Statistical Inference for Assessing Functional Connectivity of Neuronal Ensembles With Sparse Spiking Data

The ability to accurately infer functional connectivity between ensemble neurons using experimentally acquired spike train data is currently an important research objective in computational neuroscience. Point process generalized linear models and maximum likelihood estimation have been proposed as effective methods for the identification of spiking dependency between neurons. However, unfavorable experimental conditions occasionally results in insufficient data collection due to factors such as low neuronal firing rates or brief recording periods, and in these cases, the standard maximum likelihood estimate becomes unreliable. The present studies compares the performance of different statistical inference procedures when applied to the estimation of functional connectivity in neuronal assemblies with sparse spiking data. Four inference methods were compared: maximum likelihood estimation, penalized maximum likelihood estimation, using either l2 or l1 regularization, and hierarchical Bayesian estimation based on a variational Bayes algorithm. Algorithmic performances were compared using well-established goodness-of-fit measures in benchmark simulation studies, and the hierarchical Bayesian approach performed favorably when compared with the other algorithms, and this approach was then successfully applied to real spiking data recorded from the cat motor cortex. The identification of spiking dependencies in physiologically acquired data was encouraging, since their sparse nature would have previously precluded them from successful analysis using traditional methods.National Institutes of Health (U.S.) (Grant DP1-OD003646)National Institutes of Health (U.S.) (Grant Grant R01-DA015644)National Institutes of Health (U.S.) (Grant Grant R01-HL08450

STATISTICAL METHODS FOR EXPLORING NEURONAL INTERACTIONS

Generalized linear models (GLMs) offer a platform for analyzing multi-electroderecordings of neuronal spiking. We suggest an L1-regularized logistic regressionmodel to detect short-term interactions under certain experimental setups. Weestimate parameters of this model using a coordinate descent algorithm; we determinethe optimal tuning parameter using BIC, and prove its asymptotic validity. Simulationstudies of the method's performance show that this model can detect excitatoryinteractions with high sensitivity and specificity with reasonably large recordings,even when the magnitude of the interactions is small; similar results hold forinhibition for sufficiently high baseline firing rates. The method is somewhat robustto network complexity and partial observation of networks. We apply our method tomulti-electrode recording data from monkey dorsal premotor cortex (PMd). Our resultspoint to certain features of short-term interactions when a monkey plans a reach.Next, we propose a variable coefficients GLM model to assess the temporal variationof interactions across trials. We treat the parameters of interest as functions overtrials, and fit them by penalized splines. There are also nuisance parameters assumedconstant, which are mildly penalized to guarantee the finite maximum of thelog-likelihood. We choose tuning parameters for smoothness by generalized crossvalidation, and provide simultaneous confidence bands and hypothesis tests fornull models. To achieve efficient computation, some modifications are also made. Weapply our method to a subset of the monkey PMd data. Before the implementation to thereal data, simulations are done to assess the performance of the proposed model.Finally, for the logistic and Poisson models, one possible difficulty is that iterativealgorithms for estimation may not converge because of certain data configurations(called complete and quasicomplete separation for the logistic). We show that thesefeatures are likely to occur because of refractory periods of neurons, and show howstandard software deals with this difficulty. For the Poisson model, we show that suchdifficulties arise possibly due to bursting or specifics of the binning. Wecharacterize the nonconvergent configurations for both models, show that they can bedetected by linear programming methods, and propose remedies

Machine Learning Methods for Medical and Biological Image Computing

Medical and biological imaging technologies provide valuable visualization information of structure and function for an organ from the level of individual molecules to the whole object. Brain is the most complex organ in body, and it increasingly attracts intense research attentions with the rapid development of medical and bio-logical imaging technologies. A massive amount of high-dimensional brain imaging data being generated makes the design of computational methods for efficient analysis on those images highly demanded. The current study of computational methods using hand-crafted features does not scale with the increasing number of brain images, hindering the pace of scientific discoveries in neuroscience. In this thesis, I propose computational methods using high-level features for automated analysis of brain images at different levels. At the brain function level, I develop a deep learning based framework for completing and integrating multi-modality neuroimaging data, which increases the diagnosis accuracy for Alzheimer’s disease. At the cellular level, I propose to use three dimensional convolutional neural networks (CNNs) for segmenting the volumetric neuronal images, which improves the performance of digital reconstruction of neuron structures. I design a novel CNN architecture such that the model training and testing image prediction can be implemented in an end-to-end manner. At the molecular level, I build a voxel CNN classifier to capture discriminative features of the input along three spatial dimensions, which facilitate the identification of secondary structures of proteins from electron microscopy im-ages. In order to classify genes specifically expressed in different brain cell-type, I propose to use invariant image feature descriptors to capture local gene expression information from cellular-resolution in situ hybridization images. I build image-level representations by applying regularized learning and vector quantization on generated image descriptors. The developed computational methods in this dissertation are evaluated using images from medical and biological experiments in comparison with baseline methods. Experimental results demonstrate that the developed representations, formulations, and algorithms are effective and efficient in learning from brain imaging data

Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation

Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the additional requirement of parsimony. This requirement has high interpretative value, but unfortunately cannot be met by least-squares based or kernel regression methods. To this end, compressed sampling (CS) approaches, already successful in linear regression settings, can offer a viable alternative. The viability of CS for sparse Volterra and polynomial models is the core theme of this work. A common sparse regression task is initially posed for the two models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type algorithm is developed for sparse polynomial regressions. The identifiability of polynomial models is critically challenged by dimensionality. However, following the CS principle, when these models are sparse, they could be recovered by far fewer measurements. To quantify the sufficient number of measurements for a given level of sparsity, restricted isometry properties (RIP) are investigated in commonly met polynomial regression settings, generalizing known results for their linear counterparts. The merits of the novel (weighted) adaptive CS algorithms to sparse polynomial modeling are verified through synthetic as well as real data tests for genotype-phenotype analysis.Comment: 20 pages, to appear in IEEE Trans. on Signal Processin

