Patricia Wollstadt

Efficient Transfer Entropy Analysis of Non-Stationary Neural Time Series

Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of interest in neuroscience. Estimating transfer entropy from two processes requires the observation of multiple realizations of these processes to estimate associated probability density functions. To obtain these necessary observations, available estimators typically assume stationarity of processes to allow pooling of observations over time. This assumption however, is a major obstacle to the application of these estimators in neuroscience as observed processes are often non-stationary. As a solution, Gomez-Herrero and colleagues theoretically showed that the stationarity assumption may be avoided by estimating transfer entropy from an ensemble of realizations. Such an ensemble of realizations is often readily available in neuroscience experiments in the form of experimental trials. Thus, in this work we combine the ensemble method with a recently proposed transfer entropy estimator to make transfer entropy estimation applicable to non-stationary time series. We present an efficient implementation of the approach that is suitable for the increased computational demand of the ensemble methods practical application. In particular, we use a massively parallel implementation for a graphics processing unit to handle the computationally most heavy aspects of the ensemble method for transfer entropy estimation. We test the performance and robustness of our implementation on data from numerical simulations of stochastic processes. We also demonstrate the applicability of the ensemble method to magnetoencephalographic data. While we mainly evaluate the proposed method for neuroscience data, we expect it to be applicable in a variety of fields that are concerned with the analysis of information transfer in complex biological, social, and artificial systems.

Reduced predictable information in brain signals in autism spectrum disorder

Autism spectrum disorder (ASD) is a common developmental disorder characterized by communication difficulties and impaired social interaction. Recent results suggest altered brain dynamics as a potential cause of symptoms in ASD. Here, we aim to describe potential information-processing consequences of these alterations by measuring active information storage (AIS)—a key quantity in the theory of distributed computation in biological networks. AIS is defined as the mutual information between the past state of a process and its next measurement. It measures the amount of stored information that is used for computation of the next time step of a process. AIS is high for rich but predictable dynamics. We recorded magnetoencephalography (MEG) signals in 10 ASD patients and 14 matched control subjects in a visual task. After a beamformer source analysis, 12 task-relevant sources were obtained. For these sources, stationary baseline activity was analyzed using AIS. Our results showed a decrease of AIS values in the hippocampus of ASD patients in comparison with controls, meaning that brain signals in ASD were either less predictable, reduced in their dynamic richness or both. Our study suggests the usefulness of AIS to detect an abnormal type of dynamics in ASD. The observed changes in AIS are compatible with Bayesian theories of reduced use or precision of priors in ASD.

Breakdown of local information processing may underlie isoflurane anesthesia effects

The disruption of coupling between brain areas has been suggested as the mechanism underlying loss of consciousness in anesthesia. This hypothesis has been tested previously by measuring the information transfer between brain areas, and by taking reduced information transfer as a proxy for decoupling. Yet, information transfer is a function of the amount of information available in the information source—such that transfer decreases even for unchanged coupling when less source information is available. Therefore, we reconsidered past interpretations of reduced information transfer as a sign of decoupling, and asked whether impaired local information processing leads to a loss of information transfer. An important prediction of this alternative hypothesis is that changes in locally available information (signal entropy) should be at least as pronounced as changes in information transfer. We tested this prediction by recording local field potentials in two ferrets after administration of isoflurane in concentrations of 0.0%, 0.5%, and 1.0%. We found strong decreases in the source entropy under isoflurane in area V1 and the prefrontal cortex (PFC)—as predicted by our alternative hypothesis. The decrease in source entropy was stronger in PFC compared to V1. Information transfer between V1 and PFC was reduced bidirectionally, but with a stronger decrease from PFC to V1. This links the stronger decrease in information transfer to the stronger decrease in source entropy—suggesting reduced source entropy reduces information transfer. This conclusion fits the observation that the synaptic targets of isoflurane are located in local cortical circuits rather than on the synapses formed by interareal axonal projections. Thus, changes in information transfer under isoflurane seem to be a consequence of changes in local processing more than of decoupling between brain areas. We suggest that source entropy changes must be considered whenever interpreting changes in information transfer as decoupling.

