arXiv subjects

Hernando Ombao

Publications and source records attributed to Hernando Ombao.

At least 91 records · Page 5Linked to original sources

arXiv2020

Detecting Dynamic Community Structure in Functional Brain Networks Across Individuals: A Multilayer Approach

We present a unified statistical framework for characterizing community structure of brain functional networks that captures variation across individuals and evolution over time. Existing methods for community detection focus only on single-subject analysis of dynamic networks; while recent extensions to multiple-subjects analysis are limited to static networks. To overcome these limitations, we propose a multi-subject, Markov-switching stochastic block model (MSS-SBM) to identify state-related changes in brain community organization over a group of individuals. We first formulate a multilayer extension of SBM to describe the time-dependent, multi-subject brain networks. We develop a novel procedure for fitting the multilayer SBM that builds on multislice modularity maximization which can uncover a common community partition of all layers (subjects) simultaneously. By augmenting with a dynamic Markov switching process, our proposed method is able to capture a set of distinct, recurring temporal states with respect to inter-community interactions over subjects and the change points between them. Simulation shows accurate community recovery and tracking of dynamic community regimes over multilayer networks by the MSS-SBM. Application to task fMRI reveals meaningful non-assortative brain community motifs, e.g., core-periphery structure at the group level, that are associated with language comprehension and motor functions suggesting their putative role in complex information integration. Our approach detected dynamic reconfiguration of modular connectivity elicited by varying task demands and identified unique profiles of intra and inter-community connectivity across different task conditions. The proposed multilayer network representation provides a principled way of detecting synchronous, dynamic modularity in brain networks across subjects.

cs.LG↗

arXiv2020

Levels and trends in the sex ratio at birth in seven provinces of Nepal between 1980 and 2016 with probabilistic projections to 2050: a Bayesian modeling approach

The sex ratio at birth (SRB; ratio of male to female births) in Nepal has been reported without imbalance on the national level. However, the national SRB could mask the disparity within the country. Given the demographic and cultural heterogeneities in Nepal, it is crucial to model Nepal SRB on the subnational level. Prior studies on subnational SRB in Nepal are mostly based on reporting observed values from surveys and census, and no study has provided probabilistic projections. We aim to estimate and project SRB for the seven provinces of Nepal from 1980 to 2050 using a Bayesian modeling approach. We compiled an extensive database on provincial SRB of Nepal, consisting 2001, 2006, 2011, and 2016 Nepal Demographic and Health Surveys and 2011 Census. We adopted a Bayesian hierarchical time series model to estimate and project the provincial SRB, with a focus on modelling the potential SRB imbalance. In 2016, the highest SRB is estimated in Province 5 at 1.102 with a 95% credible interval (1.044, 1.127) and the lowest SRB is in Province 2 at 1.053 (1.035, 1.109). The SRB imbalance probabilities in all provinces are generally low and vary from 16% in Province 2 to 81% in Province 5. SRB imbalances are estimated to have begun at the earliest in 2001 in Province 5 with a 95% credible interval (1992, 2022) and the latest in 2017 (1998, 2040) in Province 2. We project SRB in all provinces to begin converging back to the national baseline in the mid-2030s. Our findings imply that the majority of provinces in Nepal have low risks of SRB imbalance for the period 1980-2016. However, we identify a few provinces with higher probabilities of having SRB inflation. The projected SRB is an important illustration of potential future prenatal sex discrimination and shows the need to monitor SRB in provinces with higher possibilities of SRB imbalance.

stat.AP↗

arXiv2020

Clustering Brain Signals: A Robust Approach Using Functional Data Ranking

In this paper, we analyze electroencephalograms (EEG) which are recordings of brain electrical activity. We develop new clustering methods for identifying synchronized brain regions, where the EEGs show similar oscillations or waveforms according to their spectral densities. We treat the estimated spectral densities from many epochs or trials as functional data and develop clustering algorithms based on functional data ranking. The two proposed clustering algorithms use different dissimilarity measures: distance of the functional medians and the area of the central region. The performance of the proposed algorithms is examined by simulation studies. We show that, when contaminations are present, the proposed methods for clustering spectral densities are more robust than the mean-based methods. The developed methods are applied to two stages of resting state EEG data from a male college student, corresponding to early exploration of functional connectivity in the human brain.

