Linglong Kong

QUANTILE TOMOGRAPHY: USING QUANTILES WITH MULTIVARIATE DATA

The use of quantiles to obtain insights about multivariate data is ad- dressed. It is argued that incisive insights can be obtained by considering direc- tional quantiles, the quantiles of projections. Directional quantile envelopes are proposed as a way to condense this kind of information; it is demonstrated that they are essentially halfspace (Tukey) depth levels sets, coinciding for elliptic distri- butions (in particular multivariate normal) with density contours. Relevant ques- tions concerning their indexing, the possibility of the reverse retrieval of directional quantile information, invariance with respect to affine transformations, and approx- imation/asymptotic properties are studied. It is argued that analysis in terms of directional quantiles and their envelopes offers a straightforward probabilistic inter- pretation and thus conveys a concrete quantitative meaning; the directional defini- tion can be adapted to elaborate frameworks, like estimation of extreme quantiles and directional quantile regression, the regression of depth contours on covariates. The latter facilitates the construction of multivariate growth charts—the question that motivated this development.

FADTTS: Functional Analysis of Diffusion Tensor Tract Statistics

The aim of this paper is to present a functional analysis of a diffusion tensor tract statistics (FADTTS) pipeline for delineating the association between multiple diffusion properties along major white matter fiber bundles with a set of covariates of interest, such as age, diagnostic status and gender, and the structure of the variability of these white matter tract properties in various diffusion tensor imaging studies. The FADTTS integrates five statistical tools: (i) a multivariate varying coefficient model for allowing the varying coefficient functions in terms of arc length to characterize the varying associations between fiber bundle diffusion properties and a set of covariates, (ii) a weighted least squares estimation of the varying coefficient functions, (iii) a functional principal component analysis to delineate the structure of the variability in fiber bundle diffusion properties, (iv) a global test statistic to test hypotheses of interest, and (v) a simultaneous confidence band to quantify the uncertainty in the estimated coefficient functions. Simulated data are used to evaluate the finite sample performance of FADTTS. We apply FADTTS to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment. FADTTS can be used to facilitate the understanding of normal brain development, the neural bases of neuropsychiatric disorders, and the joint effects of environmental and genetic factors on white matter fiber bundles. The advantages of FADTTS compared with the other existing approaches are that they are capable of modeling the structured inter-subject variability, testing the joint effects, and constructing their simultaneous confidence bands. However, FADTTS is not crucial for estimation and reduces to the functional analysis method for the single measure.

Spatially Varying Coefficient Model for Neuroimaging Data With Jump Discontinuities

Motivated by recent work on studying massive imaging data in various neuroimaging studies, we propose a novel spatially varying coefficient model (SVCM) to capture the varying association between imaging measures in a three-dimensional volume (or two-dimensional surface) with a set of covariates. Two stylized features of neuorimaging data are the presence of multiple piecewise smooth regions with unknown edges and jumps and substantial spatial correlations. To specifically account for these two features, SVCM includes a measurement model with multiple varying coefficient functions, a jumping surface model for each varying coefficient function, and a functional principal component model. We develop a three-stage estimation procedure to simultaneously estimate the varying coefficient functions and the spatial correlations. The estimation procedure includes a fast multiscale adaptive estimation and testing procedure to independently estimate each varying coefficient function, while preserving its edges among different piecewise-smooth regions. We systematically investigate the asymptotic properties (e.g., consistency and asymptotic normality) of the multiscale adaptive parameter estimates. We also establish the uniform convergence rate of the estimated spatial covariance function and its associated eigenvalues and eigenfunctions. Our Monte Carlo simulation and real-data analysis have confirmed the excellent performance of SVCM. Supplementary materials for this article are available online.

MULTIVARIATE VARYING COEFFICIENT MODEL FOR FUNCTIONAL RESPONSES

Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We develop several statistical inference procedures for MVCM and systematically study their theoretical properties. We first establish the weak convergence of the local linear estimate of coefficient functions, as well as its asymptotic bias and variance, and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate. We establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions. We propose a global test for linear hypotheses of varying coefficient functions, and derive its asymptotic distribution under the null hypothesis. We also propose a simultaneous confidence band for each individual effect curve. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We apply MVCM to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment.

