We begin by reviewing the statistical framework of information theory as applicable to neuroimaging data analysis. A major factor hindering wider adoption of this framework in neuroimaging is the difficulty of estimating information theoretic quantities in practice. We present a novel estimation technique that combines the statistical theory of copulas with the closed form solution for the entropy of Gaussian variables. This results in a general, computationally efficient, flexible, and robust multivariate statistical framework that provides effect sizes on a common meaningful scale, allows for unified treatment of discrete, continuous, unidimensional and multidimensional variables, and enables direct comparisons of representations from behavioral and brain responses across any recording modality. We validate the use of this estimate as a statistical test within a neuroimaging context, considering both discrete stimulus classes and continuous stimulus features. We also present examples of analyses facilitated by these developments, including application of multivariate analyses to MEG planar magnetic field gradients, and pairwise temporal interactions in evoked EEG responses. We show the benefit of considering the instantaneous temporal derivative together with the raw values of M/EEG signals as a multivariate response, how we can separately quantify modulations of amplitude and direction for vector quantities, and how we can measure the emergence of novel information over time in evoked responses. Open‐source Matlab and Python code implementing the new methods accompanies this article. Hum Brain Mapp 38:1541–1573, 2017.

The problem of how to properly quantify redundant information is an open question that has been the subject of much recent research. Redundant information refers to information about a target variable S that is common to two or more predictor variables $X_i$ . It can be thought of as quantifying overlapping information content or similarities in the representation of S between the $X_i$ . We present a new measure of redundancy which measures the common change in surprisal shared between variables at the local or pointwise level. We provide a game-theoretic operational definition of unique information, and use this to derive constraints which are used to obtain a maximum entropy distribution. Redundancy is then calculated from this maximum entropy distribution by counting only those local co-information terms which admit an unambiguous interpretation as redundant information. We show how this redundancy measure can be used within the framework of the Partial Information Decomposition (PID) to give an intuitive decomposition of the multivariate mutual information into redundant, unique and synergistic contributions. We compare our new measure to existing approaches over a range of example systems, including continuous Gaussian variables. Matlab code for the measure is provided, including all considered examples.

The entrainment of slow rhythmic auditory cortical activity to the temporal regularities in speech is considered to be a central mechanism underlying auditory perception. Previous work has shown that entrainment is reduced when the quality of the acoustic input is degraded, but has also linked rhythmic activity at similar time scales to the encoding of temporal expectations. To understand these bottom-up and top-down contributions to rhythmic entrainment, we manipulated the temporal predictive structure of speech by parametrically altering the distribution of pauses between syllables or words, thereby rendering the local speech rate irregular while preserving intelligibility and the envelope fluctuations of the acoustic signal. Recording EEG activity in human participants, we found that this manipulation did not alter neural processes reflecting the encoding of individual sound transients, such as evoked potentials. However, the manipulation significantly reduced the fidelity of auditory delta (but not theta) band entrainment to the speech envelope. It also reduced left frontal alpha power and this alpha reduction was predictive of the reduced delta entrainment across participants. Our results show that rhythmic auditory entrainment in delta and theta bands reflect functionally distinct processes. Furthermore, they reveal that delta entrainment is under top-down control and likely reflects prefrontal processes that are sensitive to acoustical regularities rather than the bottom-up encoding of acoustic features.SIGNIFICANCE STATEMENTThe entrainment of rhythmic auditory cortical activity to the speech envelope is considered to be critical for hearing. Previous work has proposed divergent views in which entrainment reflects either early evoked responses related to sound encoding or high-level processes related to expectation or cognitive selection. Using a manipulation of speech rate, we dissociated auditory entrainment at different time scales. Specifically, our results suggest that delta entrainment is controlled by frontal alpha mechanisms and thus support the notion that rhythmic auditory cortical entrainment is shaped by top-down mechanisms.

The encoding of sensory information by populations of cortical neurons forms the basis for perception but remains poorly understood. To understand the constraints of cortical population coding we analyzed neural responses to natural sounds recorded in auditory cortex of primates (Macaca mulatta). We estimated stimulus information while varying the composition and size of the considered population. Consistent with previous reports we found that when choosing subpopulations randomly from the recorded ensemble, the average population information increases steadily with population size. This scaling was explained by a model assuming that each neuron carried equal amounts of information, and that any overlap between the information carried by each neuron arises purely from random sampling within the stimulus space. However, when studying subpopulations selected to optimize information for each given population size, the scaling of information was strikingly different: a small fraction of temporally precise cells carried the vast majority of information. This scaling could be explained by an extended model, assuming that the amount of information carried by individual neurons was highly nonuniform, with few neurons carrying large amounts of information. Importantly, these optimal populations can be determined by a single biophysical marker—the neuron's encoding time scale—allowing their detection and readout within biologically realistic circuits. These results show that extrapolations of population information based on random ensembles may overestimate the population size required for stimulus encoding, and that sensory cortical circuits may process information using small but highly informative ensembles.

Despite being the focus of a thriving field of research, the biological mechanisms that underlie information integration in the brain are not yet fully understood. A theory that has gained a lot of traction in recent years suggests that multi-scale integration is regulated by a hierarchy of mutually interacting neural oscillations. In particular, there is accumulating evidence that phase-amplitude coupling (PAC), a specific form of cross-frequency interaction, plays a key role in numerous cognitive processes. Current research in the field is not only hampered by the absence of a gold standard for PAC analysis, but also by the computational costs of running exhaustive computations on large and high-dimensional electrophysiological brain signals. In addition, various signal properties and analyses parameters can lead to spurious PAC. Here, we present Tensorpac, an open-source Python toolbox dedicated to PAC analysis of neurophysiological data. The advantages of Tensorpac include (1) higher computational efficiency thanks to software design that combines tensor computations and parallel computing, (2) the implementation of all most widely used PAC methods in one package, (3) the statistical analysis of PAC measures, and (4) extended PAC visualization capabilities. Tensorpac is distributed under a BSD-3-Clause license and can be launched on any operating system (Linux, OSX and Windows). It can be installed directly via pip or downloaded from Github (https://github.com/EtienneCmb/tensorpac). By making Tensorpac available, we aim to enhance the reproducibility and quality of PAC research, and provide open tools that will accelerate future method development in neuroscience.

Seeing a speaker’s face enhances speech intelligibility in adverse environments. We investigated the underlying network mechanisms by quantifying local speech representations and directed connectivity in MEG data obtained while human participants listened to speech of varying acoustic SNR and visual context. During high acoustic SNR speech encoding by temporally entrained brain activity was strong in temporal and inferior frontal cortex, while during low SNR strong entrainment emerged in premotor and superior frontal cortex. These changes in local encoding were accompanied by changes in directed connectivity along the ventral stream and the auditory-premotor axis. Importantly, the behavioral benefit arising from seeing the speaker’s face was not predicted by changes in local encoding but rather by enhanced functional connectivity between temporal and inferior frontal cortex. Our results demonstrate a role of auditory-frontal interactions in visual speech representations and suggest that functional connectivity along the ventral pathway facilitates speech comprehension in multisensory environments.