Towards an Efficient Validation of Dynamical Whole-brain Models

2021 ◽  
Author(s):  
Kevin J. Wischnewski ◽  
Simon B. Eickhoff ◽  
Viktor K. Jirsa ◽  
Oleksandr V. Popovych
Keyword(s):  
Structural Connectivity ◽  
Three Dimensional ◽  
Bayesian Optimization ◽  
High Dimensional ◽  
Brain Dynamics ◽  
Model Parameters ◽  
Phase Oscillators ◽  
Dimensional Parameter ◽  
Whole Brain ◽  
Brain Models

Abstract Simulating the resting-state brain dynamics via mathematical whole-brain models requires an optimal selection of parameters, which determine the model’s capability to replicate empirical data. Since the parameter optimization via a grid search (GS) becomes unfeasible for high-dimensional models, we evaluate several alternative approaches to maximize the correspondence between simulated and empirical functional connectivity. A dense GS serves as a benchmark to assess the performance of four optimization schemes: Nelder-Mead Algorithm (NMA), Particle Swarm Optimization (PSO), Covariance Matrix Adaptation Evolution Strategy (CMAES) and Bayesian Optimization (BO). To compare them, we employ an ensemble of coupled phase oscillators built upon individual empirical structural connectivity of 105 healthy subjects. We determine optimal model parameters from two- and three-dimensional parameter spaces and show that the overall fitting quality of the tested methods can compete with the GS. There are, however, marked differences in the required computational resources and stability properties, which we also investigate before proposing CMAES and BO as efficient alternatives to a high-dimensional GS. For the three-dimensional case, these methods generated similar results as the GS, but within less than 6% of the computation time. Our results contribute to an efficient validation of models for personalized simulations of brain dynamics.

scholarly journals Tractography density affects whole-brain structural architecture and resting-state dynamical modeling

2020 ◽  
Author(s):  
Kyesam Jung ◽  
Simon B. Eickhoff ◽  
Oleksandr V. Popovych
Keyword(s):  
Data Processing ◽  
Resting State ◽  
Optimal Parameter ◽  
Structural Connectivity ◽  
Model Performance ◽  
Brain Dynamics ◽  
Dynamical Modeling ◽  
Whole Brain ◽  
Brain Connectome ◽  
Network Properties

AbstractDynamical modeling of the resting-state brain dynamics essentially relies on the empirical neuroimaging data utilized for the model derivation and validation. There is however still no standardized data processing for magnetic resonance imaging pipelines and the structural and functional connectomes involved in the models. In this study, we thus address how the parameters of diffusion-weighted data processing for structural connectivity (SC) can influence the validation results of the whole-brain mathematical models and search for the optimal parameter settings. On this way, we simulate the functional connectivity by systems of coupled oscillators, where the underlying network is constructed from the empirical SC and evaluate the performance of the models for varying parameters of data processing. For this, we introduce a set of simulation conditions including the varying number of total streamlines of the whole-brain tractography (WBT) used for extraction of SC, cortical parcellations based on functional and anatomical brain properties and distinct model fitting modalities. We observed that the graph-theoretical network properties of structural connectome can be affected by varying tractography density and strongly relate to the model performance. We explored free parameters of the considered models and found the optimal parameter configurations, where the model dynamics closely replicates the empirical data. We also found that the optimal number of the total streamlines of WBT can vary for different brain atlases. Consequently, we suggest a way how to improve the model performance based on the network properties and the optimal parameter configurations from multiple WBT conditions. Furthermore, the population of subjects can be stratified into subgroups with divergent behaviors induced by the varying number of WBT streamlines such that different recommendations can be made with respect to the data processing for individual subjects and brain parcellations.Author summaryThe human brain connectome at macro level provides an anatomical constitution of inter-regional connections through the white matter in the brain. Understanding the brain dynamics grounded on the structural architecture is one of the most studied and important topics actively debated in the neuroimaging research. However, the ground truth for the adequate processing and reconstruction of the human brain connectome in vivo is absent, which is crucial for evaluation of the results of the data-driven as well as model-based approaches to brain investigation. In this study we thus evaluate the effect of the whole-brain tractography density on the structural brain architecture by varying the number of total axonal fiber streamlines. The obtained results are validated throughout the dynamical modeling of the resting-state brain dynamics. We found that the tractography density may strongly affect the graph-theoretical network properties of the structural connectome. The obtained results also show that a dense whole-brain tractography is not always the best condition for the modeling, which depends on a selected brain parcellation used for the calculation of the structural connectivity and derivation of the model network. Our findings provide suggestions for the optimal data processing for neuroimaging research and brain modeling.

