arXiv subjects

Hernando Ombao

Publications and source records attributed to Hernando Ombao.

At least 37 records · Page 2Linked to original sources

arXiv2025

Nonlinear Causality in Time Series Networks: With Application to Motor Imagery vs Execution

Causal interactions in time series networks can be dynamic and nonlinear, making it difficult to identify them using conventional linear causality estimations. We propose a novel approach, called Threshold Autoregressive Modeling for Causality (TAR4C), a causality detection approach built on threshold autoregressive (TAR) models, where a potential driver (cause variable) acts both as a predictor and as a trigger (switching threshold) that governs which autoregressive process the target (effect variable) follows. Threshold nonlinearity is conceptualized here to determine causality. The flow of the target is forced to transition between regimes with distinct dynamics when the driver exceeds a data-driven threshold in the past. We propose a two-stage inference procedure: Stage 1 tests for threshold connectivity (TC); Stage 2, conditional on a detected threshold effect, estimates threshold Granger causality (TGC). TAR4C is applied to a multichannel EEG dataset collected from a motor imagery and execution experiment. Delay-dependent directional interactions are observed among channels across different sites of the EEG map. The real-world application demonstrates the usefulness of the proposed approach for determining nonlinear causal connectivity in complex time-series networks, such as brain circuitry. The proposed model-based methodology extends to other complex networks of time series.

stat.AP↗

arXiv2025

EEG-MSAF: An Interpretable Microstate Framework uncovers Default-Mode Decoherence in Early Neurodegeneration

Dementia (DEM) is a growing global health challenge, underscoring the need for early and accurate diagnosis. Electroencephalography (EEG) provides a non-invasive window into brain activity, but conventional methods struggle to capture its transient complexity. We present the \textbf{EEG Microstate Analysis Framework (EEG-MSAF)}, an end-to-end pipeline that leverages EEG microstates discrete, quasi-stable topographies to identify DEM-related biomarkers and distinguish DEM, mild cognitive impairment (MCI), and normal cognition (NC). EEG-MSAF comprises three stages: (1) automated microstate feature extraction, (2) classification with machine learning (ML), and (3) feature ranking using Shapley Additive Explanations (SHAP) to highlight key biomarkers. We evaluate on two EEG datasets: the public Chung-Ang University EEG (CAUEEG) dataset and a clinical cohort from Thessaloniki Hospital. Our framework demonstrates strong performance and generalizability. On CAUEEG, EEG-MSAF-SVM achieves \textbf{89\% $\pm$ 0.01 accuracy}, surpassing the deep learning baseline CEEDNET by \textbf{19.3\%}. On the Thessaloniki dataset, it reaches \textbf{95\% $\pm$ 0.01 accuracy}, comparable to EEGConvNeXt. SHAP analysis identifies mean correlation and occurrence as the most informative metrics: disruption of microstate C (salience/attention network) dominates DEM prediction, while microstate F, a novel default-mode pattern, emerges as a key early biomarker for both MCI and DEM. By combining accuracy, generalizability, and interpretability, EEG-MSAF advances EEG-based dementia diagnosis and sheds light on brain dynamics across the cognitive spectrum.

eess.SP↗

arXiv2025

Hodge-Decomposition of Functional Brain Networks

We propose to analyze dynamically changing brain networks by decomposing them into three orthogonal components through the Hodge decomposition. We propose to quantify the magnitude and relative strength of each component. We performed extensive simulation studies with known ground truth. The Hodge decomposition is then applied to the dynamically changing human brain networks obtained from a resting-state functional magnetic resonance imaging study. Our results indicate that the components of the Hodge decomposition contain biologically interpretable topological features that provide statistically significant findings not easily captured by traditional methods.

