cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.13275287.v4
title: An Explicit Mean-Covariance Parameterization for Multivariate Response Linear Regression

description: We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations between entries in the multivariate error random vector are proportional to the cosines of the angles between their corresponding regression coefficient matrix columns, so as the angle between two regression coefficient matrix columns decreases, the correlation between the corresponding errors increases. We highlight two models under which this parameterization arises: a latent variable reduced-rank regression model and the errors-in-variables regression model. We propose a novel nonconvex weighted residual sum of squares criterion which exploits this parameterization and admits a new class of penalized estimators. The optimization is solved with an accelerated proximal gradient descent algorithm. Our method is used to study the association between microRNA expression and cancer drug activity measured on the NCI-60 cell lines. An R package implementing our method, MCMVR, is available online.
DOI: 10.6084/m9.figshare.13519116
title: Alternating Pruned Dynamic Programming for Multiple Epidemic Change-Point Estimation

description: In this article, we study the problem of multiple change-point detection for a univariate sequence under the epidemic setting, where the behavior of the sequence alternates between a common normal state and different epidemic states. This is a nontrivial generalization of the classical (single) epidemic change-point testing problem. To explicitly incorporate the alternating structure of the problem, we propose a novel model selection based approach for simultaneous inference on both change-points and alternating states. Using the same spirit as profile likelihood, we develop a two-stage alternating pruned dynamic programming algorithm, which conducts efficient and exact optimization of the model selection criteria and has O(n2) as the worst case computational cost. As demonstrated by extensive numerical experiments, compared to classical general-purpose multiple change-point detection procedures, the proposed method improves accuracy for both change-point estimation and model parameter estimation. We further show promising applications of the proposed algorithm to multiple testing with locally clustered signals, and demonstrate its advantages over existing methods in large scale multiple testing, in DNA copy number variation detection, and in oceanographic study. Supplementary material for this article is available online.
DOI: 10.6084/m9.figshare.13519116.v3
title: Alternating Pruned Dynamic Programming for Multiple Epidemic Change-Point Estimation

description: In this article, we study the problem of multiple change-point detection for a univariate sequence under the epidemic setting, where the behavior of the sequence alternates between a common normal state and different epidemic states. This is a nontrivial generalization of the classical (single) epidemic change-point testing problem. To explicitly incorporate the alternating structure of the problem, we propose a novel model selection based approach for simultaneous inference on both change-points and alternating states. Using the same spirit as profile likelihood, we develop a two-stage alternating pruned dynamic programming algorithm, which conducts efficient and exact optimization of the model selection criteria and has O(n2) as the worst case computational cost. As demonstrated by extensive numerical experiments, compared to classical general-purpose multiple change-point detection procedures, the proposed method improves accuracy for both change-point estimation and model parameter estimation. We further show promising applications of the proposed algorithm to multiple testing with locally clustered signals, and demonstrate its advantages over existing methods in large scale multiple testing, in DNA copy number variation detection, and in oceanographic study. Supplementary material for this article is available online.
DOI: 10.6084/m9.figshare.13275287
title: An Explicit Mean-Covariance Parameterization for Multivariate Response Linear Regression

description: We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations between entries in the multivariate error random vector are proportional to the cosines of the angles between their corresponding regression coefficient matrix columns, so as the angle between two regression coefficient matrix columns decreases, the correlation between the corresponding errors increases. We highlight two models under which this parameterization arises: a latent variable reduced-rank regression model and the errors-in-variables regression model. We propose a novel nonconvex weighted residual sum of squares criterion which exploits this parameterization and admits a new class of penalized estimators. The optimization is solved with an accelerated proximal gradient descent algorithm. Our method is used to study the association between microRNA expression and cancer drug activity measured on the NCI-60 cell lines. An R package implementing our method, MCMVR, is available online.
DOI: 10.6084/m9.figshare.13333849.v3
title: Tensor Canonical Correlation Analysis With Convergence and Statistical Guarantees