stat.ME↗

arXiv2020

Multiscale modelling of replicated nonstationary time series

Within the neurosciences, to observe variability across time in the dynamics of an underlying brain process is neither new nor unexpected. Wavelets are essential in analyzing brain signals because, even within a single trial, brain signals exhibit nonstationary behaviour. However, neurological signals generated within an experiment may also potentially exhibit evolution across trials (replicates). As neurologists consider localised spectra of brain signals to be most informative, here we develop a novel wavelet-based tool capable to formally represent process nonstationarities across both time and replicate dimensions. Specifically, we propose the Replicate Locally Stationary Wavelet (RLSW) process, that captures the potential nonstationary behaviour within and across trials. Estimation using wavelets gives a natural desired time- and replicate-localisation of the process dynamics. We develop the associated spectral estimation framework and establish its asymptotic properties. By means of thorough simulation studies, we demonstrate the theoretical estimator properties hold in practice. A real data investigation into the evolutionary dynamics of the hippocampus and nucleus accumbens during an associative learning experiment, demonstrate the applicability of our proposed methodology, as well as the new insights it provides.

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arXiv2020

Semiparametric time series models driven by latent factor

We introduce a class of semiparametric time series models by assuming a quasi-likelihood approach driven by a latent factor process. More specifically, given the latent process, we only specify the conditional mean and variance of the time series and enjoy a quasi-likelihood function for estimating parameters related to the mean. This proposed methodology has three remarkable features: (i) no parametric form is assumed for the conditional distribution of the time series given the latent process; (ii) able for modelling non-negative, count, bounded/binary and real-valued time series; (iii) dispersion parameter is not assumed to be known. Further, we obtain explicit expressions for the marginal moments and for the autocorrelation function of the time series process so that a method of moments can be employed for estimating the dispersion parameter and also parameters related to the latent process. Simulated results aiming to check the proposed estimation procedure are presented. Real data analysis on unemployment rate and precipitation time series illustrate the potencial for practice of our methodology.

stat.ME↗

arXiv2020

Integer-valued autoregressive process with flexible marginal and innovation distributions

INteger Auto-Regressive (INAR) processes are usually defined by specifying the innovations and the operator, which often leads to difficulties in deriving marginal properties of the process. In many practical situations, a major modeling limitation is that it is difficult to justify the choice of the operator. To overcome these drawbacks, we propose a new flexible approach to build an INAR model: we pre-specify the marginal and innovation distributions. Hence, the operator is a consequence of specifying the desired marginal and innovation distributions. Our new INAR model has both marginal and innovations geometric distributed, being a direct alternative to the classical Poisson INAR model. Our proposed process has interesting stochastic properties such as an MA($\infty$) representation, time-reversibility, and closed-forms for the transition probabilities $h$-steps ahead, allowing for coherent forecasting. We analyze time-series counts of skin lesions using our proposed approach, comparing it with existing INAR and INGARCH models. Our model gives more adherence to the data and better forecasting performance.

stat.ME↗

arXiv2020

Probabilistic Projection of the Sex Ratio at Birth and Missing Female Births by State and Union Territory in India

The sex ratio at birth (SRB) in India has been reported imbalanced since the 1970s. Previous studies have shown a great variation in the SRB across geographic locations in India till 2016. As one of the most populous countries and in view of its great regional heterogeneity, it is crucial to produce probabilistic projections for the SRB in India at state level for the purpose of population projection and policy planning. In this paper, we implement a Bayesian hierarchical time series model to project SRB in India by state. We generate SRB probabilistic projections from 2017 to 2030 for 29 States and Union Territories (UTs) in India, and present results in 21 States/UTs with data from the Sample Registration System. Our analysis takes into account two state-specific factors that contribute to sex-selective abortion and resulting sex imbalances at birth: intensity of son preference and fertility squeeze. We project that the largest contribution to female births deficits is in Uttar Pradesh, with cumulative number of missing female births projected to be 2.0 (95% credible interval [1.9; 2.2]) million from 2017 to 2030. The total female birth deficits during 2017-2030 for the whole India is projected to be 6.8 [6.6; 7.0] million.

