arXiv subjects

Lexin Li

Publications and source records attributed to Lexin Li.

At least 55 records · Page 3Linked to original sources

arXiv2021

Generalized Connectivity Matrix Response Regression with Applications in Brain Connectivity Studies

Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose a new generalized matrix response regression model, where the observed networks are treated as matrix-valued responses and the subject covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the effect of subject covariates through a sparse slope tensor. We develop an efficient alternating gradient descent algorithm for parameter estimation, and establish the non-asymptotic error bound for the actual estimator from the algorithm, which quantifies the interplay between the computational and statistical errors. We further show the strong consistency for graph community recovery, as well as the edge selection consistency. We demonstrate the efficacy of our method through simulations and two brain connectivity studies.

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arXiv2021

Testing Mediation Effects Using Logic of Boolean Matrices

Mediation analysis is becoming an increasingly important tool in scientific studies. A central question in high-dimensional mediation analysis is to infer the significance of individual mediators. The main challenge is the sheer number of possible paths that go through all combinations of mediators. Most existing mediation inference solutions either explicitly impose that the mediators are conditionally independent given the exposure, or ignore any potential directed paths among the mediators. In this article, we propose a novel hypothesis testing procedure to evaluate individual mediation effects, while taking into account potential interactions among the mediators. Our proposal thus fills a crucial gap, and greatly extends the scope of existing mediation tests. Our key idea is to construct the test statistic using the logic of Boolean matrices, which enables us to establish the proper limiting distribution under the null hypothesis. We further employ screening, data splitting, and decorrelated estimation to reduce the bias and increase the power of the test. We show our test can control both the size and false discovery rate asymptotically, and the power of the test approaches one, meanwhile allowing the number of mediators to diverge to infinity with the sample size. We demonstrate the efficacy of our method through both simulations and a neuroimaging study of Alzheimer's disease.

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arXiv2020

Multivariate Temporal Point Process Regression

Point process modeling is gaining increasing attention, as point process type data are emerging in numerous scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression model, where both the response and the predictor can be a high-dimensional point process. We model the predictor effects through the conditional intensities using a set of basis transferring functions in a convolutional fashion. We organize the corresponding transferring coefficients in the form of a three-way tensor, then impose the low-rank, sparsity, and subgroup structures on this coefficient tensor. These structures help reduce the dimensionality, integrate information across different individual processes, and facilitate the interpretation. We develop a highly scalable optimization algorithm for parameter estimation. We derive the large sample error bound for the recovered coefficient tensor, and establish the subgroup identification consistency, while allowing the dimension of the multivariate point process to diverge. We demonstrate the efficacy of our method through both simulations and a cross-area neuronal spike trains analysis in a sensory cortex study.

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arXiv2020

Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a multilinear Bernoulli model, develop a rank-constrained likelihood-based estimation method, and obtain the theoretical accuracy guarantees. In contrast to continuous-valued problems, the binary tensor problem exhibits an interesting phase transition phenomenon according to the signal-to-noise ratio. The error bound for the parameter tensor estimation is established, and we show that the obtained rate is minimax optimal under the considered model. Furthermore, we develop an alternating optimization algorithm with convergence guarantees. The efficacy of our approach is demonstrated through both simulations and analyses of multiple data sets on the tasks of tensor completion and clustering.

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arXiv2020

Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error

High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model. While there has been a large body of literature studying sparse estimation of the transition matrix, there is a paucity of inference solutions, especially in the high-dimensional scenario. We develop inferential procedures for both the global and simultaneous testing of the transition matrix. We first develop a new sparse expectation-maximization algorithm to estimate the model parameters, and carefully characterize their estimation precisions. We then construct a Gaussian matrix, after proper bias and variance corrections, from which we derive the test statistics. Finally, we develop the testing procedures and establish their asymptotic guarantees. We study the finite-sample performance of our tests through intensive simulations, and illustrate with a brain connectivity analysis example.

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arXiv2019

Hypothesis Testing for Network Data with Power Enhancement

Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Many existing network inference solutions focus on global testing of entire networks, without comparing individual network links. Besides, the observed data often take the form of vectors or matrices, and the problem is formulated as comparing two covariance or precision matrices under a normal or matrix normal distribution. Moreover, many tests suffer from a limited power under a small sample size. In this article, we tackle the problem of network comparison, both global and simultaneous inferences, when the data come in a different format, i.e., in the form of a collection of symmetric matrices, each of which encodes the network structure of an individual subject. Such data format commonly arises in applications such as brain connectivity analysis and clinical genomics. We no longer require the underlying data to follow a normal distribution, but instead impose some moment conditions that are easily satisfied for numerous types of network data. Furthermore, we propose a power enhancement procedure, and show that it can control the false discovery, while it has the potential to substantially enhance the power of the test. We investigate the efficacy of our testing procedure through both an asymptotic analysis and a simulation study under a finite sample size. We further illustrate our method with an example of brain structural connectivity analysis.

