EEG continues to find a multitude of uses in both neuroscience research and medical practice, and independent component analysis (ICA) continues to be an important tool for analyzing EEG. A multitude of ICA algorithms for EEG decomposition exist, and in the past, their relative effectiveness has been studied. AMICA is considered the benchmark against which to compare the performance of other ICA algorithms for EEG decomposition. AMICA exposes many parameters to the user to allow for precise control of the decomposition. However, several of the parameters currently tend to be set according to “rules of thumb” shared in the EEG community. Here, 70-channel AMICA decompositions are run on data from a collection of participants while varying certain key parameters. The running time and quality of decompositions are analyzed based on two metrics, Pairwise Mutual Information (PMI) and Mutual Information Reduction (MIR), and derived recommendations for selecting parameter values are presented.

We propose a model for the density of cross-spectral coefficients using normal variance mean mixtures. We show that this model density generalizes the corresponding marginal density of the complex Wishart distribution for the cross-spectral density. The maximum likelihood estimate of parameters in the distribution is derived, and examples are given from alpha brain wave sources in separated EEG data.

We derive an asymptotic Newton algorithm for quasi-maximum likelihood estimation of the ICA mixture model, using the ordinary gradient and Hessian. The probabilistic mixture framework yields an algorithm that can accommodate non-stationary environments and arbitrary source densities. We prove asymptotic stability when the source models match the true sources. An example application to EEC segmentation is given.

A variety of Bayesian methods have recently been introduced for finding sparse representations from overcomplete dictionaries of candidate features. These methods often capitalize on latent structure inherent in sparse distributions to perform standard MAP estimation, variational Bayes, approximation using convex duality, or evidence maximization. Despite their reliance on sparsity-inducing priors however, these approaches may or may not actually lead to sparse representations in practice, and so it is a challenging task to determine which algorithm and sparse prior is appropriate. Rather than justifying prior selections and modelling assumptions based on the credibility of the full Bayesian model as is commonly done, this paper bases evaluations on the actual cost functions that emerge from each method. Two minimal conditions are postulated that ideally any sparse learning objective should satisfy. Out of all possible cost functions that can be obtained from the methods described above using (virtually) any sparse prior, a unique function is derived that satisfies these conditions. Both sparse Bayesian learning (SBL) and basis pursuit (BP) are special cases. Later, all methods are shown to be performing MAP estimation using potentially non-factorable implicit priors, which suggests new sparse learning cost functions.

The ill-posed nature of the MEG/EEG source localization problem requires the incorporation of prior assumptions when choosing an appropriate solution out of an infinite set of candidates. Bayesian methods are useful in this capacity because they allow these assumptions to be explicitly quantified. Recently, a number of empirical Bayesian approaches have been proposed that attempt a form of model selection by using the data to guide the search for an appropriate prior. While seemingly quite different in many respects, we apply a unifying framework based on automatic relevance determination (ARD) that elucidates various attributes of these methods and suggests directions for improvement. We also derive theoretical properties of this methodology related to convergence, local minima, and localization bias and explore connections with established algorithms.

We consider criteria for variational representations of non-Gaussian latent variables, and derive variational EM algorithms in general form. We establish a general equivalence among convex bounding methods, evidence based methods, and ensemble learning/Variational Bayes methods, which has previously been demonstrated only for particular cases.

Recently, relevance vector machines (RVM) have been fashioned from a sparse Bayesian learning (SBL) framework to perform supervised learn- ing using a weight prior that encourages sparsity of representation. The methodology incorporates an additional set of hyperparameters govern- ing the prior, one for each weight, and then adopts a specific approxi- mation to the full marginalization over all weights and hyperparameters. Despite its empirical success however, no rigorous motivation for this particular approximation is currently available. To address this issue, we demonstrate that SBL can be recast as the application of a rigorous vari- ational approximation to the full model by expressing the prior in a dual form. This formulation obviates the necessity of assuming any hyperpri- ors and leads to natural, intuitive explanations of why sparsity is achieved in practice.