DiME: Maximizing Mutual Information by a Difference of Matrix-Based Entropies

We introduce an information-theoretic quantity with similar properties to mutual information that can be estimated from data without making explicit assumptions on the underlying distribution. This quantity is based on a recently proposed matrix-based entropy that uses the eigenvalues of a normalized Gram matrix to compute an estimate of the eigenvalues of an uncentered covariance operator in a reproducing kernel Hilbert space. We show that a difference of matrix-based entropies (DiME) is well suited for problems involving maximization of mutual information between random variables. While many methods for such tasks can lead to trivial solutions, DiME naturally penalizes such outcomes. We provide several examples of use cases for the proposed quantity including a multi-view representation learning problem where DiME is used to encourage learning a shared representation among views with high mutual information. We also show the versatility of DiME by using it as objective function for a variety of tasks.

Exploring latent networks in resting-state fMRI using voxel-to-voxel causal modeling feature selection

Functional networks characterize the coordinated neural activity observed by functional neuroimaging. The prevalence of different networks during resting state periods provide useful features for predicting the trajectory of neurodegenerative diseases. Techniques for network estimation rely on statistical correlation or dependence between voxels. Due to the large number of voxels, rather than consider the voxel-to-voxel correlations between all voxels, a small set of seed voxels are chosen. Consequently, the network identification may depend on the selected seeds. As an alternative, we propose to fit first-order linear models with sparse priors on the coefficients to model activity across the entire set of cortical grey matter voxels as a linear combination of a smaller subset of voxels. We propose a two-stage algorithm for voxel subset selection that uses different sparsity-inducing regularization approaches to identify subject-specific causally predictive voxels. To reveal the functional networks among these voxels, we then apply independent component analysis (ICA) to model these voxels' signals as a mixture of latent sources each defining a functional network. Based on the inter-subject similarity of the sources' spatial patterns we identify independent sources that are well-matched across subjects but fail to match the independent sources from a group-based ICA. These are resting state networks, common across subjects that group ICA does not reveal. These complementary networks could help to better identify neurodegeneration, a task left for future work.

Shift-invariant waveform learning on epileptic ECoG

Seizure detection algorithms must discriminate abnormal neuronal activity associated with a seizure from normal neural activity in a variety of conditions. Our approach is to seek spatiotemporal waveforms with distinct morphology in electrocorticographic (ECoG) recordings of epileptic patients that are indicative of a subsequent seizure (preictal) versus non-seizure segments (interictal). To find these waveforms we apply a shift-invariant k-means algorithm to segments of spatially filtered signals to learn codebooks of prototypical waveforms. The frequency of the cluster labels from the codebooks is then used to train a binary classifier that predicts the class (preictal or interictal) of a test ECoG segment. We use the Matthews correlation coefficient to evaluate the performance of the classifier and the quality of the codebooks. We found that our method finds recurrent non-sinusoidal waveforms that could be used to build interpretable features for seizure prediction and that are also physiologically meaningful.

Searching for waveforms on spatially-filtered epileptic ECoG

Seizures are one of the defining symptoms in patients with epilepsy, and due to their unannounced occurrence, they can pose a severe risk for the individual that suffers it. New research efforts are showing a promising future for the prediction and preemption of imminent seizures, and with those efforts, a vast and diverse set of features have been proposed for seizure prediction algorithms. However, the data-driven discovery of nonsinusoidal waveforms for seizure prediction is lacking in the literature, which is in stark contrast with recent works that show the close connection between the waveform morphology of neural oscillations and the physiology and pathophysiology of the brain, and especially its use in effectively discriminating between normal and abnormal oscillations in electrocorticographic (ECoG) recordings of epileptic patients. Here, we explore a scalable, energy-guided waveform search strategy on spatially-projected continuous multi-day ECoG data sets. Our work shows that data-driven waveform learning methods have the potential to not only contribute features with predictive power for seizure prediction, but also to facilitate the discovery of oscillatory patterns that could contribute to our understanding of the pathophysiology and etiology of seizures.