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arXiv2019

Multimodal Neuroimaging Data Integration and Pathway Analysis

With fast advancements in technologies, the collection of multiple types of measurements on a common set of subjects is becoming routine in science. Some notable examples include multimodal neuroimaging studies for the simultaneous investigation of brain structure and function, and multi-omics studies for combining genetic and genomic information. Integrative analysis of multimodal data allows scientists to interrogate new mechanistic questions. However, the data collection and generation of integrative hypotheses is outpacing available methodology for joint analysis of multimodal measurements. In this article, we study high-dimensional multimodal data integration in the context of mediation analysis. We aim to understand the roles different data modalities play as possible mediators in the pathway between an exposure variable and an outcome. We propose a mediation model framework with two data types serving as separate sets of mediators, and develop a penalized optimization approach for parameter estimation. We study both the theoretical properties of the estimator through an asymptotic analysis, and its finite-sample performance through simulations. We illustrate our method with a multimodal brain pathway analysis having both structural and functional connectivities as mediators in the association between sex and language processing.

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arXiv2019

Paired Test of Matrix Graphs and Brain Connectivity Analysis

Inferring brain connectivity network and quantifying the significance of interactions between brain regions are of paramount importance in neuroscience. Although there have recently emerged some tests for graph inference based on independent samples, there is no readily available solution to test the change of brain network for paired and correlated samples. In this article, we develop a paired test of matrix graphs to infer brain connectivity network when the groups of samples are correlated. The proposed test statistic is both bias corrected and variance corrected, and achieves a small estimation error rate. The subsequent multiple testing procedure built on this test statistic is guaranteed to asymptotically control the false discovery rate at the pre-specified level. Both the methodology and theory of the new test are considerably different from the two independent samples framework, owing to the strong correlations of measurements on the same subjects before and after the stimulus activity. We illustrate the efficacy of our proposal through simulations and an analysis of an Alzheimer's Disease Neuroimaing Initiative dataset.

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arXiv2019

Quantifying Intrinsic Uncertainty in Classification via Deep Dirichlet Mixture Networks

With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that attaches an explicit uncertainty statement to the probabilities of classification using deep neural networks. Precisely, we view that the classification probabilities are sampled from an unknown distribution, and we propose to learn this distribution through the Dirichlet mixture that is flexible enough for approximating any continuous distribution on the simplex. We then construct credible intervals from the learned distribution to assess the uncertainty of the classification probabilities. Our approach is easy to implement, computationally efficient, and can be coupled with any deep neural network architecture. Our method leverages the crucial observation that, in many classification applications such as medical diagnosis, more than one class labels are available for each observational unit. We demonstrate the usefulness of our approach through simulations and a real data example.

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arXiv2018

Dynamic Tensor Clustering

Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap between statistical guarantee and computational efficiency for existing tensor clustering solutions. In this article, we aim to bridge this gap by proposing a new dynamic tensor clustering method, which takes into account both sparsity and fusion structures, and enjoys strong statistical guarantees as well as high computational efficiency. Our proposal is based upon a new structured tensor factorization that encourages both sparsity and smoothness in parameters along the specified tensor modes. Computationally, we develop a highly efficient optimization algorithm that benefits from substantial dimension reduction. In theory, we first establish a non-asymptotic error bound for the estimator from the structured tensor factorization. Built upon this error bound, we then derive the rate of convergence of the estimated cluster centers, and show that the estimated clusters recover the true cluster structures with a high probability. Moreover, our proposed method can be naturally extended to co-clustering of multiple modes of the tensor data. The efficacy of our approach is illustrated via simulations and a brain dynamic functional connectivity analysis from an Autism spectrum disorder study.

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arXiv2018

Mixed-Effect Time-Varying Network Model and Application in Brain Connectivity Analysis

Time-varying networks are fast emerging in a wide range of scientific and business disciplines. Most existing dynamic network models are limited to a single-subject and discrete-time setting. In this article, we propose a mixed-effect multi-subject continuous-time stochastic blockmodel that characterizes the time-varying behavior of the network at the population level, meanwhile taking into account individual subject variability. We develop a multi-step optimization procedure for a constrained stochastic blockmodel estimation, and derive the asymptotic property of the estimator. We demonstrate the effectiveness of our method through both simulations and an application to a study of brain development in youth.

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arXiv2017

STORE: Sparse Tensor Response Regression and Neuroimaging Analysis

Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity and low-rankness. It can handle both a non-symmetric and a symmetric tensor response, and thus is applicable to both structural and functional neuroimaging data. We formulate the parameter estimation as a non-convex optimization problem, and develop an efficient alternating updating algorithm. We establish a non-asymptotic estimation error bound for the actual estimator obtained from the proposed algorithm. This error bound reveals an interesting interaction between the computational efficiency and the statistical rate of convergence. When the distribution of the error tensor is Gaussian, we further obtain a fast estimation error rate which allows the tensor dimension to grow exponentially with the sample size. We illustrate the efficacy of our model through intensive simulations and an analysis of the Autism spectrum disorder neuroimaging data.

