arXiv subjects

Zhou Lan

Publications and source records attributed to Zhou Lan.

12 recordsLinked to original sources

arXiv2025

AGFS-Tractometry: A Novel Atlas-Guided Fine-Scale Tractometry Approach for Enhanced Along-Tract Group Statistical Comparison Using Diffusion MRI Tractography

Diffusion MRI (dMRI) tractography is currently the only method for in vivo mapping of the brain's white matter (WM) connections. Tractometry is an advanced tractography analysis technique for along-tract profiling to investigate the morphology and microstructural properties along the fiber tracts. Tractometry has become an essential tool for studying local along-tract differences between different populations (e.g., health vs disease). In this study, we propose a novel atlas-guided fine-scale tractometry method, namely AGFS-Tractometry, that leverages tract spatial information and permutation testing to enhance the along-tract statistical analysis between populations. There are two major contributions in AGFS-Tractometry. First, we create a novel atlas-guided tract profiling template that enables consistent, fine-scale, along-tract parcellation of subject-specific fiber tracts. Second, we propose a novel nonparametric permutation testing group comparison method to enable simultaneous analysis across all along-tract parcels while correcting for multiple comparisons. We perform experimental evaluations on synthetic datasets with known group differences and in vivo real data. We compare AGFS-Tractometry with two state-of-the-art tractometry methods, including Automated Fiber-tract Quantification (AFQ) and BUndle ANalytics (BUAN). Our results show that the proposed AGFS-Tractometry obtains enhanced sensitivity and specificity in detecting local WM differences. In the real data analysis experiments, AGFS-Tractometry can identify more regions with significant differences, which are anatomically consistent with the existing literature. Overall, these demonstrate the ability of AGFS-Tractometry to detect subtle or spatially localized WM group-level differences. The created tract profiling template and related code are available at: https://github.com/ZhengRuixi/AGFS-Tractometry.git.

q-bio.QM↗

arXiv2024

Nonparametric Modeling of Diffusion MRI Signal in Q-space

This paper describes a novel nonparametric model for modeling diffusion MRI signals in q-space. In q-space, diffusion MRI signal is measured for a sequence of magnetic strengths (b-values) and magnetic gradient directions (b-vectors). We propose a Poly-RBF model, which employs a bidirectional framework with polynomial bases to model the signal along the b-value direction and Gaussian radial bases across the b-vectors. The model can accommodate sparse data on b-values and moderately dense data on b-vectors. The utility of Poly-RBF is inspected for two applications: 1) prediction of the dMRI signal, and 2) harmonization of dMRI data collected under different acquisition protocols with different scanners. Our results indicate that the proposed Poly-RBF model can more accurately predict the unmeasured diffusion signal than its competitors such as the Gaussian process model in {\tt Eddy} of FSL. Applying it to harmonizing the diffusion signal can significantly improve the reproducibility of derived white matter microstructure measures.

stat.AP↗

arXiv2023

Mid-Long Term Daily Electricity Consumption Forecasting Based on Piecewise Linear Regression and Dilated Causal CNN

Daily electricity consumption forecasting is a classical problem. Existing forecasting algorithms tend to have decreased accuracy on special dates like holidays. This study decomposes the daily electricity consumption series into three components: trend, seasonal, and residual, and constructs a two-stage prediction method using piecewise linear regression as a filter and Dilated Causal CNN as a predictor. The specific steps involve setting breakpoints on the time axis and fitting the piecewise linear regression model with one-hot encoded information such as month, weekday, and holidays. For the challenging prediction of the Spring Festival, distance is introduced as a variable using a third-degree polynomial form in the model. The residual sequence obtained in the previous step is modeled using Dilated Causal CNN, and the final prediction of daily electricity consumption is the sum of the two-stage predictions. Experimental results demonstrate that this method achieves higher accuracy compared to existing approaches.

cs.LG↗

arXiv2022

Correlated Wishart Matrices Classification via an Expectation-Maximization Composite Likelihood-Based Algorithm

Positive-definite matrix-variate data is becoming popular in computer vision. The computer vision data descriptors in the form of Region Covariance Descriptors (RCD) are positive definite matrices, which extract the key features of the images. The RCDs are extensively used in image set classification. Some classification methods treating RCDs as Wishart distributed random matrices are being proposed. However, the majority of the current methods preclude the potential correlation among the RCDs caused by the so-called non-voxel information (e.g., subjects' ages and nose widths, etc). Modeling correlated Wishart matrices is difficult since the joint density function of correlated Wishart matrices is difficult to be obtained. In this paper, we propose an Expectation-Maximization composite likelihood-based algorithm of Wishart matrices to tackle this issue. Given the numerical studies based on the synthetic data and the real data (Chicago face data-set), our proposed algorithm performs better than the alternative methods which do not consider the correlation caused by the so-called non-voxel information. All these above demonstrate our algorithm's compelling potential in image set classification in the coming future.

