Persistent Homology in Sparse Regression and its Application to Brain Morphometry

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin

New Statistical Transfer Learning Models for Health Care Applications

abstract: Transfer learning is a sub-field of statistical modeling and machine learning. It refers to methods that integrate the knowledge of other domains (called source domains) and the data of the target domain in a mathematically rigorous and intelligent way, to develop a better model for the target domain than a model using the data of the target domain alone. While transfer learning is a promising approach in various application domains, my dissertation research focuses on the particular application in health care, including telemonitoring of Parkinson’s Disease (PD) and radiomics for glioblastoma. The first topic is a Mixed Effects Transfer Learning (METL) model that can flexibly incorporate mixed effects and a general-form covariance matrix to better account for similarity and heterogeneity across subjects. I further develop computationally efficient procedures to handle unknown parameters and large covariance structures. Domain relations, such as domain similarity and domain covariance structure, are automatically quantified in the estimation steps. I demonstrate METL in an application of smartphone-based telemonitoring of PD. The second topic focuses on an MRI-based transfer learning algorithm for non-invasive surgical guidance of glioblastoma patients. Limited biopsy samples per patient create a challenge to build a patient-specific model for glioblastoma. A transfer learning framework helps to leverage other patient’s knowledge for building a better predictive model. When modeling a target patient, not every patient’s information is helpful. Deciding the subset of other patients from which to transfer information to the modeling of the target patient is an important task to build an accurate predictive model. I define the subset of “transferrable” patients as those who have a positive rCBV-cell density correlation, because a positive correlation is confirmed by imaging theory and the its respective literature. The last topic is a Privacy-Preserving Positive Transfer Learning (P3TL) model. Although negative transfer has been recognized as an important issue by the transfer learning research community, there is a lack of theoretical studies in evaluating the risk of negative transfer for a transfer learning method and identifying what causes the negative transfer. My work addresses this issue. Driven by the theoretical insights, I extend Bayesian Parameter Transfer (BPT) to a new method, i.e., P3TL. The unique features of P3TL include intelligent selection of patients to transfer in order to avoid negative transfer and maintain patient privacy. These features make P3TL an excellent model for telemonitoring of PD using an At-Home Testing Device.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201

Integrated Structural And Functional Biomarkers For Neurodegeneration

Alzheimer\u27s Disease consists of a complex cascade of pathological processes, leading to the death of cortical neurons and development of dementia. Because it is impossible to regenerate neurons that have already died, a thorough understanding of the earlier stages of the disease, before significant neuronal death has occurred, is critical for developing disease-modifying therapies. The various components of Alzheimer\u27s Disease pathophysiology necessitate a variety of measurement techniques. Image-based measurements known as biomarkers can be used to assess cortical thinning and cerebral blood flow, but non-imaging characteristics such as performance on cognitive tests and age are also important determinants of risk of Alzheimer\u27s Disease. Incorporating the various imaging and non-imaging sources of information into a scientifically interpretable and statistically sound model is challenging. In this thesis, I present a method to include imaging data in standard regression analyses in a data-driven and anatomically interpretable manner. I also introduce a technique for disentangling the effect of cortical structure from blood flow, enabling a clearer picture of the signal carried by cerebral blood flow beyond the confounding effects of anatomical structure. In addition to these technical developments in multi-modal image analysis, I show the results of two clinically-oriented studies focusing on the relative importance of various biomarkers for predicting presence of Alzheimer\u27s Disease pathology in the earliest stages of disease. In the first, I present evidence that white matter hyperintensities, a marker of small vessel disease, are more highly associated with Alzheimer\u27s Disease pathology than current mainstream imaging biomarkers in elderly control patients. In the second, I show that once Alzheimer\u27s Disease has progressed to the point of noticeable cognitive decline, cognitive tests are as predictive of presence of Alzheimer\u27s pathology as standard imaging biomarkers. Taken together, these studies demonstrate that the relative importance of biomarkers and imaging modalities changes over the course of disease progression, and sophisticated data-driven methods for combining a variety of modalities is likely to lead to greater biological insight into the disease process than a single modality

Recent publications from the Alzheimer's Disease Neuroimaging Initiative: Reviewing progress toward improved AD clinical trials

