HSMM with Gaussian Processes emissions: A method for interpretable modeling of neuroimaging data
Poster No:
1918
Submission Type:
Abstract Submission
Authors:
Yunier Prieur-Coloma1,2, David Araya3,1, Felipe Torres1, WAEL EL-DEREDY1,4,5
Institutions:
1Brain Dynamics Laboratory, Universidad de Valparaíso, Valparaíso, Chile, 2Programa de Doctorado en Ciencias e Ingeniería para la Salud, Universidad de Valparaíso,, Valparaíso, Chile, 3Facultad de Ingeniería, Universidad Andrés Bello, Viña del Mar, Chile, 4ValgrAI, Valencian Graduate School Research Network of Artificial Intelligence, Valencia, Spain, 5Department of Electronic Engineering, School of Engineering, Universitat de València, Valencia, Spain
First Author:
Yunier Prieur-Coloma
Brain Dynamics Laboratory, Universidad de Valparaíso|Programa de Doctorado en Ciencias e Ingeniería para la Salud, Universidad de Valparaíso,
Valparaíso, Chile|Valparaíso, Chile
Brain Dynamics Laboratory, Universidad de Valparaíso|Programa de Doctorado en Ciencias e Ingeniería para la Salud, Universidad de Valparaíso,
Valparaíso, Chile|Valparaíso, Chile
Co-Author(s):
David Araya
Facultad de Ingeniería, Universidad Andrés Bello|Brain Dynamics Laboratory, Universidad de Valparaíso
Viña del Mar, Chile|Valparaíso, Chile
Facultad de Ingeniería, Universidad Andrés Bello|Brain Dynamics Laboratory, Universidad de Valparaíso
Viña del Mar, Chile|Valparaíso, Chile
WAEL EL-DEREDY
Brain Dynamics Laboratory, Universidad de Valparaíso|ValgrAI, Valencian Graduate School Research Network of Artificial Intelligence|Department of Electronic Engineering, School of Engineering, Universitat de València
Valparaíso, Chile|Valencia, Spain|Valencia, Spain
Brain Dynamics Laboratory, Universidad de Valparaíso|ValgrAI, Valencian Graduate School Research Network of Artificial Intelligence|Department of Electronic Engineering, School of Engineering, Universitat de València
Valparaíso, Chile|Valencia, Spain|Valencia, Spain
Introduction:
Cognitive function emerges from the connectivity of large-scale brain networks. The brain has the ability to adapt to changing cognitive demands and tasks, transitioning between different network configurations (brain states) [1]. Brain states require an efficient coordination between the regions across the whole brain. It is generally agreed that the coordination mechanism involves the synchronization of oscillatory modes among neuronal populations at specific frequencies. Hence, it has been hypothesized that oscillatory modes do not have a local origin, instead they are associated with synchronization among distant neural assemblies [2]. We capitalize on recent advances from interpretable machine learning methods and Hidden Semi Markov Model (HSMM) theory to propose a method for analysis of large-scale brain networks dynamics that provides a plausible interpretation of oscillatory modes from spontaneous neural activity.
Methods:
HSMM is a generative parametric model that expresses the beliefs about how a sequence of discrete states gives rise to the observed M/EEG data. Each state emits a sequence of observations through the emission model, which defines the law governing the generation of observations. In this work, we used emission models based on Multi-Output Gaussian Processes (MOGPs) with spectral kernels whose parameters enable an interpretation of the oscillatory modes in each brain state.
Our HSMM implementation assumes that each brain state is represented by a MOGP. MOGPs is a machine learning method for discovering intrinsic patterns in data by modeling statistical interdependencies between channels or brain regions [3]. A MOGPs is parametrized by a mean function, and a kernel or covariance function that express the law governing how the data correlate. We used the Cross-Spectrum Mixture (CSM) kernel to estimate the cross-covariance function between brain regions [4]. The CSM kernel provide us a biophysically consistent formulation by assuming brain regions share the same oscillatory modes. CSM kernel comprises different oscillatory modes, and its hyperparameters provide a plausible description of each one, including its energy across brain regions.
To estimate the HSMM-MOGP parameters, we used an Expectation-Maximization iterative procedure. The expectation-step involves sampling observation sequences and their corresponding states jointly, using the Forward Filtering-Backward Sampling algorithm [5]. Afterward, in the maximization step, the HSMM parameters and CSM hyperparameters are updated using the observations and states sampled in the previous expectation-step. The HSMM-MOGP is validated by generating synthetic data from two regions with known parameters a priori, and using it for model training as shown in Figure 1. Subsequently, the oscillatory modes properties estimated by the model are compared with the ground truth.
Our HSMM implementation assumes that each brain state is represented by a MOGP. MOGPs is a machine learning method for discovering intrinsic patterns in data by modeling statistical interdependencies between channels or brain regions [3]. A MOGPs is parametrized by a mean function, and a kernel or covariance function that express the law governing how the data correlate. We used the Cross-Spectrum Mixture (CSM) kernel to estimate the cross-covariance function between brain regions [4]. The CSM kernel provide us a biophysically consistent formulation by assuming brain regions share the same oscillatory modes. CSM kernel comprises different oscillatory modes, and its hyperparameters provide a plausible description of each one, including its energy across brain regions.
To estimate the HSMM-MOGP parameters, we used an Expectation-Maximization iterative procedure. The expectation-step involves sampling observation sequences and their corresponding states jointly, using the Forward Filtering-Backward Sampling algorithm [5]. Afterward, in the maximization step, the HSMM parameters and CSM hyperparameters are updated using the observations and states sampled in the previous expectation-step. The HSMM-MOGP is validated by generating synthetic data from two regions with known parameters a priori, and using it for model training as shown in Figure 1. Subsequently, the oscillatory modes properties estimated by the model are compared with the ground truth.
·Figure 1. Synthetic time series generated from an HSMM-MOGP for two regions as ground truth for model training.
Results:
HSMM-MOGP was able to estimate the parameters used to generate the dynamics in synthetic data. The CSM kernels recover the specific properties of the oscillatory modes prevailing in the stationary time segments in which their respective states are active. In Figure 2, the solid line describes the properties of the oscillatory modes considering both regions simultaneously during data simulation, while the dashed line presents the estimation of these properties after training the HSMM-MOGP. The hyperparameters of CSM kernels provided a clear meaning regarding oscillatory modes in all channels.
·Figure 2. Cross-spectrum from the CSM hyperparameters.
Conclusions:
This work presents a method for analysis of large-scale brain networks dynamics using HSMM and MOGPs. The results show the capability of the model to provide parameters that enable the interpretation of brain oscillatory modes.
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural)
EEG/MEG Modeling and Analysis 2
Methods Development 1
Multivariate Approaches
Keywords:
Data analysis
Electroencephaolography (EEG)
Machine Learning
Modeling
Multivariate
Other - brain dynamics analysis; neuroimaging data; interpretable modeling
1|2Indicates the priority used for review
Provide references using author date format
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Available: https://papers.nips.cc/paper_files/paper/2015/hash/285ab9448d2751ee57ece7f762c39095-
Abstract.html
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