stat.ME↗

arXiv2022

Spatial von-Mises Fisher Regression for Directional Data

Spatially varying directional data are routinely observed in several modern applications such as meteorology, biology, geophysics, engineering, etc. However, only a few approaches are available for covariate-dependent statistical analysis for such data. To address this gap, we propose a novel generalized linear model to analyze such that using a von Mises Fisher (vMF) distributed error structure. Using a novel link function that relies on the transformation between Cartesian and spherical coordinates, we regress the vMF-distributed directional data on the external covariates. This regression model enables us to quantify the impact of external factors on the observed directional data. Furthermore, we impose the spatial dependence using an autoregressive model, appropriately accounting for the directional dependence in the outcome. This novel specification renders computational efficiency and flexibility. In addition, a comprehensive Bayesian inferential toolbox is thoroughly developed and applied to our analysis. Subsequently, employing our regression model on the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, we gain new insights into the relationship between cognitive impairment and the orientations of brain fibers, along with examining empirical efficacy through simulation experiments. The code for implementing our proposed method is available on GitHub: https://github.com/lanzhouBWH/Spatial_VMF_Regression.

stat.AP↗

arXiv2022

Double soft-thresholded model for multi-group scalar on vector-valued image regression

In this paper, we develop a novel spatial variable selection method for scalar on vector-valued image regression in a multi-group setting. Here, 'vector-valued image' refers to the imaging datasets that contain vector-valued information at each pixel/voxel location, such as in RGB color images, multimodal medical images, DTI imaging, etc. The focus of this work is to identify the spatial locations in the image having an important effect on the scalar outcome measure. Specifically, the overall effect of each voxel is of interest. We thus develop a novel shrinkage prior by soft-thresholding the \ell_2 norm of a latent multivariate Gaussian process. It will allow us to estimate sparse and piecewise-smooth spatially varying vector-valued regression coefficient functions. For posterior inference, an efficient MCMC algorithm is developed. We establish the posterior contraction rate for parameter estimation and consistency for variable selection of the proposed Bayesian model, assuming that the true regression coefficients are Holder smooth. Finally, we demonstrate the advantages of the proposed method in simulation studies and further illustrate in an ADNI dataset for modeling MMSE scores based on DTI-based vector-valued imaging markers.

stat.ME↗

arXiv2021

Statistical Inference of Auto-correlated Eigenvalues with Applications to Diffusion Tensor Imaging

Diffusion tensor imaging (DTI) is a prevalent neuroimaging tool in analyzing the anatomical structure. The distinguishing feature of DTI is that the voxel-wise variable is a 3x3 positive definite matrix other than a scalar, describing the diffusion process at the voxel. Recently, several statistical methods have been proposed to analyze the DTI data. This paper focuses on the statistical inference of eigenvalues of DTI because it provides more transparent clinical interpretations. However, the statistical inference of eigenvalues is statistically challenging because few treat these responses as random eigenvalues. In our paper, we rely on the distribution of the Wishart matrix's eigenvalues to model the random eigenvalues. A hierarchical model which captures the eigenvalues' randomness and spatial auto-correlation is proposed to infer the local covariate effects. The Monte-Carlo Expectation-Maximization algorithm is implemented for parameter estimation. Both simulation studies and application to IXI data-set are used to demonstrate our proposal. The results show that our proposal is more proper in analyzing auto-correlated random eigenvalues compared to alternatives.

stat.ME↗

arXiv2020

A Joint Spatial Conditional Auto-Regressive Model for Estimating HIV Prevalence Rates Among Key Populations

Ending the HIV/AIDS pandemic is among the Sustainable Development Goals for the next decade. In order to overcome the gap between the need for care and the available resources, better understanding of HIV epidemics is needed to guide policy decisions, especially for key populations that are at higher risk for HIV infection. Accurate HIV epidemic estimates for key populations have been difficult to obtain because their HIV surveillance data is very limited. In this paper, we propose a so-called joint spatial conditional auto-regressive model for estimating HIV prevalence rates among key populations. Our model borrows information from both neighboring locations and dependent populations. As illustrated in the real data analysis, it provides more accurate estimates than independently fitting the sub-epidemic for each key population. In addition, we provide a study to reveal the conditions that our proposal gives a better prediction. The study combines both theoretical investigation and numerical study, revealing strength and limitations of our proposal.

stat.AP↗

arXiv2019

Probabilistic Diffusion MRI Fiber Tracking Using a Directed Acyclic Graph Auto-Regressive Model of Positive Definite Matrices

