المؤلفون: Ye, Yuting, Ho, Christine, Jiang, Ci-Ren, Lee, Wayne Tai, Huang, Haiyan

مصطلحات موضوعية: Computer Science - Machine Learning, Statistics - Machine Learning

الوصف: Hierarchical multi-label classification (HMC) has drawn increasing attention in the past few decades. It is applicable when hierarchical relationships among classes are available and need to be incorporated along with the multi-label classification whereby each object is assigned to one or more classes. There are two key challenges in HMC: i) optimizing the classification accuracy, and meanwhile ii) ensuring the given class hierarchy. To address these challenges, in this article, we introduce a new statistic called the multidimensional local precision rate (mLPR) for each object in each class. We show that classification decisions made by simply sorting objects across classes in descending order of their true mLPRs can, in theory, ensure the class hierarchy and lead to the maximization of CATCH, an objective function we introduce that is related to the area under a hit curve. This approach is the first of its kind that handles both challenges in one objective function without additional constraints, thanks to the desirable statistical properties of CATCH and mLPR. In practice, however, true mLPRs are not available. In response, we introduce HierRank, a new algorithm that maximizes an empirical version of CATCH using estimated mLPRs while respecting the hierarchy. The performance of this approach was evaluated on a synthetic data set and two real data sets; ours was found to be superior to several comparison methods on evaluation criteria based on metrics such as precision, recall, and $F_1$ score.
Comment: 34 pages, 11 figures, 9 tables

الوصول الحر: http://arxiv.org/abs/2205.07833Test

المؤلفون: Jiang, Ci-Ren, Lila, Eardi, Aston, John AD, Wang, Jane-Ling

مصطلحات موضوعية: Statistics - Methodology

الوصف: Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in both the mean function and the covariance function. However, methods of the first kind are not suitable for data that display second-order variation, while those of the second kind are time-consuming and make it difficult to perform subsequent statistical analyses on the dimension-reduced representations. To tackle these issues, we introduce an eigen-adjusted FPCA model that integrates covariates in the covariance function only through its eigenvalues. In particular, different structures on the covariate-specific eigenvalues -- corresponding to different practical problems -- are discussed to illustrate the model's flexibility as well as utility. To handle functional observations under different sampling schemes, we employ local linear smoothers to estimate the mean function and the pooled covariance function, and a weighted least square approach to estimate the covariate-specific eigenvalues. The convergence rates of the proposed estimators are further investigated under the different sampling schemes. In addition to simulation studies, the proposed model is applied to functional Magnetic Resonance Imaging scans, collected within the Human Connectome Project, for functional connectivity investigation.
Comment: 31 pages, 4 figures

الوصول الحر: http://arxiv.org/abs/2204.05622Test

المؤلفون: Ho, Christine, Ye, Yuting, Jiang, Ci-Ren, Lee, Wayne Tai, Huang, Haiyan

مصطلحات موضوعية: Statistics - Machine Learning, Computer Science - Machine Learning

الوصف: In this article we propose a novel ranking algorithm, referred to as HierLPR, for the multi-label classification problem when the candidate labels follow a known hierarchical structure. HierLPR is motivated by a new metric called eAUC that we design to assess the ranking of classification decisions. This metric, associated with the hit curve and local precision rate, emphasizes the accuracy of the first calls. We show that HierLPR optimizes eAUC under the tree constraint and some light assumptions on the dependency between the nodes in the hierarchy. We also provide a strategy to make calls for each node based on the ordering produced by HierLPR, with the intent of controlling FDR or maximizing F-score. The performance of our proposed methods is demonstrated on synthetic datasets as well as a real example of disease diagnosis using NCBI GEO datasets. In these cases, HierLPR shows a favorable result over competing methods in the early part of the precision-recall curve.
Comment: 27 pages, 9 figures

الوصول الحر: http://arxiv.org/abs/1810.07954Test

المؤلفون: Chen, Lu-Hung, Jiang, Ci-Ren

مصطلحات موضوعية: Statistics - Methodology

الوصف: The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient approach to identify the optimal LDA projections in addition to managing the noninvertibility issue of the covariance operator emerging from this extension. A conditional expectation technique is employed to tackle the challenge of projecting sparse data to the LDA directions. We study the asymptotic properties of the proposed estimators and show that asymptotically perfect classification can be achieved in certain circumstances. The performance of this new approach is further demonstrated with numerical examples.

الوصول الحر: http://arxiv.org/abs/1606.03844Test

المؤلفون: Chen, Lu-Hung, Jiang, Ci-Ren

مصطلحات موضوعية: Statistics - Methodology

الوصف: Functional principal component analysis is one of the most commonly employed approaches in functional and longitudinal data analysis and we extend it to analyze functional/longitudinal data observed on a general $d$-dimensional domain. The computational issues emerging in the extension are fully addressed with our proposed solutions. The local linear smoothing technique is employed to perform estimation because of its capabilities of performing large-scale smoothing and of handling data with different sampling schemes (possibly on irregular domain) in addition to its nice theoretical properties. Besides taking the fast Fourier transform strategy in smoothing, the modern GPGPU (general-purpose computing on graphics processing units) architecture is applied to perform parallel computation to save computation time. To resolve the out-of-memory issue due to large-scale data, the random projection procedure is applied in the eigendecomposition step. We show that the proposed estimators can achieve the classical nonparametric rates for longitudinal data and the optimal convergence rates for functional data if the number of observations per sample is of the order $(n/ \log n)^{d/4}$. Finally, the performance of our approach is demonstrated with simulation studies and the fine particulate matter (PM 2.5) data measured in Taiwan.