stat.AP↗

arXiv2019

Modeling Spectral Properties in Stationary Processes of Varying Dimensions with Applications to Brain Local Field Potential Signals

A common class of methods for analyzing of multivariate time series, stationary and nonstationary, decomposes the observed series into latent sources. Methods such as principal compoment analysis (PCA), independent component analysis (ICA) and Stationary Subspace Analysis (SSA) assume the observed multivariate process is generated by latent sources that are stationary or nonstationary. We develop a method that tracks changes in the complexity of a 32-channel local field potential (LFP) signal from a rat following an experimentally induced stroke. We study complexity through the latent sources and their dimensions that can change across epochs due to an induced shock to the cortical system. Our method compares the spread of spectral information in several multivariate stationary processes with different dimensions. A frequency specific spectral ratio (FS-ratio) statistic is proposed and its asymptotic properties are derived. The FS-ratio is blind to the dimension of the stationary process and captures the proportion of spectral information in various (user-specified) frequency bands. We apply our method to study differences in complexity and structure of the LFP before and after system shock. The analysis indicates that spectral information in the beta frequency band (12-30 Hertz) demonstrated the greatest change in structure and complexity due to the stroke.

stat.ME↗

arXiv2019

Statistical Model for Dynamically-Changing Correlation Matrices with Application to Brain Connectivity

Background: Recent studies have indicated that functional connectivity is dynamic even during rest. A common approach to modeling the dynamic functional connectivity in whole-brain resting-state fMRI is to compute the correlation between anatomical regions via sliding time windows. However, the direct use of the sample correlation matrices is not reliable due to the image acquisition and processing noises in resting-sate fMRI. New method: To overcome these limitations, we propose a new statistical model that smooths out the noise by exploiting the geometric structure of correlation matrices. The dynamic correlation matrix is modeled as a linear combination of symmetric positive-definite matrices combined with cosine series representation. The resulting smoothed dynamic correlation matrices are clustered into disjoint brain connectivity states using the k-means clustering algorithm. Results: The proposed model preserves the geometric structure of underlying physiological dynamic correlation, eliminates unwanted noise in connectivity and obtains more accurate state spaces. The difference in the estimated dynamic connectivity states between males and females is identified. Comparison with existing methods: We demonstrate that the proposed statistical model has less rapid state changes caused by noise and improves the accuracy in identifying and discriminating different states. Conclusions: We propose a new regression model on dynamically changing correlation matrices that provides better performance over existing windowed correlation and is more reliable for the modeling of dynamic connectivity.

q-bio.NC↗

arXiv2019

Modeling Dynamic Functional Connectivity with Latent Factor Gaussian Processes

Dynamic functional connectivity, as measured by the time-varying covariance of neurological signals, is believed to play an important role in many aspects of cognition. While many methods have been proposed, reliably establishing the presence and characteristics of brain connectivity is challenging due to the high dimensionality and noisiness of neuroimaging data. We present a latent factor Gaussian process model which addresses these challenges by learning a parsimonious representation of connectivity dynamics. The proposed model naturally allows for inference and visualization of time-varying connectivity. As an illustration of the scientific utility of the model, application to a data set of rat local field potential activity recorded during a complex non-spatial memory task provides evidence of stimuli differentiation.

stat.ME↗

arXiv2019

A Robust Interrupted Time Series Model for Analyzing Complex Healthcare Intervention Data