description: In many applications, such as classification of images or videos, it is of interest to develop a framework for tensor data instead of an ad-hoc way of transforming data to vectors due to the computational and under-sampling issues. In this article, we study convergence and statistical properties of two-dimensional canonical correlation analysis under an assumption that data come from a probabilistic model. We show that carefully initialized the power method converges to the optimum and provide a finite sample bound. Then we extend this framework to tensor-valued data and propose the higher-order power method, which is commonly used in tensor decomposition, to extract the canonical directions. Our method can be used effectively in a large-scale data setting by solving the inner least squares problem with a stochastic gradient descent, and we justify convergence via the theory of Lojasiewicz’s inequalities without any assumption on data generating process and initialization. For practical applications, we further develop (a) an inexact updating scheme which allows us to use the state-of-the-art stochastic gradient descent algorithm, (b) an effective initialization scheme which alleviates the problem of local optimum in nonconvex optimization, and (c) a deflation procedure for extracting several canonical components. Empirical analyses on challenging data including gene expression and air pollution indexes in Taiwan, show the effectiveness and efficiency of the proposed methodology. Our results fill a missing, but crucial, part in the literature on tensor data. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.13519116.v2
title: Alternating Pruned Dynamic Programming for Multiple Epidemic Change-Point Estimation

description: In this article, we study the problem of multiple change-point detection for a univariate sequence under the epidemic setting, where the behavior of the sequence alternates between a common normal state and different epidemic states. This is a nontrivial generalization of the classical (single) epidemic change-point testing problem. To explicitly incorporate the alternating structure of the problem, we propose a novel model selection based approach for simultaneous inference on both change-points and alternating states. Using the same spirit as profile likelihood, we develop a two-stage alternating pruned dynamic programming algorithm, which conducts efficient and exact optimization of the model selection criteria and has O(n2) as the worst case computational cost. As demonstrated by extensive numerical experiments, compared to classical general-purpose multiple change-point detection procedures, the proposed method improves accuracy for both change-point estimation and model parameter estimation. We further show promising applications of the proposed algorithm to multiple testing with locally clustered signals, and demonstrate its advantages over existing methods in large scale multiple testing, in DNA copy number variation detection, and in oceanographic study. Supplementary material for this article is available online.
DOI: 10.6084/m9.figshare.13577937
title: Model Selection With Lasso-Zero: Adding Straw to the Haystack to Better Find Needles

description: The high-dimensional linear model y=Xβ0+ϵ is considered and the focus is put on the problem of recovering the support <i>S</i><sup>0</sup> of the sparse vector β0. We introduce a new l1-based estimator, called <i>Lasso-Zero</i>, whose novelty resides in the repeated use of noise dictionaries concatenated to <i>X</i> for overfitting the response. Lasso-Zero is an extension of thresholded basis pursuit (TBP), for which we prove sign consistency for correlated Gaussian designs. Both theoretical and empirical results motivate the use of noise dictionaries to improve TBP when the coefficients’ amplitude is low. To select the threshold of Lasso-Zero, we suggest to employ a pivotal version of the quantile universal threshold (QUT) that exploits a byproduct of Lasso-Zero to avoid the need to estimate the noise level. Numerical simulations show that Lasso-Zero tuned by QUT performs well in terms of support recovery and provides an excellent trade-off between high power and few false discoveries compared to competitors. Supplemental materials for this article are available online.
DOI: 10.6084/m9.figshare.13577937.v4
title: Model Selection With Lasso-Zero: Adding Straw to the Haystack to Better Find Needles

description: The high-dimensional linear model y=Xβ0+ϵ is considered and the focus is put on the problem of recovering the support <i>S</i><sup>0</sup> of the sparse vector β0. We introduce a new l1-based estimator, called <i>Lasso-Zero</i>, whose novelty resides in the repeated use of noise dictionaries concatenated to <i>X</i> for overfitting the response. Lasso-Zero is an extension of thresholded basis pursuit (TBP), for which we prove sign consistency for correlated Gaussian designs. Both theoretical and empirical results motivate the use of noise dictionaries to improve TBP when the coefficients’ amplitude is low. To select the threshold of Lasso-Zero, we suggest to employ a pivotal version of the quantile universal threshold (QUT) that exploits a byproduct of Lasso-Zero to avoid the need to estimate the noise level. Numerical simulations show that Lasso-Zero tuned by QUT performs well in terms of support recovery and provides an excellent trade-off between high power and few false discoveries compared to competitors. Supplemental materials for this article are available online.
DOI: 10.6084/m9.figshare.13180181
title: Nonparametric Anomaly Detection on Time Series of Graphs