الوصول الحر: http://arxiv.org/abs/1510.04439Test

المؤلفون: Jiang, Ci-Ren, Aston, John A D, Wang, Jane-Ling

مصطلحات موضوعية: Statistics - Applications, Statistics - Methodology

الوصف: Positron Emission Tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. In order to provide an analysis of PET data which is free from this compartmental assumption, we propose a nonparametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis. This yields flexibility in the possible deconvolved functions while still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire 3-D volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient. The new methodology is investigated through simulations in both 1-D functions and 2-D images and also applied to a neuroimaging study whose goal is the quantification of opioid receptor concentration in the brain.
Comment: 33 pages, 10 figures

الوصول الحر: http://arxiv.org/abs/1411.2051Test

المؤلفون: Jiang, Ci-Ren, Aston, John AD, Wang, Jane-Ling

المصدر: Journal of the American Statistical Association. 111(513)

مصطلحات موضوعية: Economics, Statistics, Econometrics, Mathematical Sciences, Neurosciences, Biomedical Imaging, Networking and Information Technology R&D (NITRD), Bioengineering, Neurological, Compartmental modeling, Functional response model, Kinetic modeling, Neuroimaging, Neuroimaging., stat.AP, stat.ME, Demography, Statistics & Probability

الوصف: Positron emission tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first-order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. To provide an analysis of PET data which is free from this compartmental assumption, we propose a nonparametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis. This yields flexibility in the possible deconvolved functions while still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire three-dimensional volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient. The new methodology is investigated through simulations in both one-dimensional functions and 2D images and also applied to a neuroimaging study whose goal is the quantification of opioid receptor concentration in the brain.

وصف الملف: application/pdf

الوصول الحر: https://escholarship.org/uc/item/35k8h79sTest

المؤلفون: Jiang, Ci-Ren, Yu, Wei, Wang, Jane-Ling

المصدر: Annals of Statistics 2014, Vol. 42, No. 2, 563-591

مصطلحات موضوعية: Mathematics - Statistics Theory

الوصف: Sliced inverse regression (Duan and Li [Ann. Statist. 19 (1991) 505-530], Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]) is an appealing dimension reduction method for regression models with multivariate covariates. It has been extended by Ferr\'{e} and Yao [Statistics 37 (2003) 475-488, Statist. Sinica 15 (2005) 665-683] and Hsing and Ren [Ann. Statist. 37 (2009) 726-755] to functional covariates where the whole trajectories of random functional covariates are completely observed. The focus of this paper is to develop sliced inverse regression for intermittently and sparsely measured longitudinal covariates. We develop asymptotic theory for the new procedure and show, under some regularity conditions, that the estimated directions attain the optimal rate of convergence. Simulation studies and data analysis are also provided to demonstrate the performance of our method.
Comment: Published in at http://dx.doi.org/10.1214/13-AOS1193Test the Annals of Statistics (http://www.imstat.org/aosTest/) by the Institute of Mathematical Statistics (http://www.imstat.orgTest). With Corrections

الوصول الحر: http://arxiv.org/abs/1405.6017Test

المؤلفون: Jiang, Ci-Ren, Wang, Jane-Ling

المصدر: Annals of Statistics 2011, Vol. 39, No. 1, 362-388

مصطلحات موضوعية: Mathematics - Statistics Theory

الوصف: A new single-index model that reflects the time-dynamic effects of the single index is proposed for longitudinal and functional response data, possibly measured with errors, for both longitudinal and time-invariant covariates. With appropriate initial estimates of the parametric index, the proposed estimator is shown to be $\sqrt{n}$-consistent and asymptotically normally distributed. We also address the nonparametric estimation of regression functions and provide estimates with optimal convergence rates. One advantage of the new approach is that the same bandwidth is used to estimate both the nonparametric mean function and the parameter in the index. The finite-sample performance for the proposed procedure is studied numerically.
Comment: Published in at http://dx.doi.org/10.1214/10-AOS845Test the Annals of Statistics (http://www.imstat.org/aosTest/) by the Institute of Mathematical Statistics (http://www.imstat.orgTest)

الوصول الحر: http://arxiv.org/abs/1103.1726Test

المؤلفون: Jiang, Ci-Ren, Wang, Jane-Ling

المصدر: Annals of Statistics 2010, Vol. 38, No. 2, 1194-1226

مصطلحات موضوعية: Mathematics - Statistics Theory, 62H25, 62M15 (Primary) 62G20 (Secondary)

الوصف: Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal of this paper to develop two methods that do. In the first approach, both the mean and covariance functions depend on the covariate $Z$ and time scale $t$ while in the second approach only the mean function depends on the covariate $Z$. Both new approaches accommodate additional measurement errors and functional data sampled at regular time grids as well as sparse longitudinal data sampled at irregular time grids. The first approach to fully adjust both the mean and covariance functions adapts more to the data but is computationally more intensive than the approach to adjust the covariate effects on the mean function only. We develop general asymptotic theory for both approaches and compare their performance numerically through simulation studies and a data set.
Comment: Published in at http://dx.doi.org/10.1214/09-AOS742Test the Annals of Statistics (http://www.imstat.org/aosTest/) by the Institute of Mathematical Statistics (http://www.imstat.orgTest)

الوصول الحر: http://arxiv.org/abs/1003.0261Test