Revisiting Wiener's principle of causality — interaction-delay reconstruction using transfer entropy and multivariate analysis on delay-weighted graphs

To understand the function of networks we have to identify the structure of their interactions, but also interaction timing, as compromised timing of interactions may disrupt network function. We demonstrate how both questions can be addressed using a modified estimator of transfer entropy. Transfer entropy is an implementation of Wieners principle of observational causality based on information theory, and detects arbitrary linear and non-linear interactions. Using a modified estimator that uses delayed states of the driving system and independently optimized delayed states of the receiving system, we show that transfer entropy values peak if the delay of the state of the driving system equals the true interaction delay. In addition, we show how reconstructed delays from a bivariate transfer entropy analysis of a network can be used to label spurious interactions arising from cascade effects and apply this approach to local field potential (LFP) and magnetoencephalography (MEG) data.

A Graph Algorithmic Approach to Separate Direct from Indirect Neural Interactions

Network graphs have become a popular tool to represent complex systems composed of many interacting subunits; especially in neuroscience, network graphs are increasingly used to represent and analyze functional interactions between multiple neural sources. Interactions are often reconstructed using pairwise bivariate analyses, overlooking the multivariate nature of interactions: it is neglected that investigating the effect of one source on a target necessitates to take all other sources as potential nuisance variables into account; also combinations of sources may act jointly on a given target. Bivariate analyses produce networks that may contain spurious interactions, which reduce the interpretability of the network and its graph metrics. A truly multivariate reconstruction, however, is computationally intractable because of the combinatorial explosion in the number of potential interactions. Thus, we have to resort to approximative methods to handle the intractability of multivariate interaction reconstruction, and thereby enable the use of networks in neuroscience. Here, we suggest such an approximative approach in the form of an algorithm that extends fast bivariate interaction reconstruction by identifying potentially spurious interactions post-hoc: the algorithm uses interaction delays reconstructed for directed bivariate interactions to tag potentially spurious edges on the basis of their timing signatures in the context of the surrounding network. Such tagged interactions may then be pruned, which produces a statistically conservative network approximation that is guaranteed to contain non-spurious interactions only. We describe the algorithm and present a reference implementation in MATLAB to test the algorithm’s performance on simulated networks as well as networks derived from magnetoencephalographic data. We discuss the algorithm in relation to other approximative multivariate methods and highlight suitable application scenarios. Our approach is a tractable and data-efficient way of reconstructing approximative networks of multivariate interactions. It is preferable if available data are limited or if fully multivariate approaches are computationally infeasible.

Information theoretic evidence for predictive coding in the face processing system.

Predictive coding suggests that the brain infers the causes of its sensations by combining sensory evidence with internal predictions based on available prior knowledge. However, the neurophysiological correlates of (pre)activated prior knowledge serving these predictions are still unknown. Based on the idea that such preactivated prior knowledge must be maintained until needed, we measured the amount of maintained information in neural signals via the active information storage (AIS) measure. AIS was calculated on whole-brain beamformer-reconstructed source time courses from MEG recordings of 52 human subjects during the baseline of a Mooney face/house detection task. Preactivation of prior knowledge for faces showed as α-band-related and β-band-related AIS increases in content-specific areas; these AIS increases were behaviorally relevant in the brains fusiform face area. Further, AIS allowed decoding of the cued category on a trial-by-trial basis. Our results support accounts indicating that activated prior knowledge and the corresponding predictions are signaled in low-frequency activity (<30 Hz). SIGNIFICANCE STATEMENT Our perception is not only determined by the information our eyes/retina and other sensory organs receive from the outside world, but strongly depends also on information already present in our brains, such as prior knowledge about specific situations or objects. A currently popular theory in neuroscience, predictive coding theory, suggests that this prior knowledge is used by the brain to form internal predictions about upcoming sensory information. However, neurophysiological evidence for this hypothesis is rare, mostly because this kind of evidence requires strong a priori assumptions about the specific predictions the brain makes and the brain areas involved. Using a novel, assumption-free approach, we find that face-related prior knowledge and the derived predictions are represented in low-frequency brain activity.