Current health policy calls for greater use of evidence based care delivery services to improve patient quality and safety outcomes. Care delivery is complex, with interacting and interdependent components that challenge traditional statistical analytic techniques, in particular when modeling a time series of outcomes data that might be "interrupted" by a change in a particular method of health care delivery. Interrupted time series (ITS) is a robust quasi-experimental design with the ability to infer the effectiveness of an intervention that accounts for data dependency. Current standardized methods for analyzing ITS data do not model changes in variation and correlation following the intervention. This is a key limitation since it is plausible for data variability and dependency to change because of the intervention. Moreover, present methodology either assumes a pre-specified interruption time point with an instantaneous effect or removes data for which the effect of intervention is not fully realized. In this paper, we describe and develop a novel `Robust-ITS' model that overcomes these omissions and limitations. The Robust-ITS model formally performs inference on: (a) identifying the change point; (b) differences in pre- and post-intervention correlation; (c) differences in the outcome variance pre- and post-intervention; and (d) differences in the mean pre- and post-intervention. We illustrate the proposed method by analyzing patient satisfaction data from a hospital that implemented and evaluated a new nursing care delivery model as the intervention of interest. The Robust-ITS model is implemented in a R Shiny toolbox which is freely available to the community.

stat.AP↗

arXiv2019

Classification of EEG-Based Brain Connectivity Networks in Schizophrenia Using a Multi-Domain Connectome Convolutional Neural Network

We exploit altered patterns in brain functional connectivity as features for automatic discriminative analysis of neuropsychiatric patients. Deep learning methods have been introduced to functional network classification only very recently for fMRI, and the proposed architectures essentially focused on a single type of connectivity measure. We propose a deep convolutional neural network (CNN) framework for classification of electroencephalogram (EEG)-derived brain connectome in schizophrenia (SZ). To capture complementary aspects of disrupted connectivity in SZ, we explore combination of various connectivity features consisting of time and frequency-domain metrics of effective connectivity based on vector autoregressive model and partial directed coherence, and complex network measures of network topology. We design a novel multi-domain connectome CNN (MDC-CNN) based on a parallel ensemble of 1D and 2D CNNs to integrate the features from various domains and dimensions using different fusion strategies. Hierarchical latent representations learned by the multiple convolutional layers from EEG connectivity reveal apparent group differences between SZ and healthy controls (HC). Results on a large resting-state EEG dataset show that the proposed CNNs significantly outperform traditional support vector machine classifiers. The MDC-CNN with combined connectivity features further improves performance over single-domain CNNs using individual features, achieving remarkable accuracy of $93.06\%$ with a decision-level fusion. The proposed MDC-CNN by integrating information from diverse brain connectivity descriptors is able to accurately discriminate SZ from HC. The new framework is potentially useful for developing diagnostic tools for SZ and other disorders.

cs.LG↗

arXiv2019

Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices

Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices and propose a novel Bayesian framework based on modeling the correlations as products of unit vectors. By specifying a wide range of distributions on a sphere (e.g. the squared-Dirichlet distribution), the proposed approach induces flexible prior distributions for covariance matrices (that go beyond the commonly used inverse-Wishart prior). For modeling real-life spatio-temporal processes with complex dependence structures, we extend our method to dynamic cases and introduce unit-vector Gaussian process priors in order to capture the evolution of correlation among components of a multivariate time series. To handle the intractability of the resulting posterior, we introduce the adaptive $Δ$-Spherical Hamiltonian Monte Carlo. We demonstrate the validity and flexibility of our proposed framework in a simulation study of periodic processes and an analysis of rat's local field potential activity in a complex sequence memory task.

stat.ME↗

arXiv2018

Adaptive Mantel Test for AssociationTesting in Imaging Genetics Data

Mantel's test (MT) for association is conducted by testing the linear relationship of similarity of all pairs of subjects between two observational domains. Motivated by applications to neuroimaging and genetics data, and following the succes of shrinkage and kernel methods for prediction with high-dimensional data, we here introduce the adaptive Mantel test as an extension of the MT. By utilizing kernels and penalized similarity measures, the adaptive Mantel test is able to achieve higher statistical power relative to the classical MT in many settings. Furthermore, the adaptive Mantel test is designed to simultaneously test over multiple similarity measures such that the correct type I error rate under the null hypothesis is maintained without the need to directly adjust the significance threshold for multiple testing. The performance of the adaptive Mantel test is evaluated on simulated data, and is used to investigate associations between genetics markers related to Alzheimer's Disease and heatlhy brain physiology with data from a working memory study of 350 college students from Beijing Normal University.

