Beyond Linear Neural Envelope Tracking: A Mutual Information Approach

Abstract The human brain tracks the temporal envelope of speech, which contains essential cues for speech understanding. Linear models are the most common tool to study neural envelope tracking. However, information on how speech is processed can be lost since nonlinear relations are precluded. As an alternative, mutual information (MI) analysis can detect both linear and nonlinear relations. Yet, several different approaches to calculating MI are applied without consensus on which approach to use. Furthermore, the added value of nonlinear techniques remains a subject of debate in the field. To resolve this, we applied linear and MI analyses to electroencephalography (EEG) data of participants listening to continuous speech. Comparing the different MI approaches, we conclude that results are most reliable and robust using the Gaussian copula approach, which first transforms the data to standard Gaussians. With this approach, the MI analysis is a valid technique for studying neural envelope tracking. Like linear models, it allows spatial and temporal interpretations of speech processing, peak latency analyses, and applications to multiple EEG channels combined. Finally, we demonstrate that the MI analysis can detect nonlinear components on the single-subject level, beyond the limits of linear models. We conclude that the MI analysis is a more informative tool for studying neural envelope tracking. Significance statement In the present study, we addressed key methodological considerations for MI applications. Traditional MI methodologies require the estimation of a probability distribution at first. We show that this step can introduce a bias in the results and, consequently, severely impact interpretations. As an alternative, we propose using the parametric Gaussian copula method, which we demonstrated to be robust against biases. Second, using the parametric MI analysis, we show that there is nonlinear variance in the EEG data that the envelope of speech can explain at the single-subject level, proving its added value to neural envelope tracking. We conclude that the MI analysis is a statistically more powerful tool for studying neural envelope tracking than linear models. In addition, it retains spatial and temporal characteristics of speech processing which are lost when using more complex deep neural networks.