Modeling Dynamic Functional Connectivity with Latent Factor Gaussian Processes

Dynamic functional connectivity, as measured by the time-varying covariance of neurological signals, is believed to play an important role in many aspects of cognition. While many methods have been proposed, reliably establishing the presence and characteristics of brain connectivity is challenging due to the high dimensionality and noisiness of neuroimaging data. We present a latent factor Gaussian process model which addresses these challenges by learning a parsimonious representation of connectivity dynamics. The proposed model naturally allows for inference and visualization of connectivity dynamics. As an illustration of the scientific utility of the model, application to a data set of rat local field potential activity recorded during a complex non-spatial memory task provides evidence of stimuli differentiation.

[1]  A. V. D. Vaart,et al.  CONVERGENCE RATES OF POSTERIOR DISTRIBUTIONS FOR NONIID OBSERVATIONS By , 2018 .

[2]  Dimitri Van De Ville,et al.  The dynamic functional connectome: State-of-the-art and perspectives , 2017, NeuroImage.

[3]  Andrew Gelman,et al.  The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo , 2011, J. Mach. Learn. Res..

[4]  H. Ombao,et al.  SLEX Analysis of Multivariate Nonstationary Time Series , 2005 .

[5]  Daniel A. Handwerker,et al.  Periodic changes in fMRI connectivity , 2012, NeuroImage.

[6]  Chee-Ming Ting,et al.  Modeling Effective Connectivity in High-Dimensional Cortical Source Signals , 2016, IEEE Journal of Selected Topics in Signal Processing.

[7]  Mikkel N. Schmidt,et al.  Nonparametric Modeling of Dynamic Functional Connectivity in fMRI Data , 2016, NIPS 2015.

[8]  Tom Leonard,et al.  The Matrix-Logarithmic Covariance Model , 1996 .

[9]  A. V. D. Vaart,et al.  Convergence rates of posterior distributions for non-i.i.d. observations , 2007, 0708.0491.

[10]  Michael A. West,et al.  Time Series: Modeling, Computation, and Inference , 2010 .

[11]  N. Fortin,et al.  Nonspatial Sequence Coding in CA1 Neurons , 2016, The Journal of Neuroscience.

[12]  Steven Laureys,et al.  Human consciousness is supported by dynamic complex patterns of brain signal coordination , 2019, Science Advances.

[13]  D. Dunson,et al.  Sparse Bayesian infinite factor models. , 2011, Biometrika.

[14]  Mert R. Sabuncu,et al.  Machine learning in resting-state fMRI analysis , 2018, Magnetic resonance imaging.

[15]  Babak Shahbaba,et al.  A Bayesian supervised dual‐dimensionality reduction model for simultaneous decoding of LFP and spike train signals , 2017, Stat.

[16]  Martin A. Lindquist,et al.  Evaluating dynamic bivariate correlations in resting-state fMRI: A comparison study and a new approach , 2014, NeuroImage.

[17]  O. Aguilar,et al.  Bayesian Inference on Latent Structure in Time Series , 1998 .

[18]  James G. Scott,et al.  Handling Sparsity via the Horseshoe , 2009, AISTATS.

[19]  Chee-Ming Ting,et al.  Statistical models for brain signals with properties that evolve across trials , 2017, NeuroImage.

[20]  Dimitri Van De Ville,et al.  On spurious and real fluctuations of dynamic functional connectivity during rest , 2015, NeuroImage.

[21]  Gregor Kastner,et al.  Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models , 2016, 1602.08154.

[22]  Andrew Gordon Wilson,et al.  Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP) , 2015, ICML.

[23]  Van Der Vaart,et al.  Rates of contraction of posterior distributions based on Gaussian process priors , 2008 .

[24]  S. Balqis Samdin,et al.  Detecting State Changes in Community Structure of Functional Brain Networks Using a Markov-Switching Stochastic Block Model , 2019, 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019).

[25]  Neil D. Lawrence,et al.  Gaussian Process Latent Variable Models for Visualisation of High Dimensional Data , 2003, NIPS.

[26]  Jeff A. Bilmes,et al.  A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models , 1998 .

[27]  Nicholas Ayache,et al.  Fast and Simple Calculus on Tensors in the Log-Euclidean Framework , 2005, MICCAI.

[28]  Hongtu Zhu,et al.  Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging , 2009, Journal of the American Statistical Association.

[29]  S. Balqis Samdin,et al.  Estimating Dynamic Connectivity States in fMRI Using Regime-Switching Factor Models , 2018, IEEE Transactions on Medical Imaging.

[30]  Hernando Ombao,et al.  Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment , 2016 .

[31]  Radford M. Neal.  Slice Sampling , 2003, The Annals of Statistics.

[32]  Babak Shahbaba,et al.  Flexible Bayesian Dynamic Modeling of Covariance and Correlation Matrices , 2017 .

[33]  Hernando Ombao,et al.  Evolutionary Factor Analysis of Replicated Time Series , 2012, Biometrics.

[34]  Michael I. Jordan,et al.  Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert Spaces , 2004, J. Mach. Learn. Res..

[35]  Jiqiang Guo,et al.  Stan: A Probabilistic Programming Language. , 2017, Journal of statistical software.

[36]  A. W. Vaart,et al.  Reproducing kernel Hilbert spaces of Gaussian priors , 2008, 0805.3252.

[37]  Eswar Damaraju,et al.  Tracking whole-brain connectivity dynamics in the resting state. , 2014, Cerebral cortex.

[38]  Michael A. West,et al.  BAYESIAN MODEL ASSESSMENT IN FACTOR ANALYSIS , 2004 .

[39]  David B. Dunson,et al.  Bayesian nonparametric covariance regression , 2011, J. Mach. Learn. Res..

[40]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.