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arXiv2015

Hypothesis Testing of Matrix Graph Model with Application to Brain Connectivity Analysis

Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical dependences that are often encoded in terms of partial correlations. Such a graph is inferred from matrix-valued neuroimaging data such as electroencephalography and functional magnetic resonance imaging. There have been a good number of successful proposals for sparse precision matrix estimation under normal or matrix normal distribution; however, this family of solutions do not offer a statistical significance quantification for the estimated links. In this article, we adopt a matrix normal distribution framework and formulate the brain connectivity analysis as a precision matrix hypothesis testing problem. Based on the separable spatial-temporal dependence structure, we develop oracle and data-driven procedures to test the global hypothesis that all spatial locations are conditionally independent, which are shown to be particularly powerful against the sparse alternatives. In addition, simultaneous tests for identifying conditional dependent spatial locations with false discovery rate control are proposed in both oracle and data-driven settings. Theoretical results show that the data-driven procedures perform asymptotically as well as the oracle procedures and enjoy certain optimality properties. The empirical finite-sample performance of the proposed tests is studied via simulations, and the new tests are applied on a real electroencephalography data analysis.

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arXiv2015

Parsimonious Tensor Response Regression

Aiming at abundant scientific and engineering data with not only high dimensionality but also complex structure, we study the regression problem with a multidimensional array (tensor) response and a vector predictor. Applications include, among others, comparing tensor images across groups after adjusting for additional covariates, which is of central interest in neuroimaging analysis. We propose parsimonious tensor response regression adopting a generalized sparsity principle. It models all voxels of the tensor response jointly, while accounting for the inherent structural information among the voxels. It effectively reduces the number of free parameters, leading to feasible computation and improved interpretation. We achieve model estimation through a nascent technique called the envelope method, which identifies the immaterial information and focuses the estimation based upon the material information in the tensor response. We demonstrate that the resulting estimator is asymptotically efficient, and it enjoys a competitive finite sample performance. We also illustrate the new method on two real neuroimaging studies.

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arXiv2014

Tensor Generalized Estimating Equations for Longitudinal Imaging Analysis

In an increasing number of neuroimaging studies, brain images, which are in the form of multidimensional arrays (tensors), have been collected on multiple subjects at multiple time points. Of scientific interest is to analyze such massive and complex longitudinal images to diagnose neurodegenerative disorders and to identify disease relevant brain regions. In this article, we treat those problems in a unifying regression framework with image predictors, and propose tensor generalized estimating equations (GEE) for longitudinal imaging analysis. The GEE approach takes into account intra-subject correlation of responses, whereas a low rank tensor decomposition of the coefficient array enables effective estimation and prediction with limited sample size. We propose an efficient estimation algorithm, study the asymptotics in both fixed $p$ and diverging $p$ regimes, and also investigate tensor GEE with regularization that is particularly useful for region selection. The efficacy of the proposed tensor GEE is demonstrated on both simulated data and a real data set from the Alzheimer's Disease Neuroimaging Initiative (ADNI).

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arXiv2013

High-dimensional influence measure

Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the sample size. Our proposal can be viewed as a high-dimensional counterpart to the classical Cook's distance. However, whereas the Cook's distance quantifies the individual observation's influence on the least squares regression coefficient estimate, our new diagnosis measure captures the influence on the marginal correlations, which in turn exerts serious influence on downstream analysis including coefficient estimation, variable selection and screening. Moreover, we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity. Availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection. Both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure.

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arXiv2013

Tucker Tensor Regression and Neuroimaging Analysis

Large-scale neuroimaging studies have been collecting brain images of study individuals, which take the form of two-dimensional, three-dimensional, or higher dimensional arrays, also known as tensors. Addressing scientific questions arising from such data demands new regression models that take multidimensional arrays as covariates. Simply turning an image array into a long vector causes extremely high dimensionality that compromises classical regression methods, and, more seriously, destroys the inherent spatial structure of array data that possesses wealth of information. In this article, we propose a family of generalized linear tensor regression models based upon the Tucker decomposition of regression coefficient arrays. Effectively exploiting the low rank structure of tensor covariates brings the ultrahigh dimensionality to a manageable level that leads to efficient estimation. We demonstrate, both numerically that the new model could provide a sound recovery of even high rank signals, and asymptotically that the model is consistently estimating the best Tucker structure approximation to the full array model in the sense of Kullback-Liebler distance. The new model is also compared to a recently proposed tensor regression model that relies upon an alternative CANDECOMP/PARAFAC (CP) decomposition.

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arXiv2012

Regularized Matrix Regression

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained for each combination of two underlying variables. To address scientific questions arising from those data, new regression methods that take matrices as covariates are needed, and sparsity or other forms of regularization are crucial due to the ultrahigh dimensionality and complex structure of the matrix data. The popular lasso and related regularization methods hinge upon the sparsity of the true signal in terms of the number of its nonzero coefficients. However, for the matrix data, the true signal is often of, or can be well approximated by, a low rank structure. As such, the sparsity is frequently in the form of low rank of the matrix parameters, which may seriously violate the assumption of the classical lasso. In this article, we propose a class of regularized matrix regression methods based on spectral regularization. Highly efficient and scalable estimation algorithm is developed, and a degrees of freedom formula is derived to facilitate model selection along the regularization path. Superior performance of the proposed method is demonstrated on both synthetic and real examples.

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