scholarly journals Efficient ensemble generation for uncertain correlated parameters in atmospheric chemical models

2021 ◽  
Author(s):  
Annika Vogel ◽  
Hendrik Elbern
Keyword(s):  
Forecast Model ◽  
High Dimensional ◽  
Biogenic Emissions ◽  
Model Parameters ◽  
Emission Rates ◽  
Model Uncertainties ◽  
Dimensional Parameter ◽  
Novel Approach ◽  
Correlated Parameters ◽  
Ensemble Generation

Abstract. Atmospheric chemical forecasts highly rely on various model parameters, which are often insufficiently known, as emission rates and deposition velocities. However, a reliable estimation of resulting uncertainties by an ensemble of forecasts is impaired by the high-dimensionality of the system. This study presents a novel approach to efficiently perturb atmospheric-chemical model parameters according to their leading coupled uncertainties. The algorithm is based on the idea that the forecast model acts as a dynamical system inducing multi-variational correlations of model uncertainties. The specific algorithm presented in this study is designed for parameters which depend on local environmental conditions and consists of three major steps: (1) an efficient assessment of various sources of model uncertainties spanned by independent sensitivities, (2) an efficient extraction of leading coupled uncertainties using eigenmode decomposition, and (3) an efficient generation of perturbations for high-dimensional parameter fields by the Karhunen-Loéve expansion. Due to their perceived simulation challenge the method has been applied to biogenic emissions of five trace gases, considering state-dependent sensitivities to local atmospheric and terrestrial conditions. Rapidly decreasing eigenvalues state high spatial- and cross-correlations of regional biogenic emissions, which are represented by a low number of dominating components. Consequently, leading uncertainties can be covered by low number of perturbations enabling ensemble sizes of the order of 10 members. This demonstrates the suitability of the algorithm for efficient ensemble generation for high-dimensional atmospheric chemical parameters.

scholarly journals New Estimators of the Bayes Factor for Models with High-Dimensional Parameter and/or Latent Variable Spaces

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 399
Author(s):  
Anna Pajor
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Bayes Factor ◽  
High Dimensional ◽  
Model Parameters ◽  
Posterior Odds ◽  
Dimensional Parameter ◽  
Data Set ◽  
Multivariate Stochastic Volatility ◽  
Competing Models

Formal Bayesian comparison of two competing models, based on the posterior odds ratio, amounts to estimation of the Bayes factor, which is equal to the ratio of respective two marginal data density values. In models with a large number of parameters and/or latent variables, they are expressed by high-dimensional integrals, which are often computationally infeasible. Therefore, other methods of evaluation of the Bayes factor are needed. In this paper, a new method of estimation of the Bayes factor is proposed. Simulation examples confirm good performance of the proposed estimators. Finally, these new estimators are used to formally compare different hybrid Multivariate Stochastic Volatility–Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MSV-MGARCH) models which have a large number of latent variables. The empirical results show, among other things, that the validity of reduction of the hybrid MSV-MGARCH model to the MGARCH specification depends on the analyzed data set as well as on prior assumptions about model parameters.

scholarly journals A METHOD FOR INTEGRATIVE ANALYSIS OF LOCAL AND GLOBAL BRAIN DYNAMICS

