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1. Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series

   https://doi.org/10.1109/ICASSP43922.2022.9747446  

   Tugnait, Jitendra K. ( May 2022 , ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) |)

   We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso based frequency-domain formulation of the problem has been considered in the literature where the objective is to estimate the sparse inverse power spectral density (PSD) of the data. The CIG is then inferred from the estimated inverse PSD. In this paper we investigate use of a sparse-group log-sum penalty (LSP) instead of sparse-group lasso penalty. An alternating direction method of multipliers (ADMM) approach for iterative optimization of the non-convex problem is presented. We provide sufficient conditions for local convergence in the Frobenius norm of the inverse PSD estimators to the true value. This results also yields a rate of convergence. We illustrate our approach using numerical examples utilizing both synthetic and real data.
2. Consistency of Sparse-Group Lasso Graphical Model Selection for Time Series

   https://doi.org/10.1109/IEEECONF51394.2020.9443298  

   Tugnait, Jitendra K. ( November 2020 , 2020 54th Asilomar Conference on Signals, Systems, and Computers)

   We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. A p-variate Gaussian time series graphical model associated with an undirected graph with p vertices is defined as the family of time series that obey the conditional independence restrictions implied by the edge set of the graph. A sparse-group lasso-based frequency-domain formulation of the problem has been considered in the literature where the objective is to estimate the inverse power spectral density (PSD) of the data via optimization of a sparse-group lasso based penalized log-likelihood cost function that is formulated in the frequency-domain. The CIG is then inferred from the estimated inverse PSD. In this paper we establish sufficient conditions for consistency of the inverse PSD estimator resulting from the sparse-group graphical lasso-based approach.
3. Graph Learning From Multivariate Dependent Time Series Via A Multi-Attribute Formulation

   https://doi.org/10.1109/ICASSP43922.2022.9746603  

   Tugnait, Jitendra K. ( May 2022 , ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))

   We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges.
4. Sparse-Group Non-convex Penalized Multi-Attribute Graphical Model Selection

   https://doi.org/10.23919/EUSIPCO54536.2021.9616255  

   Tugnait, Jitendra K. ( August 2021 , 2021 29th European Signal Processing Conference (EUSIPCO))

   We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one associates a scalar random variable with each node. In multi-attribute graphical models, each node represents a random vector. In this paper we consider a sparse-group smoothly clipped absolute deviation (SG-SCAD) penalty instead of sparse-group lasso (SGL) penalty to regularize the problem. We analyze an SG-SCAD-penalized log-likelihood based objective function to establish consistency of a local estimator of inverse covariance. A numerical example is presented to illustrate the advantage of SG-SCAD-penalty over the usual SGL-penalty.
5. Salience of low-frequency entrainment to visual signal for classification points to predictive processing in sign language. In Proceedings of 30th Annual Computational Neuroscience Meeting: CNS*2021

   https://doi.org/10.1007/s10827-021-00801-9  

   E. Malaia, L.K. Ford ( December 2021 , Journal of Computational Neuroscience)

   Objectively differentiating patient mental states based on electrical activity, as opposed to overt behavior, is a fundamental neuroscience problem with medical applications, such as identifying patients in locked-in state vs. coma. Electroencephalography (EEG), which detects millisecond-level changes in brain activity across a range of frequencies, allows for assessment of external stimulus processing by the brain in a non-invasive manner. We applied machine learning methods to 26-channel EEG data of 24 fluent Deaf signers watching videos of sign language sentences (comprehension condition), and the same videos reversed in time (non-comprehension condition), to objectively separate vision-based high-level cognition states. While spectrotemporal parameters of the stimuli were identical in comprehension vs. non-comprehension conditions, the neural responses of participants varied based on their ability to linguistically decode visual data. We aimed to determine which subset of parameters (specific scalp regions or frequency ranges) would be necessary and sufficient for high classification accuracy of comprehension state. Optical flow, characterizing distribution of velocities of objects in an image, was calculated for each pixel of stimulus videos using MATLAB Vision toolbox. Coherence between optical flow in the stimulus and EEG neural response (per video, per participant) was then computed using canonical component analysis with NoiseTools toolbox. Peakmore »correlations were extracted for each frequency for each electrode, participant, and video. A set of standard ML algorithms were applied to the entire dataset (26 channels, frequencies from .2 Hz to 12.4 Hz, binned in 1 Hz increments), with consistent out-of-sample 100% accuracy for frequencies in .2-1 Hz range for all regions, and above 80% accuracy for frequencies < 4 Hz. Sparse Optimal Scoring (SOS) was then applied to the EEG data to reduce the dimensionality of the features and improve model interpretability. SOS with elastic-net penalty resulted in out-of-sample classification accuracy of 98.89%. The sparsity pattern in the model indicated that frequencies between 0.2–4 Hz were primarily used in the classification, suggesting that underlying data may be group sparse. Further, SOS with group lasso penalty was applied to regional subsets of electrodes (anterior, posterior, left, right). All trials achieved greater than 97% out-of-sample classification accuracy. The sparsity patterns from the trials using 1 Hz bins over individual regions consistently indicated frequencies between 0.2–1 Hz were primarily used in the classification, with anterior and left regions performing the best with 98.89% and 99.17% classification accuracy, respectively. While the sparsity pattern may not be the unique optimal model for a given trial, the high classification accuracy indicates that these models have accurately identified common neural responses to visual linguistic stimuli. Cortical tracking of spectro-temporal change in the visual signal of sign language appears to rely on lower frequencies proportional to the N400/P600 time-domain evoked response potentials, indicating that visual language comprehension is grounded in predictive processing mechanisms.« less