q-bio.NC↗

arXiv2025

Club Exco: clustering brain extreme communities from multi-channel EEG data

Current methods for clustering brain networks over time often rely on cross-dependence measures computed from the entire range of EEG signals, which can obscure information specific to extreme neural activity. To overcome this, we introduce Club Exco, a novel clustering method grounded in extreme value theory, designed to detect brain communities with co-occurring high-amplitude EEG events. By focusing on tail behavior, Club Exco isolates extreme-value synchrony across channels, offering new insights into seizure dynamics. We apply Club Exco to neonatal EEG recordings from 30 patients (13 seizure-free and 17 with clinically confirmed seizures). Our method identifies robust ``brain extreme communities'' and constructs Extreme Connectivity Persistence matrices that summarize how often channels exhibit synchronous extremes across time. Seizure patients exhibit more persistent and variable clustering among non-adjacent regions, suggesting seizure propagation, while non-seizure patients show more consistent clustering in anatomically adjacent regions. Compared to coherence-based methods (e.g., Hierarchical Cluster Coherence procedure), Club Exco captures distinct, seizure-associated connectivity patterns, especially in high-amplitude segments. These results highlight Club Exco's potential to characterize extreme neural events and inform clinical understanding of seizure localization and spread.

stat.ME↗

arXiv2025

Functional-Coefficient Models for Multivariate Time Series in Designed Experiments: with Applications to Brain Signals

To study the neurophysiological basis of attention deficit hyperactivity disorder (ADHD), clinicians use electroencephalography (EEG) which record neuronal electrical activity on the cortex. Instead of focusing on single-channel spectral power, a novel framework for investigating interactions (dependence) between channels in the entire network is proposed. Although dependence measures such as coherence and partial directed coherence (PDC) are well explored in studying brain connectivity, these measures only capture linear dependence. Moreover, in designed clinical experiments, these dependence measures are observed to vary across subjects even within a homogeneous group. To address these limitations, we propose the mixed-effects functional-coefficient autoregressive (MXFAR) model which captures between-subject variation by incorporating subject-specific random effects. The advantages of the MXFAR model are the following: (i) it captures potential non-linear dependence between channels; (ii) it is nonparametric and hence flexible and robust to model mis-specification; (iii) it can capture differences between groups when they exist; (iv) it accounts for variation across subjects; (v) the framework easily incorporates well-known inference methods from mixed-effects models; (vi) it can be generalized to accommodate various covariates and factors. Then, we formulate a novel non-linear spectral measure, the functional partial directed coherence (fPDC), to extract dynamic cross-dependence patterns at different frequency oscillations. Finally, we apply the proposed MXFAR-fPDC framework to analyze multichannel EEG signals and report novel findings on altered brain functional networks in ADHD patients.

stat.AP↗

arXiv2025

FCPCA: Fuzzy clustering of high-dimensional time series based on common principal component analysis

Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption that clusters are sufficiently separated with little overlap. However, real-world data often defy this assumption, exhibiting overlapping distributions or overlapping clouds of points and blurred boundaries between clusters. Fuzzy clustering offers a compelling alternative by allowing partial membership in multiple clusters, making it well-suited for these ambiguous scenarios. Despite its advantages, current fuzzy clustering methods primarily focus on univariate time series, and for multivariate cases, even datasets of moderate dimensionality become computationally prohibitive. This challenge is further exacerbated when dealing with time series of varying lengths, leaving a clear gap in addressing the complexities of modern datasets. This work introduces a novel fuzzy clustering approach based on common principal component analysis to address the aforementioned shortcomings. Our method has the advantage of efficiently handling high-dimensional multivariate time series by reducing dimensionality while preserving critical temporal features. Extensive numerical results show that our proposed clustering method outperforms several existing approaches in the literature. An interesting application involving brain signals from different drivers recorded from a simulated driving experiment illustrates the potential of the approach.

stat.ME↗

arXiv2025

Granger Causality in High-Dimensional Networks of Time Series

A novel approach is developed for discovering directed connectivity between specified pairs of nodes in a high-dimensional network (HDN) of brain signals. To accurately identify causal connectivity for such specified objectives, it is necessary to properly address the influence of all other nodes within the network. The proposed procedure herein starts with the estimation of a low-dimensional representation of the other nodes in the network utilizing (frequency-domain-based) spectral dynamic principal component analysis (sDPCA). The resulting scores can then be removed from the nodes of interest, thus eliminating the confounding effect of other nodes within the HDN. Accordingly, causal interactions can be dissected between nodes that are isolated from the effects of the network. Extensive simulations have demonstrated the effectiveness of this approach as a tool for causality analysis in complex time series networks. The proposed methodology has also been shown to be applicable to multichannel EEG networks.