stat.ME↗

arXiv2018

Assessing Health Care Interventions via an Interrupted Time Series Model: Study Power and Design Considerations

The delivery and assessment of quality health care is complex with many interacting and interdependent components. In terms of research design and statistical analysis, this complexity and interdependency makes it difficult to assess the true impact of interventions designed to improve patient health care outcomes. Interrupted time series (ITS) is a quasi-experimental design developed for inferring the effectiveness of a health policy intervention while accounting for temporal dependence within a single system or unit. Current standardized ITS methods do not simultaneously analyze data for several units, nor are there methods to test for the existence of a change point and to assess statistical power for study planning purposes in this context. To address this limitation we propose the `Robust Multiple ITS' (R-MITS) model, appropriate for multi-unit ITS data, that allows for inference regarding the estimation of a global change point across units in the presence of a potentially lagged (or anticipatory) treatment effect. Under the R-MITS model, one can formally test for the existence of a change point and estimate the time delay between the formal intervention implementation and the over-all-unit intervention effect. We conducted empirical simulation studies to assess the type one error rate of the testing procedure, power for detecting specified change-point alternatives, and accuracy of the proposed estimating methodology. R-MITS is illustrated by analyzing patient satisfaction data from a hospital that implemented and evaluated a new care delivery model in multiple units.

stat.ME↗

arXiv2018

Short-segment heart sound classification using an ensemble of deep convolutional neural networks

This paper proposes a framework based on deep convolutional neural networks (CNNs) for automatic heart sound classification using short-segments of individual heart beats. We design a 1D-CNN that directly learns features from raw heart-sound signals, and a 2D-CNN that takes inputs of two- dimensional time-frequency feature maps based on Mel-frequency cepstral coefficients (MFCC). We further develop a time-frequency CNN ensemble (TF-ECNN) combining the 1D-CNN and 2D-CNN based on score-level fusion of the class probabilities. On the large PhysioNet CinC challenge 2016 database, the proposed CNN models outperformed traditional classifiers based on support vector machine and hidden Markov models with various hand-crafted time- and frequency-domain features. Best classification scores with 89.22% accuracy and 89.94% sensitivity were achieved by the ECNN, and 91.55% specificity and 88.82% modified accuracy by the 2D-CNN alone on the test set.

cs.SD↗

arXiv2018

Fisher information matrix of binary time series

A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating the historical data as covariate inputs, standard errors of estimates of GLM parameters computed using the empirical Fisher information do not fully account the auto-correlation in the data. To overcome this serious limitation, we derive the exact conditional Fisher information matrix of a general logistic autoregressive model with endogenous covariates for any series length $T$. Moreover, we also develop an iterative computational formula that allows for relatively easy implementation of the proposed estimator. Our simulation studies show that confidence intervals derived using the exact Fisher information matrix tend to be narrower than those utilizing the empirical Fisher information matrix while maintaining type I error rates at or below nominal levels. Further, we establish that the exact Fisher information matrix approaches, as T tends to infinity, the asymptotic Fisher information matrix previously derived for binary time series data. The developed exact conditional Fisher information matrix is applied to time-series data on respiratory rate among a cohort of expectant mothers where it is found to provide narrower confidence intervals for functionals of scientific interest and lead to greater statistical power when compared to the empirical Fisher information matrix.

math.ST↗

arXiv2018

Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States

Motivated by the problem of predicting sleep states, we develop a mixed effects model for binary time series with a stochastic component represented by a Gaussian process. The fixed component captures the effects of covariates on the binary-valued response. The Gaussian process captures the residual variations in the binary response that are not explained by covariates and past realizations. We develop a frequentist modeling framework that provides efficient inference and more accurate predictions. Results demonstrate the advantages of improved prediction rates over existing approaches such as logistic regression, generalized additive mixed model, models for ordinal data, gradient boosting, decision tree and random forest. Using our proposed model, we show that previous sleep state and heart rates are significant predictors for future sleep states. Simulation studies also show that our proposed method is promising and robust. To handle computational complexity, we utilize Laplace approximation, golden section search and successive parabolic interpolation. With this paper, we also submit an R-package (HIBITS) that implements the proposed procedure.

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