INTRODUCTION: The Alzheimer's Disease Neuroimaging Initiative (ADNI) has continued development and standardization of methodologies for biomarkers and has provided an increased depth and breadth of data available to qualified researchers. This review summarizes the over 400 publications using ADNI data during 2014 and 2015. METHODS: We used standard searches to find publications using ADNI data. RESULTS: (1) Structural and functional changes, including subtle changes to hippocampal shape and texture, atrophy in areas outside of hippocampus, and disruption to functional networks, are detectable in presymptomatic subjects before hippocampal atrophy; (2) In subjects with abnormal β-amyloid deposition (Aβ+), biomarkers become abnormal in the order predicted by the amyloid cascade hypothesis; (3) Cognitive decline is more closely linked to tau than Aβ deposition; (4) Cerebrovascular risk factors may interact with Aβ to increase white-matter (WM) abnormalities which may accelerate Alzheimer's disease (AD) progression in conjunction with tau abnormalities; (5) Different patterns of atrophy are associated with impairment of memory and executive function and may underlie psychiatric symptoms; (6) Structural, functional, and metabolic network connectivities are disrupted as AD progresses. Models of prion-like spreading of Aβ pathology along WM tracts predict known patterns of cortical Aβ deposition and declines in glucose metabolism; (7) New AD risk and protective gene loci have been identified using biologically informed approaches; (8) Cognitively normal and mild cognitive impairment (MCI) subjects are heterogeneous and include groups typified not only by "classic" AD pathology but also by normal biomarkers, accelerated decline, and suspected non-Alzheimer's pathology; (9) Selection of subjects at risk of imminent decline on the basis of one or more pathologies improves the power of clinical trials; (10) Sensitivity of cognitive outcome measures to early changes in cognition has been improved and surrogate outcome measures using longitudinal structural magnetic resonance imaging may further reduce clinical trial cost and duration; (11) Advances in machine learning techniques such as neural networks have improved diagnostic and prognostic accuracy especially in challenges involving MCI subjects; and (12) Network connectivity measures and genetic variants show promise in multimodal classification and some classifiers using single modalities are rivaling multimodal classifiers. DISCUSSION: Taken together, these studies fundamentally deepen our understanding of AD progression and its underlying genetic basis, which in turn informs and improves clinical trial desig

L1 methods for shrinkage and correlation

This dissertation explored the idea of L1 norm in solving two statistical problems including multiple linear regression and diagnostic checking in time series. In recent years L1 shrinkage methods have become popular in linear regression as they can achieve simultaneous variable selection and parameter estimation. Their objective functions containing a least squares term and an L1 penalty term which can produce sparse solutions (Fan and Li, 2001). Least absolute shrinkage and selection operator (Lasso) was the first L1 penalized method proposed and has been widely used in practice. But the Lasso estimator has noticeable bias and is inconsistent for variable selection. Zou (2006) proposed adaptive Lasso and proved its oracle properties under some regularity conditions. We investigate the performance of adaptive Lasso by applying it to the problem of multiple undocumented change-point detection in climate. Artificial factors such as relocation of weather stations, recalibration of measurement instruments and city growth can cause abrupt mean shifts in historical temperature data. These changes do not reflect the true atmospheric evolution and unfortunately are often undocumented due to various reasons. It is imperative to locate the occurrence of these abrupt mean shifts so that raw data can be adjusted to only display the true atmosphere evolution. We have built a special linear model which accounts for long-term temperature change (global warming) by linear trend and is featured by p = n (the number of variables equals the number of observations). We apply adaptive Lasso to estimate the underlying sparse model and allow the trend parameter to be unpenalized in the objective function. Bayesian Information Criterion (BIC) and the CM criterion (Caussinus and Mestre, 2004) are used to select the finalized model. Multivariate t simultaneous confidence intervals can post-select the change-points detected by adaptive Lasso to attenuate overestimation. Considering that the oracle properties of adaptive Lasso are obtained under the condition of linear independence between predictor variables, adaptive Lasso should be used with caution since it is not uncommon for real data sets to have multicollinearity. Zou and Hastie (2005) proposed elastic net whose objective function involves both L1 and L2 penalties and claimed its superiority over Lasso in prediction. This procedure can identify a sparse model due to the L1 penalty and can tackle multicollinearity due to the L2 penalty. Although Lasso and elastic net are favored over ordinary least squares and ridge regression because of their functionality of variable selection, in presence of multicollinearity ridge regression can outperform both Lasso and elastic net in prediction. The salient point is that no regression method dominates in all cases (Fan and Li, 2001, Zou, 2006, Zou and Hastie, 2005). One major flaw of both Lasso and elastic net is the unnecessary bias brought by constraining all parameters to be penalized by the same norm. In this dissertation we propose a general and flexible framework for variable selection and estimation in linear regression. Our objective function automatically allows each parameter to be unpenalized, penalized by L1, L2 or both norms based on parameter significance and variable correlation. The resulting estimator not only can identify the correct set of significant variables with a large probability but also has smaller bias for nonzero parameters. Our procedure is a combinatorial optimization problem which can be solved by exhaustive search or genetic algorithm (as a surrogate to computation time). Aimed at a descriptive model, BIC is chosen as the model selection criterion. Another application of the L1 norm considered in this dissertation is portmanteau tests in time series. The first step in time series regression is to determine if significant serial correlation is present. If initial investigations indicate significant serial correlation, the second step is to fit an autoregressive moving average (ARMA) process to parameterize the correlation function. Portmanteau tests are commonly used to detect serial correlation or assess the goodness-of-fit of the ARMA model in these two steps. For small samples the commonly employed Ljung-Box portmanteau test (Ljung and Box, 1978) can have low power. It is beneficial to have a more powerful small sample test for detecting significant correlation. We develop such a test by considering the Cauchy estimator of correlation. While the usual sample correlation is estimated through L2 norm, the Cauchy estimator is based on L1 norm. Asymptotic properties of the test statistic are obtained. The test compares very favorably with the Box-Pierce/Ljung-Box statistics in detecting autoregressive alternatives