stat.AP↗

arXiv2025

Time-Varying Dispersion Integer-Valued GARCH Models

We propose a general class of INteger-valued Generalized AutoRegressive Conditionally Heteroscedastic (INGARCH) processes by allowing time-varying mean and dispersion parameters, which we call time-varying dispersion INGARCH (tv-DINGARCH) models. More specifically, we consider mixed Poisson INGARCH models and allow for dynamic modeling of the dispersion parameter (as well as the mean), similar to the spirit of the ordinary GARCH models. We derive conditions to obtain first and second-order stationarity, and ergodicity as well. Estimation of the parameters is addressed and their associated asymptotic properties are established as well. A restricted bootstrap procedure is proposed for testing constant dispersion against time-varying dispersion. Monte Carlo simulation studies are presented for checking point estimation, standard errors, and the performance of the restricted bootstrap approach. We apply the tv-DINGARCH process to model the weekly number of reported measles infections in North Rhine-Westphalia, Germany, from January 2001 to May 2013, and compare its performance to the ordinary INGARCH approach.

stat.ME↗

arXiv2025

From Density to Void: Why Brain Networks Fail to Reveal Complex Higher-Order Structures

In brain network analysis using resting-state fMRI, there is growing interest in modeling higher-order interactions beyond simple pairwise connectivity via persistent homology. Despite the promise of these advanced topological tools, robust and consistently observed higher-order interactions over time remain elusive. In this study, we investigate why conventional analyses often fail to reveal complex higher-order structures - such as interactions involving four or more nodes - and explore whether such interactions truly exist in functional brain networks. We utilize a simplicial complex framework often used in persistent homology to address this question.

q-bio.NC↗

arXiv2025

SFC-GAN: A Generative Adversarial Network for Brain Functional and Structural Connectome Translation

Modern brain imaging technologies have enabled the detailed reconstruction of human brain connectomes, capturing structural connectivity (SC) from diffusion MRI and functional connectivity (FC) from functional MRI. Understanding the intricate relationships between SC and FC is vital for gaining deeper insights into the brain's functional and organizational mechanisms. However, obtaining both SC and FC modalities simultaneously remains challenging, hindering comprehensive analyses. Existing deep generative models typically focus on synthesizing a single modality or unidirectional translation between FC and SC, thereby missing the potential benefits of bi-directional translation, especially in scenarios where only one connectome is available. Therefore, we propose Structural-Functional Connectivity GAN (SFC-GAN), a novel framework for bidirectional translation between SC and FC. This approach leverages the CycleGAN architecture, incorporating convolutional layers to effectively capture the spatial structures of brain connectomes. To preserve the topological integrity of these connectomes, we employ a structure-preserving loss that guides the model in capturing both global and local connectome patterns while maintaining symmetry. Our framework demonstrates superior performance in translating between SC and FC, outperforming baseline models in similarity and graph property evaluations compared to ground truth data, each translated modality can be effectively utilized for downstream classification.

cs.CV↗

arXiv2024

Measuring Information Transfer Between Nodes in a Brain Network through Spectral Transfer Entropy

Brain connectivity characterizes interactions between different regions of a brain network during resting-state or performance of a cognitive task. In studying brain signals such as electroencephalograms (EEG), one formal approach to investigating connectivity is through an information-theoretic causal measure called transfer entropy (TE). To enhance the functionality of TE in brain signal analysis, we propose a novel methodology that captures cross-channel information transfer in the frequency domain. Specifically, we introduce a new measure, the spectral transfer entropy (STE), to quantify the magnitude and direction of information flow from a band-specific oscillation of one channel to another band-specific oscillation of another channel. The main advantage of our proposed approach is that it formulates TE in a novel way to perform inference on band-specific oscillations while maintaining robustness to the inherent problems associated with filtering. In addition, an advantage of STE is that it allows adjustments for multiple comparisons to control false positive rates. Another novel contribution is a simple yet efficient method for estimating STE using vine copula theory. This method can produce an exact zero estimate of STE (which is the boundary point of the parameter space) without the need for bias adjustments. With the vine copula representation, a null copula model, which exhibits zero STE, is defined, thus enabling straightforward significance testing through standard resampling. Lastly, we demonstrate the advantage of the proposed STE measure through numerical experiments and provide interesting and novel findings on the analysis of EEG data in a visual-memory experiment.

