arXiv subjects

Mayrim Vega-Hernández

Publications and source records attributed to Mayrim Vega-Hernández.

3 recordsLinked to original sources

arXiv2021

A Multi-objective Evolutionary Algorithm for EEG Inverse Problem

In this paper, we proposed a multi-objective approach for the EEG Inverse Problem. This formulation does not need unknown parameters that involve empirical procedures. Due to the combinatorial characteristics of the problem, this alternative included evolutionary strategies to resolve it. The result is a Multi-objective Evolutionary Algorithm based on Anatomical Restrictions (MOEAAR) to estimate distributed solutions. The comparative tests were between this approach and 3 classic methods of regularization: LASSO, Ridge-L and ENET-L. In the experimental phase, regression models were selected to obtain sparse and distributed solutions. The analysis involved simulated data with different signal-to-noise ratio (SNR). The indicators for quality control were Localization Error, Spatial Resolution and Visibility. The MOEAAR evidenced better stability than the classic methods in the reconstruction and localization of the maximum activation. The norm L0 was used to estimate sparse solutions with the evolutionary approach and its results were relevant.

cs.NE↗

arXiv2021

Multiple penalized least squares and sign constraints with modified Newton-Raphson algorithms: application to EEG source imaging

Multiple penalized least squares (MPLS) models are a flexible approach to find adaptive least squares solutions required to be simultaneously sparse and smooth. This is particularly important when addressing real-life inverse problems where there is no ground truth available, such as electrophysiological source imaging. In this work we formalize a modified Newton-Raphson (MNR) algorithm to estimate general MPLS models and propose its extension to perform efficient optimization over the active set of selected features (AMNR). This algorithm can be used to minimize continuously differentiable objective functions with multiple restrictions, including sign constraints. We show that these algorithms provide solutions with acceptable reconstruction in simulated scenarios that do not cope with model assumptions, and for low n/p ratios. We then use both algorithms for estimating different electroencephalography (EEG) inverse models with multiple penalties. We also show how the AMNR allows us to estimate new models in the EEG inverse problem context, such as nonnegative versions of Smooth Garrote and Smooth LASSO. Synthetic data were used for a comparison between solutions obtained using the two algorithms proposed here and the least angle regression (LARS) algorithm, according to well-known quality measures. A visual event-related EEG from healthy young subjects and a resting-state EEG study on the relationship between cognitive ageing and walking speed decline in active elders, were used to illustrate the usefulness of the proposed methods in the analysis of real experimental data.

stat.AP↗

arXiv2016

Empirical bayes formulation of the elastic net and mixed-norm models: application to the eeg inverse problem

The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem, due to the non-uniqueness of the solution, and many kinds of prior information have been used to constrain it. A combination of smoothness (L2 norm-based) and sparseness (L1 norm-based) constraints is a flexible approach that have been pursued by important examples such as the Elastic Net (ENET) and mixed-norm (MXN) models. The former is used to find solutions with a small number of smooth non-zero patches, while the latter imposes sparseness and smoothness simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using computationally intensive Monte Carlo/Expectation Maximization methods. In this work we attempt to solve the EEG IP using a Bayesian framework for models based on mixtures of L1/L2 norms penalization functions (Laplace/Normal priors) such as ENET and MXN. We propose a Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using simple but realistic simulations we found that our methods are able to recover complicated source setups more accurately and with a more robust variable selection than the ENET and LASSO solutions using classical algorithms. We also solve the EEG IP using data coming from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods, as compared with other known methods such as LORETA, ENET and LASSO FUSION using the classical regularization approach.

stat.ME↗