Converting Neuroimaging Big Data to information: Statistical Frameworks for interpretation of Image Driven Biomarkers and Image Driven Disease Subtyping

Large scale clinical trials and population based research studies collect huge amounts of neuroimaging data. Machine learning classifiers can potentially use these data to train models that diagnose brain related diseases from individual brain scans. In this dissertation we address two distinct challenges that beset a wider adoption of these tools for diagnostic purposes. The first challenge that besets the neuroimaging based disease classification is the lack of a statistical inference machinery for highlighting brain regions that contribute significantly to the classifier decisions. In this dissertation, we address this challenge by developing an analytic framework for interpreting support vector machine (SVM) models used for neuroimaging based diagnosis of psychiatric disease. To do this we first note that permutation testing using SVM model components provides a reliable inference mechanism for model interpretation. Then we derive our analysis framework by showing that under certain assumptions, the permutation based null distributions associated with SVM model components can be approximated analytically using the data themselves. Inference based on these analytic null distributions is validated on real and simulated data. p-Values computed from our analysis can accurately identify anatomical features that differentiate groups used for classifier training. Since the majority of clinical and research communities are trained in understanding statistical p-values rather than machine learning techniques like the SVM, we hope that this work will lead to a better understanding SVM classifiers and motivate a wider adoption of SVM models for image based diagnosis of psychiatric disease. A second deficiency of learning based neuroimaging diagnostics is that they implicitly assume that, `a single homogeneous pattern of brain changes drives population wide phenotypic differences\u27. In reality it is more likely that multiple patterns of brain deficits drive the complexities observed in the clinical presentation of most diseases. Understanding this heterogeneity may allow us to build better classifiers for identifying such diseases from individual brain scans. However, analytic tools to explore this heterogeneity are missing. With this in view, we present in this dissertation, a framework for exploring disease heterogeneity using population neuroimaging data. The approach we present first computes difference images by comparing matched cases and controls and then clusters these differences. The cluster centers define a set of deficit patterns that differentiates the two groups. By allowing for more than one pattern of difference between two populations, our framework makes a radical departure from traditional tools used for neuroimaging group analyses. We hope that this leads to a better understanding of the processes that lead to disease and also that it ultimately leads to improved image based disease classifiers

Computational Methods for Analysis of Resting State Functional Connectivity and Their Application to Study of Aging

