Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models

By Jean Daunizeau, Karl J. Friston, Stefan J. Kiebel. 2009

199 citations recorded by the source corpus.

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Subfields: Artificial Intelligence, Signal Processing

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Citations in the corpus

Semi-analytical approximations to statistical moments of sigmoid and softmax mappings of normal variables (2017, background): “We also expose a few niche applications of these approximations, which mainly arise in the context of variational Bayesian inference (Beal, 2003; Daunizeau et al., 2009; Friston et al., 2007; Smídl and Quinn, 2006) on specific generative models.”
Health, USA Reviewed by: (2010, unknown): “Note that GCM of fMRI data is the youngest of these methods, and important theoretical considerations have been discussed recently (Friston, 2009; Roebroeck et al., 2009a,b).”
The Social Bayesian Brain: Does Mentalizing Make a Difference When We Learn? (2014, background): “Citation: Devaine M, Hollard G, Daunizeau J (2014) The Social Bayesian Brain: Does Mentalizing Make a Difference When We Learn?”
Brain covariance selection: better individual functional connectivity models using population prior (2010, methodology): “Although the proposed framework shares with so-called effectiv connectivity models (SEM [11], DCM [12]) the formulation in terms of graphical model, it is fundamentally different in that these approaches are designed to test the coefficients of (small) gr phical models in a hypothesis-driven framewo”
Uncertainty in perception and the Hierarchical Gaussian Filter (2014, methodology): “For our simulation study, we used VB as implemented in the DAVB toolbox, available at http://goo . gl/As8p7 (Daunizeau et al., 2009, 2014).”
Effective connectivity: Influence, causality and biophysical modeling (2011, unknown): “State model Parametric Non-parametric Parametric Non-parametric Generic Linear canonical HRF (Glover, 1999) Linear spline HRF (Marrelec et al., 2003) GCM (Bressler and Seth, 2010) Switching VAR (Smith et al., 2010a) Neural ﬁ elds (Daunizeau et al., 2009c) in the brain.”
Criticality in the brain: A synthesis of neurobiology, models and cognition. (2017, methodology): “Third, computational models of neural systems that are based upon criticality should be tested closely against empirical data using appropriate frameworks (Daunizeau et al., 2009; Penny, 2012) that”
Ten Simple Rules for Dynamic Causal Modelling (2009, unknown): “For example, the GLM for fMRI data and source reconstruction methods for EEG/MEG can be thought of as special cases of DCMs (for details, see Daunizeau et al., 2009b; Kiebel et al., 2006; Stephan et al., 2007a).”
VBA: A Probabilistic Treatment of Nonlinear Models for Neurobiological and Behavioural Data (2014, methodology): “N The root folder (/DAVB) contains a core set of (matlab) routines that implement the VB approach to stochastic nonlinear state-space models [15].”
Network modelling methods for FMRI (2011, unknown): “While there is some early work on stochastic DCMs that may be able to address this (Daunizeau et al., 2009), established DCM methods require that the “input” timings be specified in advance—something that is clearly not known for resting data.”