Separating Stimulus-Induced and Background Components of Dynamic Functional Connectivity in Naturalistic fMRI

We consider the challenges in extracting stimulus-related neural dynamics from other intrinsic processes and noise in naturalistic functional magnetic resonance imaging (fMRI). Most studies rely on inter-subject correlations (ISC) of low-level regional activity and neglect varying responses in individuals. We propose a novel, data-driven approach based on low-rank plus sparse (L+S) decomposition to isolate stimulus-driven dynamic changes in brain functional connectivity (FC) from the background noise, by exploiting shared network structure among subjects receiving the same naturalistic stimuli. The time-resolved multi-subject FC matrices are modeled as a sum of a low-rank component of correlated FC patterns across subjects, and a sparse component of subject-specific, idiosyncratic background activities. To recover the shared low-rank subspace, we introduce a fused version of principal component pursuit (PCP) by adding a fusion-type penalty on the differences between the columns of the low-rank matrix. The method improves the detection of stimulus-induced group-level homogeneity in the FC profile while capturing inter-subject variability. We develop an efficient algorithm via a linearized alternating direction method of multipliers to solve the fused-PCP. Simulations show accurate recovery by the fused-PCP even when a large fraction of FC edges are severely corrupted. When applied to natural fMRI data, our method reveals FC changes that were time-locked to auditory processing during movie watching, with dynamic engagement of sensorimotor systems for speech-in-noise. It also provides a better mapping to auditory content in the movie than ISC

Modeling effective connectivity in high-dimensional cortical source signals

To study the effective connectivity among sources in a densely voxelated (high-dimensional) cortical surface, we develop the source-space factor VAR model. The first step in our procedure is to estimate cortical activity from multichannel electroencephalograms (EEG) using anatomically constrained brain imaging methods. Following parcellation of the cortical surface into disjoint regions of interest (ROIs), latent factors within each ROI are computed using principal component analysis. These factors are ROI-specific low-rank approximations (or representations) which allow for efficient estimation of connectivity in the high-dimensional cortical source space. The second step is to model effective connectivity between ROIs by fitting a VAR model jointly on all the latent processes. Measures of cortical connectivity, in particular partial directed coherence, are formulated using the VAR parameters. We illustrate the proposed model to investigate connectivity and interactions between cortical ROIs during rest

Forecasting non-stationary time series by wavelet process modelling

Many time series in the applied sciences display a time-varying second order structure. In this article, we address the problem of how to forecast these nonstationary time series by means of non-decimated wavelets. Using the class of Locally Stationary Wavelet processes, we introduce a new predictor based on wavelets and derive the prediction equations as a generalisation of the Yule-Walker equations. We propose an automatic computational procedure for choosing the parameters of the forecasting algorithm. Finally, we apply the prediction algorithm to a meteorological time series

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 to be imbalanced since the 1970s. Previous studies have shown there is a great variation in the SRB between geographic locations across India till 2016. Considering the enormous population and regional heterogeneity of India, producing probabilistic SRB projections at the state level is crucial for policy planning and population projection. In this paper, we implement a Bayesian hierarchical time series model to project the SRB across India by state. We generate SRB probabilistic projections from 2017 to 2030 for 29 States and Union Territories (UTs) in India, and present results for 21 States/UTs with data available from the Sample Registration System. Our analysis takes into account two state-specific factors that contribute to sex-selective abortion in India, resulting in sex imbalances at birth: the intensity of son preference and fertility squeeze. We project that the highest deficits in female births will occur in Uttar Pradesh, with a cumulative number of missing female births of 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 of India is projected to be 6.8 [6.6; 7.0] million

A markov-switching model approach to heart sound segmentation and classification

Objective: We consider challenges in accurate segmentation of heart sound signals recorded under noisy clinical environments for subsequent classification of pathological events. Existing state-of-the-art solutions to heart sound segmentation use probabilistic models such as hidden Markov models (HMMs), which, however, are limited by its observation independence assumption and rely on pre-extraction of noise-robust features. Methods: We propose a Markov-switching autoregressive (MSAR) process to model the raw heart sound signals directly, which allows efficient segmentation of the cyclical heart sound states according to the distinct dependence structure in each state. To enhance robustness, we extend the MSAR model to a switching linear dynamic system (SLDS) that jointly model both the switching AR dynamics of underlying heart sound signals and the noise effects. We introduce a novel algorithm via fusion of switching Kalman filter and the duration-dependent Viterbi algorithm, which incorporates the duration of heart sound states to improve state decoding. Results: Evaluated on Physionet/CinC Challenge 2016 dataset, the proposed MSAR-SLDS approach significantly outperforms the hidden semi-Markov model (HSMM) in heart sound segmentation based on raw signals and comparable to a feature-based HSMM. The segmented labels were then used to train Gaussian-mixture HMM classifier for identification of abnormal beats, achieving high average precision of 86.1% on the same dataset including very noisy recordings. Conclusion: The proposed approach shows noticeable performance in heart sound segmentation and classification on a large noisy dataset. Significance: It is potentially useful in developing automated heart monitoring systems for pre-screening of heart pathologies

Haar-Fisz estimation of evolutionary wavelet spectra

We propose a new 'Haar–Fisz' technique for estimating the time-varying, piecewise constant local variance of a locally stationary Gaussian time series. We apply our technique to the estimation of the spectral structure in the locally stationary wavelet model. Our method combines Haar wavelets and the variance stabilizing Fisz transform. The resulting estimator is mean square consistent, rapidly computable and easy to implement, and performs well in practice. We also introduce the 'Haar–Fisz transform', a device for stabilizing the variance of scaled χ2-data and bringing their distribution close to Gaussianity