stat.ME↗

arXiv2024

A Robust Topological Framework for Detecting Regime Changes in Multi-Trial Experiments with Application to Predictive Maintenance

We present a general and flexible framework for detecting regime changes in complex, non-stationary data across multi-trial experiments. Traditional change point detection methods focus on identifying abrupt changes within a single time series (single trial), targeting shifts in statistical properties such as the mean, variance, and spectrum over time within that sole trial. In contrast, our approach considers changes occurring across trials, accommodating changes that may arise within individual trials due to experimental inconsistencies, such as varying delays or event duration. By leveraging diverse metrics to analyze time-frequency characteristics specifically topological changes in the spectrum and spectrograms, our approach offers a comprehensive framework for detecting such variations. Our approach can handle different scenarios with various statistical assumptions, including varying levels of stationarity within and across trials, making our framework highly adaptable. We validate our approach through simulations using time-varying autoregressive processes that exhibit different regime changes. Our results demonstrate the effectiveness of detecting changes across trials under diverse conditions. Furthermore, we illustrate the effectiveness of our method by applying it to predictive maintenance using the NASA bearing dataset. By analyzing the time-frequency characteristics of vibration signals recorded by accelerometers, our approach accurately identifies bearing failures, showcasing its strong potential for early fault detection in mechanical systems.

stat.ME↗

arXiv2024

Granger Causality for Mixed Time Series Generalized Linear Models: A Case Study on Multimodal Brain Connectivity

This paper is motivated by studies in neuroscience experiments to understand interactions between nodes in a brain network using different types of data modalities that capture different distinct facets of brain activity. To assess Granger-causality, we introduce a flexible framework through a general class of models that accommodates mixed types of data (binary, count, continuous, and positive components) formulated in a generalized linear model (GLM) fashion. Statistical inference for causality is performed based on both frequentist and Bayesian approaches, with a focus on the latter. Here, we develop a procedure for conducting inference through the proposed Bayesian mixed time series model. By introducing spike and slab priors for some parameters in the model, our inferential approach guides causality order selection and provides proper uncertainty quantification. The proposed methods are then utilized to study the rat spike train and local field potentials (LFP) data recorded during the olfaction working memory task. The proposed methodology provides critical insights into the causal relationship between the rat spiking activity and LFP spectral power. Specifically, power in the LFP beta band is predictive of spiking activity 300 milliseconds later, providing a novel analytical tool for this area of emerging interest in neuroscience and demonstrating its usefulness and flexibility in the study of causality in general.

stat.ME↗

arXiv2024

Correlation-Adjusted Simultaneous Testing for Ultra High-dimensional Grouped Data

Epigenetics plays a crucial role in understanding the underlying molecular processes of several types of cancer as well as the determination of innovative therapeutic tools. To investigate the complex interplay between genetics and environment, we develop a novel procedure to identify differentially methylated probes (DMPs) among cases and controls. Statistically, this translates to an ultra high-dimensional testing problem with sparse signals and an inherent grouping structure. When the total number of variables being tested is massive and typically exhibits some degree of dependence, existing group-wise multiple comparisons adjustment methods lead to inflated false discoveries. We propose a class of Correlation-Adjusted Simultaneous Testing (CAST) procedures incorporating the general dependence among probes within and between genes to control the false discovery rate (FDR). Simulations demonstrate that CASTs have superior empirical power while maintaining the FDR compared to the benchmark group-wise. Moreover, while the benchmark fails to control FDR for small-sized grouped correlated data, CAST exhibits robustness in controlling FDR across varying group sizes. In bladder cancer data, the proposed CAST method confirms some existing differentially methylated probes implicated with the disease (Langevin, et. al., 2014). However, CAST was able to detect novel DMPs that the previous study (Langevin, et. al., 2014) failed to identify. The CAST method can accurately identify significant potential biomarkers and facilitates informed decision-making aligned with precision medicine in the context of complex data analysis.

