to conditional heteroscedasticity under standard exclusion restriction, that is, the orthogonality between the instruments and the error terms. Moreover, when the instruments are independent of the structural error term, the permutation AR tests are exact, hence, robust to heavy tails. As such, these tests share the strengths of the rank-based tests and the wild bootstrap AR tests. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
DOI: 10.6084/m9.figshare.27604536.v1
title: Coefficient Shape Alignment in Multiple Functional Regression

description: In multivariate functional data analysis, different functional covariates often exhibit homogeneity. The covariates with pronounced homogeneity can be analyzed jointly within the same group, offering a parsimonious approach to modeling multivariate functional data. In this paper, a novel grouped multiple functional regression model with a new regularization approach termed <i>“coefficient shape alignment”</i> is developed to tackle functional covariates homogeneity. The modeling procedure includes two steps: first aggregate covariates into disjoint groups using the new regularization approach; then the grouped multiple functional regression model is established based on the detected grouping structure. In this grouped model, the coefficient functions of covariates in the same group share the same shape, invariant to scaling. The new regularization approach works by penalizing differences in the shape of the coefficients. We establish conditions under which the true grouping structure can be accurately identified and derive the asymptotic properties of the model estimates. Extensive simulation studies are conducted to assess the finite-sample performance of the proposed methods. The practical applicability of the model is demonstrated through real data analysis in the context of sugar quality evaluation. This work offers a novel framework for analyzing the homogeneity of functional covariates and constructing parsimonious models for multivariate functional data.
DOI: 10.6084/m9.figshare.27604536.v2
title: Coefficient Shape Alignment in Multiple Functional Linear Regression

description: In multivariate functional data analysis, different functional covariates often exhibit homogeneity. The covariates with pronounced homogeneity can be analyzed jointly within the same group, offering a parsimonious approach to modeling multivariate functional data. In this article, a novel grouped multiple functional regression model with a new regularization approach termed “coefficient shape alignment” is developed to tackle functional covariates homogeneity. The modeling procedure includes two steps: first aggregate covariates into disjoint groups using the new regularization approach; then the grouped multiple functional regression model is established based on the detected grouping structure. In this grouped model, the coefficient functions of covariates in the same group share the same shape, invariant to scaling. The new regularization approach works by penalizing coefficient shape discrepancy. We establish the conditions under which the true grouping structure can be accurately identified and derive the asymptotic properties of the model estimates. Extensive simulation studies are conducted to assess the finite-sample performance of the proposed methods. The practical applicability of the model is demonstrated through real data analysis in the context of sugar quality evaluation. This work offers a novel framework for analyzing the homogeneity of functional covariates and constructing parsimonious models for multivariate functional data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
DOI: 10.6084/m9.figshare.27195233
title: Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models

description: Latent Gaussian process (GP) models are flexible probabilistic nonparametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is a fast method with asymptotic convergence guarantees to approximate marginal likelihoods and posterior predictive distributions for non-Gaussian likelihoods. Unfortunately, the computational complexity of combined Vecchia-Laplace approximations grows faster than linearly in the sample size when used in combination with direct solver methods such as the Cholesky decomposition. Computations with Vecchia-Laplace approximations can thus become prohibitively slow precisely when the approximations are usually the most accurate, that is, on large datasets. In this article, we present iterative methods to overcome this drawback. Among other things, we introduce and analyze several preconditioners, derive new convergence results, and propose novel methods for accurately approximating predictive variances. We analyze our proposed methods theoretically and in experiments with simulated and real-world data. In particular, we obtain a speed-up of an order of magnitude compared to Cholesky-based calculations and a 3-fold increase in prediction accuracy in terms of the continuous ranked probability score compared to a state-of-the-art method on a large satellite dataset. All methods are implemented in a free C++ software library with high-level Python and R packages. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
DOI: 10.6084/m9.figshare.27195233.v1
title: Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models

description: Latent Gaussian process (GP) models are flexible probabilistic nonparametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is a fast method with asymptotic convergence guarantees to approximate marginal likelihoods and posterior predictive distributions for non-Gaussian likelihoods. Unfortunately, the computational complexity of combined Vecchia-Laplace approximations grows faster than linearly in the sample size when used in combination with direct solver methods such as the Cholesky decomposition. Computations with Vecchia-Laplace approximations can thus become prohibitively slow precisely when the approximations are usually the most accurate, that is, on large datasets. In this article, we present iterative methods to overcome this drawback. Among other things, we introduce and analyze several preconditioners, derive new convergence results, and propose novel methods for accurately approximating predictive variances. We analyze our proposed methods theoretically and in experiments with simulated and real-world data. In particular, we obtain a speed-up of an order of magnitude compared to Cholesky-based calculations and a 3-fold increase in prediction accuracy in terms of the continuous ranked probability score compared to a state-of-the-art method on a large satellite dataset. All methods are implemented in a free C++ software library with high-level Python and R packages. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
DOI: 10.6084/m9.figshare.27236781
title: Deep Regression Learning with Optimal Loss Function