Exposure to urban air pollution and bone health in clinically healthy six-year-old-children

Air pollution induces systemic inflammation, as well as respiratory, myocardial and brain inflammation in children. Peak bone mass is influenced by environmental factors. We tested the hypothesis that six-year-olds with lifetime exposures to urban air pollution will have alterations in inflammatory markers and bone mineral density (BMD) as opposed to low-polluted city residents when matched for BMI, breast feeding history, skin phototype, age, sex and socioeconomic status. This pilot study included 20 children from Mexico City (MC) (6.17 years ± 0.63 years) and 15 controls (6.27 years ± 0.76 years). We performed full paediatric examinations, a history of outdoor exposures, seven-day dietary recalls, serum inflammatory markers and dual-energy X-ray absorptiometry (DXA). Children in MC had significantly higher concentrations of IL-6 (p=0.001), marked reductions in total blood neutrophils (p= 0.0002) and an increase in monocytes (p=0.005). MC children also had an insufficient Vitamin D intake and spent less time outdoors than controls (p<0.001) in an environment characterized by decreased UV light, with ozone and fine particulates concentrations above standard values. There were no significant differences between the cohorts in DXA Z scores. The impact of systemic inflammation, vitamin D insufficiency, air pollution, urban violence and poverty may have long-term bone detrimental outcomes in exposed paediatric populations as they grow older, increasing the risk of low bone mass and osteoporosis. The selection of reference populations for DXA must take into account air pollution exposures.

Partial functional linear quantile regression for neuroimaging data analysis

We propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial quantile regression (PQR) basis for estimating functional coefficients. We further extend our partial quantile covariance techniques to functional composite quantile regression (CQR) defining partial composite quantile covariance. There are three major contributions. (1) We define partial quantile covariance between two scalar variables through linear quantile regression. We compute PQR basis by sequentially maximizing the partial quantile covariance between the response and projections of functional covariates. (2) In order to efficiently extract PQR basis, we develop a SIMPQR algorithm analog to simple partial least squares (SIMPLS). (3) Under the homoscedasticity assumption, we extend our techniques to partial composite quantile covariance and use it to find the partial composite quantile regression (PCQR) basis. The SIMPQR algorithm is then modified to obtain the SIMPCQR algorithm. Two simulation studies show the superiority of our proposed methods. Two real data from ADHD-200 sample and ADNI are analyzed using our proposed methods.

Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits

Genetic studies often involve quantitative traits. Identifying genetic features that influence quantitative traits can help to uncover the etiology of diseases. Quantile regression method considers the conditional quantiles of the response variable, and is able to characterize the underlying regression structure in a more comprehensive manner. On the other hand, genetic studies often involve high-dimensional genomic features, and the underlying regression structure may be heterogeneous in terms of both effect sizes and sparsity. To account for the potential genetic heterogeneity, including the heterogeneous sparsity, a regularized quantile regression method is introduced. The theoretical property of the proposed method is investigated, and its performance is examined through a series of simulation studies. A real dataset is analyzed to demonstrate the application of the proposed method.

Multivariate varying coefficient models for DTI tract statistics

Diffusion tensor imaging (DTI) is important for characterizing the structure of white matter fiber bundles as well as detailed tissue properties along these fiber bundles in vivo. There has been extensive interest in the analysis of diffusion properties measured along fiber tracts as a function of age, diagnostic status, and gender, while controlling for other clinical variables. However, the existing methods have several limitations including the independent analysis of diffusion properties, a lack of method for accounting for multiple covariates, and a lack of formal statistical inference, such as estimation theory and hypothesis testing. This paper presents a statistical framework, called VCMTS, to specifically address these limitations. The VCMTS framework consists of four integrated components: a varying coefficient model for characterizing the association between fiber bundle diffusion properties and a set of covariates, the local polynomial kernel method for estimating smoothed multiple diffusion properties along individual fiber bundles, global and local test statistics for testing hypotheses of interest along fiber tracts, and a resampling method for approximating the p-value of the global test statistic. The proposed methodology is applied to characterizing the development of four diffusion properties along the splenium and genu of the corpus callosum tract in a study of neurodevelopment in healthy rhesus monkeys. Significant time effects on the four diffusion properties were found.

Model-Robust Designs for Quantile Regression

We give methods for the construction of designs for regression models, when the purpose of the investigation is the estimation of the conditional quantile function, and the estimation method is quantile regression. The designs are robust against misspecified response functions, and against unanticipated heteroscedasticity. The methods are illustrated by example, and in a case study in which they are applied to growth charts.

Growing Story Forest Online from Massive Breaking News

We describe our experience of implementing a news content organization system at Tencent that discovers events from vast streams of breaking news and evolves news story structures in an online fashion. Our real-world system has distinct requirements in contrast to previous studies on topic detection and tracking (TDT) and event timeline or graph generation, in that we 1) need to accurately and quickly extract distinguishable events from massive streams of long text documents that cover diverse topics and contain highly redundant information, and 2) must develop the structures of event stories in an online manner, without repeatedly restructuring previously formed stories, in order to guarantee a consistent user viewing experience. In solving these challenges, we propose Story Forest, a set of online schemes that automatically clusters streaming documents into events, while connecting related events in growing trees to tell evolving stories. We conducted extensive evaluation based on 60 GB of real-world Chinese news data, although our ideas are not language-dependent and can easily be extended to other languages, through detailed pilot user experience studies. The results demonstrate the superior capability of Story Forest to accurately identify events and organize news text into a logical structure that is appealing to human readers, compared to multiple existing algorithm frameworks.