2,015 research outputs found
Multiscale Bayesian State Space Model for Granger Causality Analysis of Brain Signal
Modelling time-varying and frequency-specific relationships between two brain
signals is becoming an essential methodological tool to answer heoretical
questions in experimental neuroscience. In this article, we propose to estimate
a frequency Granger causality statistic that may vary in time in order to
evaluate the functional connections between two brain regions during a task. We
use for that purpose an adaptive Kalman filter type of estimator of a linear
Gaussian vector autoregressive model with coefficients evolving over time. The
estimation procedure is achieved through variational Bayesian approximation and
is extended for multiple trials. This Bayesian State Space (BSS) model provides
a dynamical Granger-causality statistic that is quite natural. We propose to
extend the BSS model to include the \`{a} trous Haar decomposition. This
wavelet-based forecasting method is based on a multiscale resolution
decomposition of the signal using the redundant \`{a} trous wavelet transform
and allows us to capture short- and long-range dependencies between signals.
Equally importantly it allows us to derive the desired dynamical and
frequency-specific Granger-causality statistic. The application of these models
to intracranial local field potential data recorded during a psychological
experimental task shows the complex frequency based cross-talk between amygdala
and medial orbito-frontal cortex.
Keywords: \`{a} trous Haar wavelets; Multiple trials; Neuroscience data;
Nonstationarity; Time-frequency; Variational methods
The published version of this article is
Cekic, S., Grandjean, D., Renaud, O. (2018). Multiscale Bayesian state-space
model for Granger causality analysis of brain signal. Journal of Applied
Statistics. https://doi.org/10.1080/02664763.2018.145581
Probabilistic Methodology and Techniques for Artefact Conception and Development
The purpose of this paper is to make a state of the art on probabilistic methodology and techniques for artefact conception and development. It is the 8th deliverable of the BIBA (Bayesian Inspired Brain and Artefacts) project. We first present the incompletness problem as the central difficulty that both living creatures and artefacts have to face: how can they perceive, infer, decide and act efficiently with incomplete and uncertain knowledge?. We then introduce a generic probabilistic formalism called Bayesian Programming. This formalism is then used to review the main probabilistic methodology
and techniques. This review is organized in 3 parts: first the probabilistic models from Bayesian networks to Kalman filters and from sensor fusion to CAD systems, second the inference techniques and finally the learning and model acquisition and comparison methodologies. We conclude with the perspectives of the BIBA project as they rise from this state of the art
A Bayesian perspective on classical control
The connections between optimal control and Bayesian inference have long been
recognised, with the field of stochastic (optimal) control combining these
frameworks for the solution of partially observable control problems. In
particular, for the linear case with quadratic functions and Gaussian noise,
stochastic control has shown remarkable results in different fields, including
robotics, reinforcement learning and neuroscience, especially thanks to the
established duality of estimation and control processes. Following this idea we
recently introduced a formulation of PID control, one of the most popular
methods from classical control, based on active inference, a theory with roots
in variational Bayesian methods, and applications in the biological and neural
sciences. In this work, we highlight the advantages of our previous formulation
and introduce new and more general ways to tackle some existing problems in
current controller design procedures. In particular, we consider 1) a
gradient-based tuning rule for the parameters (or gains) of a PID controller,
2) an implementation of multiple degrees of freedom for independent responses
to different types of signals (e.g., two-degree-of-freedom PID), and 3) a novel
time-domain formalisation of the performance-robustness trade-off in terms of
tunable constraints (i.e., priors in a Bayesian model) of a single cost
functional, variational free energy.Comment: 8 pages, Accepted at IJCNN 202
Sparse online variational Bayesian regression
This work considers variational Bayesian inference as an inexpensive and
scalable alternative to a fully Bayesian approach in the context of
sparsity-promoting priors. In particular, the priors considered arise from
scale mixtures of Normal distributions with a generalized inverse Gaussian
mixing distribution. This includes the variational Bayesian LASSO as an
inexpensive and scalable alternative to the Bayesian LASSO introduced in [65].
It also includes a family of priors which more strongly promote sparsity. For
linear models the method requires only the iterative solution of deterministic
least squares problems. Furthermore, for p unknown covariates the method can be
implemented exactly online with a cost of in computation and
in memory per iteration -- in other words, the cost per iteration is
independent of n, and in principle infinite data can be considered. For large
an approximation is able to achieve promising results for a cost of
per iteration, in both computation and memory. Strategies for hyper-parameter
tuning are also considered. The method is implemented for real and simulated
data. It is shown that the performance in terms of variable selection and
uncertainty quantification of the variational Bayesian LASSO can be comparable
to the Bayesian LASSO for problems which are tractable with that method, and
for a fraction of the cost. The present method comfortably handles ,
on a laptop in less than 30 minutes, and , overnight
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