2021 ◽  
Author(s):  
Robyn L. Miller ◽  
Victor M Vergara ◽  
Vince Calhoun
Keyword(s):  
Resting State ◽  
Network Connectivity ◽  
High Dimensional ◽  
Group Differences ◽  
Brain Dynamics ◽  
Whole Brain ◽  
Time Resolved ◽  
Localized Patterns ◽  
Global Brain ◽  
The Brain

The most common pipelines for studying time-varying network connectivity in resting state functional magnetic resonance imaging (rs-fMRI) operate at the whole brain level, capturing a small discrete set of 'states' that best represent time-resolved joint measures of connectivity over all network pairs in the brain. This whole-brain hidden Markov model (HMM) approach 'uniformizes' the dynamics over what is typically more than 1000 pairs of networks, forcing each time-resolved high-dimensional observation into its best-matched high-dimensional state. While straightforward and convenient, this HMM simplification obscures functional and temporal nonstationarities that could reveal systematic, informative features of resting state brain dynamics at a more granular scale. We introduce a framework for studying functionally localized dynamics that intrinsically embeds them within a whole-brain HMM frame of reference. The approach is validated in a large rs-fMRI schizophrenia study where it identifies group differences in localized patterns of entropy and dynamics that help explain consistently observed differences between schizophrenia patients and controls in occupancy of whole-brain dFNC states more mechanistically.

scholarly journals Parameter inference on brain network models with unknown node dynamics and spatial heterogeneity

2021 ◽  
Author(s):  
Viktor Sip ◽  
Spase Petkoski ◽  
Meysam Hashemi ◽  
Viktor K Jirsa
Keyword(s):  
Synthetic Data ◽  
Brain Network ◽  
Training Data ◽  
Neural Mass Model ◽  
Brain Dynamics ◽  
Model Parameters ◽  
Special Focus ◽  
Mass Model ◽  
Whole Brain ◽  
Neural Mass

Model-based data analysis of whole-brain dynamics links the observed data to model parameters in a network of neural masses. In recent years a special focus was placed on the role of regional variance of model parameters for the emergent activity. Such analyses however depend on the properties of the employed neural mass model, which is often obtained through a series of major simplifications or analogies. Here we propose a data-driven approach where the neural mass model needs not to be specified. Building on the recent progresses in identification of dynamical systems with neural networks, we propose a method to infer from the functional data both the neural mass model representing the regional dynamics as well as the region- and subject-specific parameters, while respecting the known network structure. We demonstrate on two synthetic data sets that our method is able to recover the original model parameters, and that the trained generative model produces dynamics resembling the training data both on the regional level and on the whole-brain level. The present approach opens a novel way to the analysis of resting-state fMRI with possible applications in understanding the changes of whole-brain dynamics during aging or in neurodegenerative diseases.

scholarly journals Constraining the parameters of high-dimensional models with active learning

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Sascha Caron ◽  
Tom Heskes ◽  
Sydney Otten ◽  
Bob Stienen
Keyword(s):  
Active Learning ◽  
Particle Physics ◽  
High Energy Physics ◽  
High Energy ◽  
Physical Models ◽  
High Dimensional ◽  
Physical Parameters ◽  
Model Parameters ◽  
Dimensional Parameter ◽  
Parameter Spaces

AbstractConstraining the parameters of physical models with $$>5-10$$>5-10 parameters is a widespread problem in fields like particle physics and astronomy. The generation of data to explore this parameter space often requires large amounts of computational resources. The commonly used solution of reducing the number of relevant physical parameters hampers the generality of the results. In this paper we show that this problem can be alleviated by the use of active learning. We illustrate this with examples from high energy physics, a field where simulations are often expensive and parameter spaces are high-dimensional. We show that the active learning techniques query-by-committee and query-by-dropout-committee allow for the identification of model points in interesting regions of high-dimensional parameter spaces (e.g. around decision boundaries). This makes it possible to constrain model parameters more efficiently than is currently done with the most common sampling algorithms and to train better performing machine learning models on the same amount of data. Code implementing the experiments in this paper can be found on GitHub "Image missing"

scholarly journals Synchronization dependent on spatial structures of a mesoscopic whole-brain network