Diffusion MRI is a neuroimaging technique measuring the anatomical structure of tissues. Using diffusion MRI to construct the connections of tissues, known as fiber tracking, is one of the most important uses of diffusion MRI. Many techniques are available recently but few properly quantify statistical uncertainties. In this paper, we propose a directed acyclic graph auto-regressive model of positive definite matrices and apply a probabilistic fiber tracking algorithm. We use both real data analysis and numerical studies to demonstrate our proposal.

stat.ME↗

arXiv2019

Geostatistical Modeling of Positive Definite Matrices: An Application to Diffusion Tensor Imaging

Geostatistical modeling for continuous point-referenced data has been extensively applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging characterizing the brain structure produces a positive definite (p.d.) matrix for each voxel. Current geostatistical modeling has not been extended to p.d. matrices because introducing spatial dependence among positive definite matrices properly is challenging. In this paper, we use the spatial Wishart process, a spatial stochastic process (random field) where each p.d. matrix-variate marginally follows a Wishart distribution, and spatial dependence between random matrices is induced by latent Gaussian processes. This process is valid on an uncountable collection of spatial locations and is almost surely continuous, leading to a reasonable means of modeling spatial dependence. Motivated by a DTI dataset of cocaine users, we propose a spatial matrix-variate regression model based on the spatial Wishart process. A problematic issue is that the spatial Wishart process has no closed-form density function. Hence, we propose approximation methods to obtain a feasible working model. A local likelihood approximation method is also applied to achieve fast computation. The simulation studies and real data analysis demonstrate that the working model produces reliable inference and improved performance compared to other methods.

stat.ME↗

arXiv2019

A Spatial Bayesian Semiparametric Mixture Model for Positive Definite Matrices with Applications to Diffusion Tensor Imaging

Diffusion tensor imaging (DTI) is a popular magnetic resonance imaging technique used to characterize microstructural changes in the brain. DTI studies quantify the diffusion of water molecules in a voxel using an estimated 3x3 symmetric positive definite diffusion tensor matrix. Statistical analysis of DTI data is challenging because the data are positive definite matrices. Matrix-variate information is often summarized by a univariate quantity, such as the fractional anisotropy (FA), leading to a loss of information. Furthermore, DTI analyses often ignore the spatial association of neighboring voxels, which can lead to imprecise estimates. Although the spatial modeling literature is abundant, modeling spatially dependent positive definite matrices is challenging. To mitigate these issues, we propose a matrix-variate Bayesian semiparametric mixture model, where the positive definite matrices are distributed as a mixture of inverse Wishart distributions with the spatial dependence captured by a Markov model for the mixture component labels. Conjugacy and the double Metropolis-Hastings algorithm result in fast and elegant Bayesian computing. Our simulation study shows that the proposed method is more powerful than non-spatial methods. We also apply the proposed method to investigate the effect of cocaine use on brain structure. The contribution of our work is to provide a novel statistical inference tool for DTI analysis by extending spatial statistics to matrix-variate data.

stat.ME↗

arXiv2013

Practical Design for Multiple-Antenna Cognitive Radio Networks with Coexistence Constraint

In this paper we investigate the practical design for the multiple-antenna cognitive radio (CR) networks sharing the geographically used or unused spectrum. We consider a single cell network formed by the primary users (PU), which are half-duplex two-hop relay channels and the secondary users (SU) are single user additive white Gaussian noise channels. In addition, the coexistence constraint which requires PUs' coding schemes and rates unchanged with the emergence of SU, should be satisfied. The contribution of this paper are twofold. First, we explicitly design the scheme to pair the SUs to the existing PUs in a single cell network. Second, we jointly design the nonlinear precoder, relay beamformer, and the transmitter and receiver beamformers to minimize the sum mean square error of the SU system. In the first part, we derive an approximate relation between the relay ratio, chordal distance and strengths of the vector channels, and the transmit powers. Based on this relation, we are able to solve the optimal pairing between SUs and PUs efficiently. In the second part, considering the feasibility of implementation, we exploit the Tomlinson-Harashima precoding instead of the dirty paper coding to mitigate the interference at the SU receiver, which is known side information at the SU transmitter. To complete the design, we first approximate the optimization problem as a convex one. Then we propose an iterative algorithm to solve it with CVX. This joint design exploits all the degrees of design. To the best of our knowledge, both the two parts have never been considered in the literature. Numerical results show that the proposed pairing scheme outperforms the greedy and random pairing with low complexity. Numerical results also show that even if all the channel matrices are full rank, under which the simple zero forcing scheme is infeasible, the proposed scheme can still work well.

cs.IT↗