Spatio-temporal modeling of EEG features for understanding working memory Jinbo Bi Joint work with Tingyang Xu, Chi-Ming Chen, Jason Johannesen University of Connecticut Yale University

Outline The main technical idea EEG data analysis problem The proposed approach – GEE + regularization Our algorithm Preliminary experimental results Summary Before I get to the details of our problem and the proposed approach, I would like to introduce our main technical idea, which is fairly straightforward. Then we introduce the problem. Our approach is a bit more complicated because it is built on top of the generalized estimating equations. We briefly review the algorithm we used to solve this formulation, then show some preliminary results and then give a summary.

Main idea Variables are observed/measured at different locations and different time points Temporal line Spatial line The features

Main idea If we build a linear model using all features, the coefficients in the model form another matrix, we want it to have sparsity patterns Temporal line Spatial line The coefficient matrix W The features X

Main idea The idea is to decompose the W matrix into a summation of two matrices of the same dimension, and then impose different sparsity-inducing regularizers. = + W U V

Main idea For instance, the widely-used L1,2 matrix norm computes the summation of the L2 norm of individual row vectors in a matrix, and enforces the row sparsity of a matrix U V

EEG data analysis problem EEG recording provides a powerful method to study neural dynamics of human cognition (e.g., working memory) EEG recording Montage An illustration of a BCI program

EEG data analysis problem Stenberg tests Baseline Encoding Retention Retrieval A sample trial of Sternberg experiment depicting stages of information processing. Time Courses are extracted for EEG analysis based on memory span of 4 letters The outcome is if a person responded correctly (-1 incorrect).

EEG data analysis problem Our data 37 schizophrenia, 6 healthy controls Each individual has 90 trials of Stenberg in each of the 3 sessions Baseline Encoding Retention Retrieval Amplitudes of EEG in 5 frequency bands: delta, theta, alpha, beta, and gamma Fz Cz Oz

The proposed approach Our method combines the generalized estimating equation and the proposed regularizer Generalized estimating equations is a set of methods that expand the generalized linear models, but estimate both expectation and the covariance of the outcome The parameters are W and α

The proposed approach The parameters W and α are estimated by minimizing the so-called deviance function, i.e., Deviance(W,α) – the difference between the likelihood of observing the actual y and the likelihood of observing the mean The deviance function is not explicit for an arbitrary distribution, but its gradient can be computed for the exponential families We propose

Our FISTA-based algorithm We solve our problem using FISTA – fast iterative shrinkage thresholding algorithm We solve alternatively between (U,V) and α We use a FISTA algorithm to solve for (U,V) which is an alternating proximal gradient method that solves U and V alternatively using proximal operators We use the original GEE updating formula to update α because when U and V are fixed, the proposed formulation is exactly same as GEE formulation when W is fixed

Our FISTA-based algorithm The algorithm globally converges to an optimal solution of the problem with a convergence rate of quadratic order Under some regularity conditions, optimizing the proposed formula yields an asymptotically consistent and normally distributed estimator where

Preliminary experimental results We preliminarily tested this algorithm on EEG feature analysis – to predict if a person answers the Stenberg test correctly (0) and incorrectly (1) based on the EEG features 37 schizophrenia and 6 healthy controls, separate classifiers for schizophrenia and health controls After data cleaning, each patient on average has 83 trials and incorrect answer rate is 27.2% Each health control on average has 87 trials, and incorrect answer rate is 14.7% Using multiple three-fold cross validation to tune parameters λ’s

Preliminary experimental results We first compared with the classic GEE method We report the area under the ROC curves (AUCs) Our method outperformed GEE consistently in four different kinds of covariance assumptions

Preliminary experimental results We demonstrate the selected features and stages in the classifiers The strongest feature is the engagement of fontal alpha during encoding and retention, which replicate an early report that used a separate sample. Schizophrenia: Rows are features; columns are stages of information processing

Preliminary experimental results We demonstrate the selected features and stages in the classifiers Based on these models, the two groups showed remarkably different patterns. EEG activity in higher frequency bands appear to be associated with the incorrect trial response for SZ, but not with that of health controls. For healthy controls, engaging the low frequency activity, especially delta, was associated with incorrent responses for healthy controls. The important stages were identified the same for schizophrenia and controls. Healthy controls: Rows are features; columns are stages of information processing

Summary We used a new learning formulation to select EEG features along the temporal and spatial dimensions This new method also simultaneously models the sample correlation via the GEE A new accelerated gradient descent algorithm can efficiently solve the related optimization problem Preliminary results show that the EEG features selected between SZ and HC are rather different Future work … The take-home message is the following.

References Chen et al, Gaba level, gamma oscillation, and working memory performance in schizophrenia, NeuroImage: Clinical, 4:531-539, 2014. Beck et al, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM Journal on Imaging Science, 2(1):183-202, 2009. Xu et al, Longitudinal LASSO: jointly learning features and temporal contingency for outcome prediction, to appear in ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), 2015. http://www.labhealthinfo.uconn.edu/ Thank you!! Here are some references. Thank you for your attention.