The functional organization of the brain and its variability over the life-span can be studied using resting state functional MRI (rsfMRI). It can be used to define a macro-connectome\u27 describing functional interactions in the brain at the scale of major brain regions, facilitating the description of large-scale functional systems and their change over the lifespan. The connectome typically consists of thousands of links between hundreds of brain regions, making subsequent group-level analyses difficult. Furthermore, existing methods for group-level analyses are not equipped to identify heterogeneity in patient or otherwise affected populations. In this thesis, we incorporated recent advances in sparse representations for modeling spatial patterns of functional connectivity. We show that the resulting Sparse Connectivity Patterns (SCPs) are reproducible and capture major directions of variance in the data. Each SCP is associated with a scalar value that is proportional to the average connectivity within all the regions of that SCP. Thus, the SCP framework provides an interpretable basis for subsequent group-level analyses. Traditional univariate approaches are limited in their ability to detect heterogeneity in diseased/aging populations in a two-group comparison framework. To address this issue, we developed a Mixture-Of-Experts (MOE) method that combines unsupervised modeling of mixtures of distributions with supervised learning of classifiers, allowing discovery of multiple disease/aging phenotypes and the affected individuals associated with each pattern. We applied our methods to the Baltimore Longitudinal Study of Aging (BLSA), to find multiple advanced aging phenotypes. We built normative trajectories of functional and structural brain aging, which were used to identify individuals who seem resilient to aging, as well as individuals who show advanced signs of aging. Using MOE, we discovered five distinct patterns of advanced aging. Combined with neuro-cognitive data, we were able to further characterize one group as consisting of individuals with early-stage dementia. Another group had focal hippocampal atrophy, yet had higher levels of connectivity and somewhat higher cognitive performance, suggesting these individuals were recruiting their cognitive reserve to compensate for structural losses. These results demonstrate the utility of the developed methods, and pave the way for a broader understanding of the complexity of brain aging

Data Analytics and Performance Enhancement in Edge-Cloud Collaborative Internet of Things Systems

Based on the evolving communications, computing and embedded systems technologies, Internet of Things (IoT) systems can interconnect not only physical users and devices but also virtual services and objects, which have already been applied to many different application scenarios, such as smart home, smart healthcare, and intelligent transportation. With the rapid development, the number of involving devices increases tremendously. The huge number of devices and correspondingly generated data bring critical challenges to the IoT systems. To enhance the overall performance, this thesis aims to address the related technical issues on IoT data processing and physical topology discovery of the subnets self-organized by IoT devices. First of all, the issues on outlier detection and data aggregation are addressed through the development of recursive principal component analysis (R-PCA) based data analysis framework. The framework is developed in a cluster-based structure to fully exploit the spatial correlation of IoT data. Specifically, the sensing devices are gathered into clusters based on spatial data correlation. Edge devices are assigned to the clusters for the R-PCA based outlier detection and data aggregation. The outlier-free and aggregated data are forwarded to the remote cloud server for data reconstruction and storage. Moreover, a data reduction scheme is further proposed to relieve the burden on the trunk link for data uploading by utilizing the temporal data correlation. Kalman filters (KFs) with identical parameters are maintained at the edge and cloud for data prediction. The amount of data uploading is reduced by using the data predicted by the KF in the cloud instead of uploading all the practically measured data. Furthermore, an unmanned aerial vehicle (UAV) assisted IoT system is particularly designed for large-scale monitoring. Wireless sensor nodes are flexibly deployed for environmental sensing and self-organized into wireless sensor networks (WSNs). A physical topology discovery scheme is proposed to construct the physical topology of WSNs in the cloud server to facilitate performance optimization, where the physical topology indicates both the logical connectivity statuses of WSNs and the physical locations of WSN nodes. The physical topology discovery scheme is implemented through the newly developed parallel Metropolis-Hastings random walk based information sampling and network-wide 3D localization algorithms, where UAVs are served as the mobile edge devices and anchor nodes. Based on the physical topology constructed in the cloud, a UAV-enabled spatial data sampling scheme is further proposed to efficiently sample data from the monitoring area by using denoising autoencoder (DAE). By deploying the encoder of DAE at the UAV and decoder in the cloud, the data can be partially sampled from the sensing field and accurately reconstructed in the cloud. In the final part of the thesis, a novel autoencoder (AE) neural network based data outlier detection algorithm is proposed, where both encoder and decoder of AE are deployed at the edge devices. Data outliers can be accurately detected by the large fluctuations in the squared error generated by the data passing through the encoder and decoder of the AE