Understanding Huntington\u27s disease using Machine Learning Approaches

Huntington’s disease (HD) is a debilitating neurodegenerative disorder with a complex pathophysiology. Despite extensive studies to study the disease, the sequence of events through which mutant Huntingtin (mHtt) protein executes its action still remains elusive. The phenotype of HD is an outcome of numerous processes initiated by the mHtt protein along with other proteins that act as either suppressors or enhancers of the effects of mHtt protein and PolyQ aggregates. Utilizing an integrative systems biology approach, I construct and analyze a Huntington’s disease integrome using human orthologs of protein interactors of wild type and mHtt protein. Analysis of this integrome using unsupervised machine learning methods reveals a novel connection linking mHtt protein with chromosome condensation and DNA repair. I generate a list of candidate genes that upon validation in a yeast and drosophila model of HD are shown to affect the mHtt phenotype and provide an in-vivo evidence of our hypothesis. A separate supervised machine learning approach is applied to build a classifier model that predicts protein interactors of wild type and mHtt protein. Both the machine learning models that I employ, have important applications for Huntington’s disease in predicting both protein and genetic interactions of huntingtin protein and can be easily extended to other PolyQ and neurodegenerative disorders such as Alzheimer’s and Parkinson’s disease

Improved dynamic connection detection power in estimated dynamic functional connectivity considering multivariate dependencies between brain regions

To estimate dynamic functional connectivity (dFC), the conventional method of sliding window correlation (SWC) suffers from poor performance of dynamic connection detection. This stems from the equal weighting of observations, suboptimal time scale, nonsparse output, and the fact that it is bivariate. To overcome these limitations, we exploited the kernel-reweighted logistic regression (KELLER) algorithm, a method that is common in genetic studies, to estimate dFC in resting state functional magnetic resonance imaging (rs-fMRI) data. KELLER can estimate dFC through estimating both spatial and temporal patterns of functional connectivity between brain regions. This paper compares the performance of the proposed KELLER method with current methods (SWC and tapered-SWC (T-SWC) with different window lengths) based on both simulated and real rs-fMRI data. Estimated dFC networks were assessed for detecting dynamically connected brain region pairs with hypothesis testing. Simulation results revealed that KELLER can detect dynamic connections with a statistical power of 87.35% compared with 70.17% and 58.54% associated with T-SWC (p-value = .001) and SWC (p-value \u3c.001), respectively. Results of these different methods applied on real rs-fMRI data were investigated for two aspects: calculating the similarity between identified mean dynamic pattern and identifying dynamic pattern in default mode network (DMN). In 68% of subjects, the results of T-SWC with window length of 100 s, among different window lengths, demonstrated the highest similarity to those of KELLER. With regards to DMN, KELLER estimated previously reported dynamic connection pairs between dorsal and ventral DMN while SWC-based method was unable to detect these dynamic connections

EXTRACTING NEURONAL DYNAMICS AT HIGH SPATIOTEMPORAL RESOLUTIONS: THEORY, ALGORITHMS, AND APPLICATION

Analyses of neuronal activity have revealed that various types of neurons, both at the single-unit and population level, undergo rapid dynamic changes in their response characteristics and their connectivity patterns in order to adapt to variations in the behavioral context or stimulus condition. In addition, these dynamics often admit parsimonious representations. Despite growing advances in neural modeling and data acquisition technology, a unified signal processing framework capable of capturing the adaptivity, sparsity and statistical characteristics of neural dynamics is lacking. The objective of this dissertation is to develop such a signal processing methodology in order to gain a deeper insight into the dynamics of neuronal ensembles underlying behavior, and consequently a better understanding of how brain functions. The first part of this dissertation concerns the dynamics of stimulus-driven neuronal activity at the single-unit level. We develop a sparse adaptive filtering framework for the identification of neuronal response characteristics from spiking activity. We present a rigorous theoretical analysis of our proposed sparse adaptive filtering algorithms and characterize their performance guarantees. Application of our algorithms to experimental data provides new insights into the dynamics of attention-driven neuronal receptive field plasticity, with a substantial increase in temporal resolution. In the second part, we focus on the network-level properties of neuronal dynamics, with the goal of identifying the causal interactions within neuronal ensembles that underlie behavior. Building up on the results of the first part, we introduce a new measure of causality, namely the Adaptive Granger Causality (AGC), which allows capturing the sparsity and dynamics of the causal influences in a neuronal network in a statistically robust and computationally efficient fashion. We develop a precise statistical inference framework for the estimation of AGC from simultaneous recordings of the activity of neurons in an ensemble. Finally, in the third part we demonstrate the utility of our proposed methodologies through application to synthetic and real data. We first validate our theoretical results using comprehensive simulations, and assess the performance of the proposed methods in terms of estimation accuracy and tracking capability. These results confirm that our algorithms provide significant gains in comparison to existing techniques. Furthermore, we apply our methodology to various experimentally recorded data from electrophysiology and optical imaging: 1) Application of our methods to simultaneous spike recordings from the ferret auditory and prefrontal cortical areas reveals the dynamics of top-down and bottom-up functional interactions underlying attentive behavior at unprecedented spatiotemporal resolutions; 2) Our analyses of two-photon imaging data from the mouse auditory cortex shed light on the sparse dynamics of functional networks under both spontaneous activity and auditory tone detection tasks; and 3) Application of our methods to whole-brain light-sheet imaging data from larval zebrafish reveals unique insights into the organization of functional networks involved in visuo-motor processing