stat.ME↗

arXiv2024

Classification of High-dimensional Time Series in Spectral Domain using Explainable Features

Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which can be restrictive for real-world applications. In this article, we propose a model-based approach for classifying high-dimensional stationary time series by assuming sparsity in the difference between inverse SDMs. Our approach emphasizes the interpretability of model parameters, making it especially suitable for fields like neuroscience, where understanding differences in brain network connectivity across various states is crucial. The estimators for model parameters demonstrate consistency under appropriate conditions. We further propose using standard deep learning optimizers for parameter estimation, employing techniques such as mini-batching and learning rate scheduling. Additionally, we introduce a method to screen the most discriminatory frequencies for classification, which exhibits the sure screening property under general conditions. The flexibility of the proposed model allows the significance of covariates to vary across frequencies, enabling nuanced inferences and deeper insights into the underlying problem. The novelty of our method lies in the interpretability of the model parameters, addressing critical needs in neuroscience. The proposed approaches have been evaluated on simulated examples and the `Alert-vs-Drowsy' EEG dataset.

stat.ML↗

arXiv2024

Granger Causality using Neural Networks

Dependence between nodes in a network is an important concept that pervades many areas including finance, politics, sociology, genomics and the brain sciences. One way to characterize dependence between components of a multivariate time series data is via Granger Causality (GC). Standard traditional approaches to GC estimation / inference commonly assume linear dynamics, however such simplification does not hold in many real-world applications where signals are inherently non-linear. In such cases, imposing linear models such as vector autoregressive (VAR) models can lead to mis-characterization of true Granger Causal interactions. To overcome this limitation, Tank et al (IEEE Transactions on Pattern Analysis and Machine Learning, 2022) proposed a solution that uses neural networks with sparse regularization penalties. The regularization encourages learnable weights to be sparse, which enables inference on GC. This paper overcomes the limitations of current methods by leveraging advances in machine learning and deep learning which have been demonstrated to learn hidden patterns in the data. We propose novel classes of models that can handle underlying non-linearity in a computationally efficient manner, simultaneously providing GC and lag order selection. Firstly, we present the Learned Kernel VAR (LeKVAR) model that learns kernel parameterized by a shared neural net followed by penalization on learnable weights to discover GC structure. Secondly, we show one can directly decouple lags and individual time series importance via decoupled penalties. This is important as we want to select the lag order during the process of GC estimation. This decoupling acts as a filtering and can be extended to any DL model including Multi-Layer Perceptrons (MLP), Recurrent Neural Networks (RNN), Long Short Term Memory Networks (LSTM), Transformers etc, for simultaneous GC estimation and lag selection.

stat.ML↗

arXiv2024

Topological Analysis of Seizure-Induced Changes in Brain Hierarchy Through Effective Connectivity

Traditional Topological Data Analysis (TDA) methods, such as Persistent Homology (PH), rely on distance measures (e.g., cross-correlation, partial correlation, coherence, and partial coherence) that are symmetric by definition. While useful for studying topological patterns in functional brain connectivity, the main limitation of these methods is their inability to capture the directional dynamics - which is crucial for understanding effective brain connectivity. We propose the Causality-Based Topological Ranking (CBTR) method, which integrates Causal Inference (CI) to assess effective brain connectivity with Hodge Decomposition (HD) to rank brain regions based on their mutual influence. Our simulations confirm that the CBTR method accurately and consistently identifies hierarchical structures in multivariate time series data. Moreover, this method effectively identifies brain regions showing the most significant interaction changes with other regions during seizures using electroencephalogram (EEG) data. These results provide novel insights into the brain's hierarchical organization and illuminate the impact of seizures on its dynamics.

q-bio.NC↗

arXiv2024

Statistics of Extremes for Neuroscience

This chapter illustrates how tools from univariate and multivariate statistics of extremes can complement classical methods used to study brain signals and enhance the understanding of brain activity and connectivity during specific cognitive tasks or abnormal episodes, such as an epileptic seizure.

stat.AP↗