Blending generative models with deep learning for multidimensional phenotypic prediction from brain connectivity data

Network science as a discipline has provided us with foundational machinery to study complex relational entities such as social networks, genomics, econometrics etc. The human brain is a complex network that has recently garnered immense interest within the data science community. Connectomics or the study of the underlying connectivity patterns in the brain has become an important field of study for the characterization of various neurological disorders such as Autism, Schizophrenia etc. Such connectomic studies have provided several fundamental insights into its intrinsic organisation and implications on our behavior and health. This thesis proposes a collection of mathematical models that are capable of fusing information from functional and structural connectivity with phenotypic information. Here, functional connectivity is measured by resting state functional MRI (rs-fMRI), while anatomical connectivity is captured using Diffusion Tensor Imaging (DTI). The phenotypic information of interest could refer to continuous measures of behavior or cognition, or may capture levels of impairment in the case of neuropsychiatric disorders. We first develop a joint network optimization framework to predict clinical severity from rs-fMRI connectivity matrices. This model couples two key terms into a unified optimization framework: a generative matrix factorization and a discriminative linear regression model. We demonstrate that the proposed joint inference strategy is successful in generalizing to prediction of impairments in Autism Spectrum Disorder (ASD) when compared with several machine learning, graph theoretic and statistical baselines. At the same time, the model is capable of extracting functional brain biomarkers that are informative of individual measures of clinical severity. We then present two modeling extensions to non-parametric and neural network regression models that are coupled with the same generative framework. Building on these general principles, we extend our framework to incorporate multimodal information from Diffusion Tensor Imaging (DTI) and dynamic functional connectivity. At a high level, our generative matrix factorization now estimates a time-varying functional decomposition. At the same time, it is guided by anatomical connectivity priors in a graph-based regularization setup. This connectivity model is coupled with a deep network that predicts multidimensional clinical characterizations and models the temporal dynamics of the functional scan. This framework allows us to simultaneously explain multiple impairments, isolate stable multi-modal connectivity signatures, and study the evolution of various brain states at rest. Lastly, we shift our focus to end-to-end geometric frameworks. These are designed to characterize the complementarity between functional and structural connectivity data spaces, while using clinical information as a secondary guide. As an alternative to the previous generative framework for functional connectivity, our representation learning scheme of choice is a matrix autoencoder that is crafted to reflect the underlying data geometry. This is coupled with a manifold alignment model that maps from function to structure and a deep network that maps to phenotypic information. We demonstrate that the model reliably recovers structural connectivity patterns across individuals, while robustly extracting predictive yet interpretable brain biomarkers. Finally, we also present a preliminary analytical and experimental exposition on the theoretical aspects of the matrix autoencoder representation

The topology of structural brain connectivity in diseases and spatio-temporal connectomics

The brain is a complex system, composed of multiple neural units interconnected at different spatial and temporal scales. Diffusion MRI allows probing in vivo the anatomical connectivity between different cortical areas through white matter tracts. In parallel, functional MRI records neural-related signals of brain activity. Particularly, during rest (in absence of specific external task) reproducible dynamical patterns of functional synchronization have been shown across different brain areas. This rich information can be conveniently represented in the form of a graph, a mathematical object where nodes correspond to cortical regions and are connected by edges representing anatomical connections. On the top of this structural network, or brain connectome, individual nodes are associated to functional signals representing neural activity over observation periods. Network science has fundamentally contributed to the characterization of the human connectome. The brain is a small-world network, able to combine segregation and integration aspects. These properties allow functional specialization on the one side, and efficient communication between distant brain areas on the other side, supporting complex cognitive and executive functions. Graph theoretical methods quantify brain topological properties, and allow their comparison between different populations and conditions. In fact, brain connectivity patterns and interdependences between anatomical substrate and functional synchronization have been proved to be impaired in a variety of brain disorders, and to change across human development and aging. Despite these important advancements in the understanding of the brain structure and functioning, many questions are currently unanswered. It is not clear for instance how structural connectivity features are related to individual cognitive capabilities and deficits, and if they have the concrete potential to distinguish pathological subgroups for early diagnosis of brain diseases. Most importantly, it is not yet understood how the connectome topology relates to specific brain functions, and how the transmission of information happens on the top of the structural connectivity infrastructure in order to generate observed functional dynamics. This thesis was motivated by these interdisciplinary inputs, and is the result of a strong interaction between biological and clinical questions on the one hand, and methodological development needs on the other hand. First, we have contributed to the characterization of the human connectome in health and pathologies by adapting and developing network measures for the description of the brain architecture at different scales. Particularly, we have focused on the topological characterization of subnetworks role within the overall brain network. Importantly, we have shown that the topological alteration of distinct brain subsystems may be a biomarker for different brain disorders. Second, we have proposed an original network model for the joint representation of brain structural and functional connectivity properties. This flexible spatio-temporal framework allows the investigation of functional dynamics at multiple temporal scales. Importantly, the investigation of spatio-temporal graphs in healthy subjects have allowed to disclose temporal relationships between local brain activations in resting state recordings, and has highlighted functional communication principles across the brain structural network