2018 ◽  
Author(s):  
Hannah Choi ◽  
Stefan Mihalas
Keyword(s):  
Power Law ◽  
Brain Connectivity ◽  
Structural Connectivity ◽  
Brain Regions ◽  
Brain Network ◽  
Mammalian Brain ◽  
Phase Oscillators ◽  
Whole Brain ◽  
Mapping Algorithm ◽  
Complex Structural

We study how the spatial structure of connectivity shapes synchronization in a system of coupled phase oscillators on a mammalian whole-brain network at the mesoscopic level. Complex structural connectivity of the mammalian brain is believed to underlie the versatility of neural computations. The Allen Mouse Brain Connectivity Atlas constructed from viral tracing experiments together with a new mapping algorithm reveals that the connectivity has a significant spatial dependence: the connection strength decreases with distance between the regions, following a power law. However, there are a number of residuals above the power-law fit, predominantly for long-range connections. We show how these strong connections between distal brain regions promote rapid transitions between highly localized synchronization and more global synchronization as the amount of dispersion in the frequency distribution changes. This may explain the brain’s ability to switch rapidly between global and modularized computations.

scholarly journals Efficient ensemble generation for uncertain correlated parameters in atmospheric chemical models: a case study for biogenic emissions from EURAD-IM version 5

2021 ◽  
Vol 14 (9) ◽  
pp. 5583-5605
Author(s):  
Annika Vogel ◽  
Hendrik Elbern
Keyword(s):  
Forecast Model ◽  
High Dimensional ◽  
Biogenic Emissions ◽  
Model Parameters ◽  
Emission Rates ◽  
Parameter Uncertainties ◽  
Model Uncertainties ◽  
Dimensional Parameter ◽  
Correlated Parameters ◽  
Ensemble Generation

Abstract. Atmospheric chemical forecasts heavily rely on various model parameters, which are often insufficiently known, such as emission rates and deposition velocities. However, a reliable estimation of resulting uncertainties with an ensemble of forecasts is impaired by the high dimensionality of the system. This study presents a novel approach, which substitutes the problem into a low-dimensional subspace spanned by the leading uncertainties. It is based on the idea that the forecast model acts as a dynamical system inducing multivariate correlations of model uncertainties. This enables an efficient perturbation of high-dimensional model parameters according to their leading coupled uncertainties. The specific algorithm presented in this study is designed for parameters that depend on local environmental conditions and consists of three major steps: (1) an efficient assessment of various sources of model uncertainties spanned by independent sensitivities, (2) an efficient extraction of leading coupled uncertainties using eigenmode decomposition, and (3) an efficient generation of perturbations for high-dimensional parameter fields by the Karhunen–Loéve expansion. Due to their perceived simulation challenge, the method has been applied to biogenic emissions of five trace gases, considering state-dependent sensitivities to local atmospheric and terrestrial conditions. Rapidly decreasing eigenvalues state that highly correlated uncertainties of regional biogenic emissions can be represented by a low number of dominant components. Depending on the required level of detail, leading parameter uncertainties with dimensions of 𝒪(106) can be represented by a low number of about 10 ensemble members. This demonstrates the suitability of the algorithm for efficient ensemble generation for high-dimensional atmospheric chemical parameters.

scholarly journals Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4290
Author(s):  
Dongmei Zhang ◽  
Yuyang Zhang ◽  
Bohou Jiang ◽  
Xinwei Jiang ◽  
Zhijiang Kang
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Processes ◽  
Latent Variable ◽  
History Matching ◽  
Latent Variable Models ◽  
High Dimensional ◽  
Model Parameters ◽  
Variable Model ◽  
Assisted History Matching ◽  
Proxy Models

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

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