description: In this article, we develop a novel efficient and robust nonparametric regression estimator under a framework of a feedforward neural network (FNN). There are several interesting characteristics for the proposed estimator. First, the loss function is built upon an estimated maximum likelihood function, which integrates the information from observed data as well as the information from the data distribution. Consequently, the resulting estimator has desirable optimal properties, such as efficiency. Second, different from the traditional maximum likelihood estimation (MLE), the proposed method avoids the specification of the distribution, making it adaptable to various distributions such as heavy tails and multimodal or heterogeneous distributions. Third, the proposed loss function relies on probabilities rather than direct observations as in least square loss, contributing to the robustness of the proposed estimator. Finally, the proposed loss function involves a nonparametric regression function only. This enables the direct application of the existing packages, simplifying the computational and programming requirements. We establish the large sample property of the proposed estimator in terms of its excess risk and minimax near-optimal rate. The theoretical results demonstrate that the proposed estimator is equivalent to the true MLE where the density function is known in terms of excess risk. Our simulation studies show that the proposed estimator outperforms the existing methods based on prediction accuracy, efficiency and robustness. Particularly, it is comparable to the MLE with the known density and even gets slightly better as the sample size increases. This implies that the adaptive and data-driven loss function from the estimated density may offer an additional avenue for capturing valuable information. We further apply the proposed method to four real data examples, resulting in significantly reduced out-of-sample prediction errors compared to existing methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
DOI: 10.6084/m9.figshare.27236781.v2
title: Deep Regression Learning with Optimal Loss Function

description: In this article, we develop a novel efficient and robust nonparametric regression estimator under a framework of a feedforward neural network (FNN). There are several interesting characteristics for the proposed estimator. First, the loss function is built upon an estimated maximum likelihood function, which integrates the information from observed data as well as the information from the data distribution. Consequently, the resulting estimator has desirable optimal properties, such as efficiency. Second, different from the traditional maximum likelihood estimation (MLE), the proposed method avoids the specification of the distribution, making it adaptable to various distributions such as heavy tails and multimodal or heterogeneous distributions. Third, the proposed loss function relies on probabilities rather than direct observations as in least square loss, contributing to the robustness of the proposed estimator. Finally, the proposed loss function involves a nonparametric regression function only. This enables the direct application of the existing packages, simplifying the computational and programming requirements. We establish the large sample property of the proposed estimator in terms of its excess risk and minimax near-optimal rate. The theoretical results demonstrate that the proposed estimator is equivalent to the true MLE where the density function is known in terms of excess risk. Our simulation studies show that the proposed estimator outperforms the existing methods based on prediction accuracy, efficiency and robustness. Particularly, it is comparable to the MLE with the known density and even gets slightly better as the sample size increases. This implies that the adaptive and data-driven loss function from the estimated density may offer an additional avenue for capturing valuable information. We further apply the proposed method to four real data examples, resulting in significantly reduced out-of-sample prediction errors compared to existing methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
DOI: 10.6084/m9.figshare.27307761
title: Statistical and Computational Efficiency for Smooth Tensor Estimation with Unknown Permutations

description: We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation systems, neuroimaging, community detection, and multiway comparison applications. Here, we develop a general family of smooth tensor models up to arbitrary index permutations; the model incorporates the popular tensor block models and Lipschitz hypergraphon models as special cases. We show that a constrained least-squares estimator in the block-wise polynomial family achieves the minimax error bound. A phase transition phenomenon is revealed with respect to the smoothness threshold needed for optimal recovery. In particular, we find that a polynomial of degree up to (m−2)(m+1)/2 is sufficient for accurate recovery of order-<i>m</i> tensors, whereas higher degrees exhibit no further benefits. This phenomenon reveals the intrinsic distinction for smooth tensor estimation problems with and without unknown permutations. Furthermore, we provide an efficient polynomial-time Borda count algorithm that provably achieves the optimal rate under monotonicity assumptions. The efficacy of our procedure is demonstrated through both simulations and Chicago crime data analysis. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
DOI: 10.6084/m9.figshare.27236781.v1
title: Deep regression learning with optimal loss function