On the information theory of clustering, registration, and blockchains

Progress in data science depends on the collection and storage of large volumes of reliable data, efficient and consistent inference based on this data, and trusting such computations made by untrusted peers. Information theory provides the means to analyze statistical inference algorithms, inspires the design of statistically consistent learning algorithms, and informs the design of large-scale systems for information storage and sharing. In this thesis, we focus on the problems of reliability, universality, integrity, trust, and provenance in data storage, distributed computing, and information processing algorithms and develop technical solutions and mathematical insights using information-theoretic tools. In unsupervised information processing we consider the problems of data clustering and image registration. In particular, we evaluate the performance of the max mutual information method for image registration by studying its error exponent and prove its universal asymptotic optimality. We further extend this to design the max multiinformation method for universal multi-image registration and prove its universal asymptotic optimality. We then evaluate the non-asymptotic performance of image registration to understand the effects of the properties of the image transformations and the channel noise on the algorithms. In data clustering we study the problem of independence clustering of sources using multivariate information functionals. In particular, we define consistent image clustering algorithms using the cluster information, and define a new multivariate information functional called illum information that inspires other independence clustering methods. We also consider the problem of clustering objects based on labels provided by temporary and long-term workers in a crowdsourcing platform. Here we define budget-optimal universal clustering algorithms using distributional identicality and temporal dependence in the responses of workers. For the problem of reliable data storage, we consider the use of blockchain systems, and design secure distributed storage codes to reduce the cost of cold storage of blockchain ledgers. Additionally, we use dynamic zone allocation strategies to enhance the integrity and confidentiality of these systems, and frame optimization problems for designing codes applicable for cloud storage and data insurance. Finally, for the problem of establishing trust in computations over untrusting peer-to-peer networks, we develop a large-scale blockchain system by defining the validation protocols and compression scheme to facilitate an efficient audit of computations that can be shared in a trusted manner across peers over the immutable blockchain ledger. We evaluate the system over some simple synthetic computational experiments and highlights its capacity in identifying anomalous computations and enhancing computational integrity

Behavior quantification as the missing link between fields: Tools for digital psychiatry and their role in the future of neurobiology

The great behavioral heterogeneity observed between individuals with the same psychiatric disorder and even within one individual over time complicates both clinical practice and biomedical research. However, modern technologies are an exciting opportunity to improve behavioral characterization. Existing psychiatry methods that are qualitative or unscalable, such as patient surveys or clinical interviews, can now be collected at a greater capacity and analyzed to produce new quantitative measures. Furthermore, recent capabilities for continuous collection of passive sensor streams, such as phone GPS or smartwatch accelerometer, open avenues of novel questioning that were previously entirely unrealistic. Their temporally dense nature enables a cohesive study of real-time neural and behavioral signals. To develop comprehensive neurobiological models of psychiatric disease, it will be critical to first develop strong methods for behavioral quantification. There is huge potential in what can theoretically be captured by current technologies, but this in itself presents a large computational challenge -- one that will necessitate new data processing tools, new machine learning techniques, and ultimately a shift in how interdisciplinary work is conducted. In my thesis, I detail research projects that take different perspectives on digital psychiatry, subsequently tying ideas together with a concluding discussion on the future of the field. I also provide software infrastructure where relevant, with extensive documentation. Major contributions include scientific arguments and proof of concept results for daily free-form audio journals as an underappreciated psychiatry research datatype, as well as novel stability theorems and pilot empirical success for a proposed multi-area recurrent neural network architecture.Comment: PhD thesis cop

Contemporary Natural Philosophy and Philosophies - Part 1

This book is a printed edition of the Special Issue titled "Contemporary Natural Philosophy and Philosophies" - Part 1 that was published in the journal Philosophies