Anesthesia-related changes in information transfer may be caused by reduction in local information generation.

In anesthesia research it is an open question how general anesthetics lead to loss of consciousness (LOC). It has been proposed that LOC may be caused by the disruption of cortical information processing, preventing information integration. Therefore, recent studies investigating information processing under anesthesia focused on changes in information transfer, measured by transfer entropy (TE). However, often this complex technique was not applied rigorously, using time series in symbolic representation, or using TE differences without accounting for neural conduction delays, or without accounting for signal history.

Need for and challenges facing functional communication as outcome parameter in AD clinical trials.

This paper (1) highlights the relevance of functional communication as an outcome parameter in Alzheimer disease (AD) clinical trials; (2) identifies studies that have reported functional communication outcome measures in AD clinical trials; (3) critically reviews the scales of functional communication used in recent AD clinical trials by summarizing the sources of information, characteristics, and available psychometric data for these scales; and (4) evaluates whether these measures actually or partially assess functional communication. To provide direction for future research and generate suggestions to assist in the development of a valid and reliable functional communication scale for the needs of AD clinical trials, we have included not only functional communication scales, but also related concepts that give thought-provoking impulses for the development of a functional communication scale. As outcome measures for AD clinical trials, the 6 identified papers use 6 different scales, for functional communication and for related concepts. All of the scales appear to have questionable psychometric properties, but still provide a promising basis for the creation of a functional communication scale. We conclude with concrete suggestions on how to combine the advantages of the existing scales for future research aimed at developing a valid and reliable functional communication scale for the needs of AD clinical trials.

Quantifying Information Modification in Developing Neural Networks via Partial Information Decomposition

Information processing performed by any system can be conceptually decomposed into the transfer, storage and modification of information—an idea dating all the way back to the work of Alan Turing. However, formal information theoretic definitions until very recently were only available for information transfer and storage, not for modification. This has changed with the extension of Shannon information theory via the decomposition of the mutual information between inputs to and the output of a process into unique, shared and synergistic contributions from the inputs, called a partial information decomposition (PID). The synergistic contribution in particular has been identified as the basis for a definition of information modification. We here review the requirements for a functional definition of information modification in neuroscience, and apply a recently proposed measure of information modification to investigate the developmental trajectory of information modification in a culture of neurons vitro, using partial information decomposition. We found that modification rose with maturation, but ultimately collapsed when redundant information among neurons took over. This indicates that this particular developing neural system initially developed intricate processing capabilities, but ultimately displayed information processing that was highly similar across neurons, possibly due to a lack of external inputs. We close by pointing out the enormous promise PID and the analysis of information modification hold for the understanding of neural systems.

Predictive coding over the lifespan: Increased reliance on perceptual priors in older adults — a magnetoencephalography and dynamic causal modelling study

Aging is accompanied by unisensory decline; but to compensate for this, two complementary strategies are potentially relied upon increasingly: first, older adults integrate more information from different sensory organs. Second, according to predictive coding (PC) we form ‘templates’ (internal models or ‘priors’) of the environment through our experiences. It is through increased life experience that older adults may rely more on these templates compared to younger adults. Multisensory integration and predictive coding would be effective strategies for the perception of near-threshold stimuli, but they come at the cost of integrating irrelevant information. Their role can be studied in multisensory illusions because these require the integration of different sensory information, as well as an internal model of the world that can take precedence over sensory input. Here, we elicited a classic multisensory illusion, the sound-induced flash illusion, in younger (mean: 27 yrs) and older (mean: 67 yrs) adult participants while recording the magnetoencephalogram. Older adults perceived more illusions than younger adults. Older adults had increased pre-stimulus beta(β)-band activity compared to younger adults as predicted by microcircuit theories of predictive coding, which suggest priors and predictions are linked to β-band activity. In line with our hypothesis, transfer entropy analysis and dynamic causal models of pre-stimulus MEG data revealed a stronger illusion-related modulation of cross-modal connectivity from auditory to visual cortices in older compared to younger adults. We interpret this as the neural correlate of increased reliance on a cross-modal predictive template in older adults that is leading to the illusory percept.