description: Identifying change points and/or anomalies in dynamic network structures has become increasingly popular across various domains, from neuroscience to telecommunication to finance. One particular objective of anomaly detection from a neuroscience perspective is the reconstruction of the dynamic manner of brain region interactions. However, most statistical methods for detecting anomalies have the following unrealistic limitation for brain studies and beyond: that is, network snapshots at different time points are assumed to be independent. To circumvent this limitation, we propose a distribution-free framework for anomaly detection in dynamic networks. First, we present each network snapshot of the data as a linear object and find its respective univariate characterization via local and global network topological summaries. Second, we adopt a change point detection method for (weakly) dependent time series based on efficient scores, and enhance the finite sample properties of change point method by approximating the asymptotic distribution of the test statistic using the sieve bootstrap. We apply our method to simulated and to real data, particularly, two functional magnetic resonance imaging (fMRI) datasets and the Enron communication graph. We find that our new method delivers impressively accurate and realistic results in terms of identifying locations of true change points compared to the results reported by competing approaches. The new method promises to offer a deeper insight into the large-scale characterizations and functional dynamics of the brain and, more generally, into the intrinsic structure of complex dynamic networks. Supplemental materials for this article are available online.
DOI: 10.6084/m9.figshare.13266362.v2
title: Kriging Riemannian Data via Random Domain Decompositions

description: Data taking value on a Riemannian manifold and observed over a complex spatial domain are becoming more frequent in applications, e.g. in environmental sciences and in geoscience. The analysis of these data needs to rely on local models to account for the non stationarity of the generating random process, the nonlinearity of the manifold and the complex topology of the domain. In this paper, we propose to use a random domain decomposition approach to estimate an ensemble of local models and then to aggregate the predictions of the local models through Fréchet averaging. The algorithm is introduced in complete generality and is valid for data belonging to any smooth Riemannian manifold but it is then described in details for the case of the manifold of positive definite matrices, the hypersphere and the Cholesky manifold. The predictive performances of the method are explored via simulation studies for covariance matrices and correlation matrices, where the Cholesky manifold geometry is used. Finally, the method is illustrated on an environmental dataset observed over the Chesapeake Bay (USA).
DOI: 10.6084/m9.figshare.13275287.v3
title: An Explicit Mean-Covariance Parameterization for Multivariate Response Linear Regression

description: We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations between entries in the multivariate error random vector are proportional to the cosines of the angles between their corresponding regression coefficient matrix columns, so as the angle between two regression coefficient matrix columns decreases, the correlation between the corresponding errors increases. We highlight two models under which this parameterization arises: a latent variable reduced-rank regression model and the errors-in-variables regression model. We propose a novel nonconvex weighted residual sum of squares criterion which exploits this parameterization and admits a new class of penalized estimators. The optimization is solved with an accelerated proximal gradient descent algorithm. Our method is used to study the association between microRNA expression and cancer drug activity measured on the NCI-60 cell lines. An R package implementing our method, MCMVR, is available online.
DOI: 10.6084/m9.figshare.13180181.v3
title: Nonparametric Anomaly Detection on Time Series of Graphs

description: Identifying change points and/or anomalies in dynamic network structures has become increasingly popular across various domains, from neuroscience to telecommunication to finance. One particular objective of anomaly detection from a neuroscience perspective is the reconstruction of the dynamic manner of brain region interactions. However, most statistical methods for detecting anomalies have the following unrealistic limitation for brain studies and beyond: that is, network snapshots at different time points are assumed to be independent. To circumvent this limitation, we propose a distribution-free framework for anomaly detection in dynamic networks. First, we present each network snapshot of the data as a linear object and find its respective univariate characterization via local and global network topological summaries. Second, we adopt a change point detection method for (weakly) dependent time series based on efficient scores, and enhance the finite sample properties of change point method by approximating the asymptotic distribution of the test statistic using the sieve bootstrap. We apply our method to simulated and to real data, particularly, two functional magnetic resonance imaging (fMRI) datasets and the Enron communication graph. We find that our new method delivers impressively accurate and realistic results in terms of identifying locations of true change points compared to the results reported by competing approaches. The new method promises to offer a deeper insight into the large-scale characterizations and functional dynamics of the brain and, more generally, into the intrinsic structure of complex dynamic networks. Supplemental materials for this article are available online.
DOI: 10.6084/m9.figshare.13577937.v3
title: Model Selection With Lasso-Zero: Adding Straw to the Haystack to Better Find Needles

