Novel Statistical Methods for EEG-Based Brain-Computer Interfaces

Abstract

In the first project, we propose a Bayesian generative model to fit the probability distribution of multi-trial EEG signals in the BCI system. Existing machine learning methods focus on constructing the ERP classifiers, but they pay less attention to interpreting brain activity due to the overlap between adjacent EEG signal segments during the signal pre-processing procedure; our model explicitly addresses this challenge by developing a new Gaussian Process (GP)-based model to estimate the spatial-temporal varying trajectories of P300 ERP responses. The proposed model can select important time windows in which the average brain activity in response to the target and non-target stimuli is different (split) or the same (merge); thus, The GP is termed the split-and-merge GP (SMGP). We also propose a participant-specific information criterion for brain region ranking and selection. Our inference results provide statistical evidence of P300 ERP responses, help design user-specific profiles for efficient BCIs, and demonstrate the importance of ERPs from the visual cortex for P300 speller performance. We design extensive simulation studies based on the database from the University of Michigan Direct Brain Interface Lab (UM-DBI). The robustness and reproducibility of our analysis is justified by cross-participant comparisons and extensive simulation studies.

In the second project, we develop a sequence-based algorithm for adaptive stimulus selection by Thompson sampling in the multi-armed bandit (MAB) problem with multiple selections. Thompson sampling is a heuristic algorithm for sequential decision making that addresses the exploration-exploitation dilemma in the MAB problem. It chooses the optimal action by maximizing the expected reward function with respect to the posterior distribution of the parameters. During each sequence, the algorithm selects a random subset of stimulus groups with a fixed size by the posterior probability, aiming to identify all target stimuli and to improve spelling speed by reducing unnecessary non-target stimuli. In addition, we adopt an efficient method to compute stimulus-specific rewards based on classifier scores under the Bayesian inference framework. We further improve spelling efficiency by integrating a language model into the prior specification. We perform simulations to compare different configurations of stimulus selection paradigms and show that the proposed adaptive stimulus selection performs more efficiently than the conventional paradigm.

In the third project, we propose a BAyesian SemI-supervised Classification (BASIC) method for data integration of EEG-BCI data from multiple participants. Calibration in BCI refers to the procedure of training the classifier. The existing calibration method only uses data from participants themselves with lengthy training time and thus introducing the noise due to attention shifts and mental fatigue. BASIC aims to reduce the calibration time of a new participant by borrowing information from calibration data of the source participants, which can improve classification accuracy and communication efficiency in the usage of ERP-BCI. BASIC specifies the joint distribution of stimulus-specific EEG signals among source participants via a Bayesian hierarchical mixture model. The posterior inference on BASIC is based on the new participant and selected source participants that are ``similar'' to the new participant to construct a potentially more powerful classifier. We demonstrate the advantages of BASIC using extensive simulations designed according to the EEG-BCI data collected from the UM-DBI.