5,895 research outputs found
Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling
Identifying a coupled dynamical system out of many plausible candidates, each
of which could serve as the underlying generator of some observed measurements,
is a profoundly ill posed problem that commonly arises when modelling real
world phenomena. In this review, we detail a set of statistical procedures for
inferring the structure of nonlinear coupled dynamical systems (structure
learning), which has proved useful in neuroscience research. A key focus here
is the comparison of competing models of (ie, hypotheses about) network
architectures and implicit coupling functions in terms of their Bayesian model
evidence. These methods are collectively referred to as dynamical casual
modelling (DCM). We focus on a relatively new approach that is proving
remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid
evaluation and comparison of models that differ in their network architecture.
We illustrate the usefulness of these techniques through modelling
neurovascular coupling (cellular pathways linking neuronal and vascular
systems), whose function is an active focus of research in neurobiology and the
imaging of coupled neuronal systems
Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been
used to model sparsity-inducing priors that realize a class of concave penalty
functions for the regression task in real-valued signal models. Motivated by
the relative scarcity of formal tools for SBL in complex-valued models, this
paper proposes a GSM model - the Bessel K model - that induces concave penalty
functions for the estimation of complex sparse signals. The properties of the
Bessel K model are analyzed when it is applied to Type I and Type II
estimation. This analysis reveals that, by tuning the parameters of the mixing
pdf different penalty functions are invoked depending on the estimation type
used, the value of the noise variance, and whether real or complex signals are
estimated. Using the Bessel K model, we derive a sparse estimator based on a
modification of the expectation-maximization algorithm formulated for Type II
estimation. The estimator includes as a special instance the algorithms
proposed by Tipping and Faul [1] and by Babacan et al. [2]. Numerical results
show the superiority of the proposed estimator over these state-of-the-art
estimators in terms of convergence speed, sparseness, reconstruction error, and
robustness in low and medium signal-to-noise ratio regimes.Comment: The paper provides a new comprehensive analysis of the theoretical
foundations of the proposed estimators. Minor modification of the titl
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