description: The high-dimensional linear model y=Xβ0+ϵ is considered and the focus is put on the problem of recovering the support <i>S</i><sup>0</sup> of the sparse vector β0. We introduce a new l1-based estimator, called <i>Lasso-Zero</i>, whose novelty resides in the repeated use of noise dictionaries concatenated to <i>X</i> for overfitting the response. Lasso-Zero is an extension of thresholded basis pursuit (TBP), for which we prove sign consistency for correlated Gaussian designs. Both theoretical and empirical results motivate the use of noise dictionaries to improve TBP when the coefficients’ amplitude is low. To select the threshold of Lasso-Zero, we suggest to employ a pivotal version of the quantile universal threshold (QUT) that exploits a byproduct of Lasso-Zero to avoid the need to estimate the noise level. Numerical simulations show that Lasso-Zero tuned by QUT performs well in terms of support recovery and provides an excellent trade-off between high power and few false discoveries compared to competitors. Supplemental materials for this article are available online.
DOI: 10.6084/m9.figshare.13180181.v2
title: Nonparametric Anomaly Detection on Time Series of Graphs

description: Identifying change points and/or anomalies in dynamic network structures has become increasingly popular across various domains, from neuroscience to telecommunication to finance. One particular objective of anomaly detection from a neuroscience perspective is the reconstruction of the dynamic manner of brain region interactions. However, most statistical methods for detecting anomalies have the following unrealistic limitation for brain studies and beyond: that is, network snapshots at different time points are assumed to be independent. To circumvent this limitation, we propose a distribution-free framework for anomaly detection in dynamic networks. First, we present each network snapshot of the data as a linear object and find its respective univariate characterization via local and global network topological summaries. Second, we adopt a change point detection method for (weakly) dependent time series based on efficient scores, and enhance the finite sample properties of change point method by approximating the asymptotic distribution of the test statistic using the sieve bootstrap. We apply our method to simulated and to real data, particularly, two functional magnetic resonance imaging (fMRI) datasets and the Enron communication graph. We find that our new method delivers impressively accurate and realistic results in terms of identifying locations of true change points compared to the results reported by competing approaches. The new method promises to offer a deeper insight into the large-scale characterizations and functional dynamics of the brain and, more generally, into the intrinsic structure of complex dynamic networks. Supplemental materials for this article are available online.
DOI: 10.6084/m9.figshare.13275269.v1
title: Additive Functional Cox Model

description: We propose the Additive Functional Cox Model to flexibly quantify the association between functional covariates and time to event data. The model extends the linear functional proportional hazards model by allowing the association between the functional covariate and log hazard to vary non-linearly in both the functional domain and the value of the functional covariate. Additionally, we introduce critical transformations of the functional covariate which address the weak model identifiability in areas of information sparsity and discuss their impact on interpretation and inference. We also introduce a novel estimation procedure that accounts for identifiability constraints directly during model fitting. Methods are applied to the National Health and Nutrition Examination Survey (NHANES) 2003-2006 accelerometry data and quantify new and interpretable circadian patterns of physical activity that are associated with all-cause mortality. We also introduce a simple and novel simulation framework for generating survival data with functional predictors which resemble the observed data. The accompanying inferential R software is fast, open source and publicly available. Our data application and simulations are fully reproducible through the accompanying vignette.
DOI: 10.6084/m9.figshare.13143714
title: Particle MCMC With Poisson Resampling: Parallelization and Continuous Time Models

description: We introduce a new version of particle filter in which the number of “children” of a particle at a given time has a Poisson distribution. As a result, the number of particles is random and varies with time. An advantage of this scheme is that descendants of different particles can evolve independently. It makes easy to parallelize computations. Moreover, particle filter with Poisson resampling is readily adapted to the case when a hidden process is a continuous time, piecewise deterministic semi-Markov process. We show that the basic techniques of particle MCMC, namely particle independent Metropolis-Hastings, particle Gibbs sampler and its version with ancestor sampling, work under our Poisson resampling scheme. Our version of particle Gibbs sampler is uniformly ergodic under the same assumptions as its standard counterpart. We present simulation results which indicate that our algorithms can compete with the existing methods. Supplemental materials for this article are available online.
DOI: 10.6084/m9.figshare.13180187.v4
title: Modeling Nonstationary Extreme Dependence With Stationary Max-Stable Processes and Multidimensional Scaling

description: Modeling the joint distribution of extreme events at multiple locations is a challenging task with important applications. In this study, we use max-stable models to study extreme daily precipitation events in Switzerland. The nonstationarity of the spatial process at hand involves important challenges, which are often dealt with by using a stationary model in a so-called climate space, with well-chosen covariates. Here, we instead choose to warp the weather stations under study in a latent space of higher dimension using multidimensional scaling (MDS). Two methods are proposed to define target dissimilarity matrices, based respectively on extremal coefficients and on pairwise likelihoods. Results suggest that the proposed methods allow capturing complex spatial dependences of spatial extreme precipitations, enabling in turn to reliably extrapolate functionals such as extremal coefficients. Supplemental materials for this article are available online.