description: In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of a feedforward neural network (FNN). There are several interesting characteristics for the proposed estimator. First, the loss function is built upon an estimated maximum likelihood function, which integrates the information from observed data as well as the information from the data distribution. Consequently, the resulting estimator has desirable optimal properties, such as efficiency. Second, different from the traditional maximum likelihood estimation (MLE), the proposed method avoids the specification of the distribution, making it adaptable to various distributions such as heavy tails and multimodal or heterogeneous distributions. Third, the proposed loss function relies on probabilities rather than direct observations as in least square loss, contributing to the robustness of the proposed estimator. Finally, the proposed loss function involves a nonparametric regression function only. This enables the direct application of the existing packages, simplifying the computational and programming requirements. We establish the large sample property of the proposed estimator in terms of its excess risk and minimax near-optimal rate. The theoretical results demonstrate that the proposed estimator is equivalent to the true MLE where the density function is known in terms of excess risk. Our simulation studies show that the proposed estimator outperforms the existing methods based on prediction accuracy, efficiency and robustness. Particularly, it is comparable to the MLE with the known density and even gets slightly better as the sample size increases. This implies that the adaptive and data-driven loss function from the estimated density may offer an additional avenue for capturing valuable information. We further apply the proposed method to four real data examples, resulting in significantly reduced out-of-sample prediction errors compared to existing methods.
DOI: 10.6084/m9.figshare.27307761.v2
title: Statistical and Computational Efficiency for Smooth Tensor Estimation with Unknown Permutations

description: We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation systems, neuroimaging, community detection, and multiway comparison applications. Here, we develop a general family of smooth tensor models up to arbitrary index permutations; the model incorporates the popular tensor block models and Lipschitz hypergraphon models as special cases. We show that a constrained least-squares estimator in the block-wise polynomial family achieves the minimax error bound. A phase transition phenomenon is revealed with respect to the smoothness threshold needed for optimal recovery. In particular, we find that a polynomial of degree up to (m−2)(m+1)/2 is sufficient for accurate recovery of order-<i>m</i> tensors, whereas higher degrees exhibit no further benefits. This phenomenon reveals the intrinsic distinction for smooth tensor estimation problems with and without unknown permutations. Furthermore, we provide an efficient polynomial-time Borda count algorithm that provably achieves the optimal rate under monotonicity assumptions. The efficacy of our procedure is demonstrated through both simulations and Chicago crime data analysis. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
DOI: 10.6084/m9.figshare.27307761.v1
title: Statistical and computational efficiency for smooth tensor estimation with unknown permutations

description: We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation systems, neuroimaging, community detection, and multiway comparison applications. Here, we develop a general family of smooth tensor models up to arbitrary index permutations; the model incorporates the popular tensor block models and Lipschitz hypergraphon models as special cases. We show that a constrained least-squares estimator in the block-wise polynomial family achieves the minimax error bound. A phase transition phenomenon is revealed with respect to the smoothness threshold needed for optimal recovery. In particular, we find that a polynomial of degree up to (m−2)(m+1)/2 is sufficient for accurate recovery of order-m tensors, whereas higher degrees exhibit no further benefits. This phenomenon reveals the intrinsic distinction for smooth tensor estimation problems with and without unknown permutations. Furthermore, we provide an efficient polynomial-time Borda count algorithm that provably achieves the optimal rate under monotonicity assumptions. The efficacy of our procedure is demonstrated through both simulations and Chicago crime data analysis.
DOI: 10.15468/dl.76y83x
title: Occurrence Download

description: A dataset containing 5 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Aedes albopictus (Skuse, 1894)",
 "Country is Costa Rica",
 "Year is greater than or equal to 1500"
 ]
}

 The dataset includes 5 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0015536-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.6xnd37
title: Occurrence Download

description: A dataset containing 138 species occurrences available in GBIF matching the query:
{
 "and" : [
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "TaxonKey is Bothrocophias hyoprora (Amaral, 1935)"
 ]
}

 The dataset includes 138 records from 24 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0015537-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.jxqua9
title: Occurrence Download

description: A dataset containing 3198 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Symphodus mediterraneus (Linnaeus, 1758)",
 "HasCoordinate is true",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 3198 records from 43 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0015538-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.qgutzs
title: Occurrence Download

description: A dataset containing 6767 species occurrences available in GBIF matching the query:
{
 "and" : [
 "BasisOfRecord is Human Observation",
 "CoordinateUncertaintyInMeters 0.0-10000.0",
 "Country is United States of America",
 "TaxonKey is Centaurea stoebe L."
 ]
}

 The dataset includes 6767 records from 3 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0015540-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.