MERLiN: Mixture Effect Recovery in Linear Networks

Causal inference concerns the identification of cause-effect relationships between variables, e.g. establishing whether a stimulus affects activity in a certain brain region. The observed variables themselves often do not constitute meaningful causal variables, however, and linear combinations need to be considered. In electroencephalographic studies, for example, one is not interested in establishing cause-effect relationships between electrode signals (the observed variables), but rather between cortical signals (the causal variables) which can be recovered as linear combinations of electrode signals. We introduce MERLiN (Mixture Effect Recovery in Linear Networks), a family of causal inference algorithms that implement a novel means of constructing causal variables from non-causal variables. We demonstrate through application to EEG data how the basic MERLiN algorithm can be extended for application to different (neuroimaging) data modalities. Given an observed linear mixture, the algorithms can recover a causal variable that is a linear effect of another given variable. That is, MERLiN allows us to recover a cortical signal that is affected by activity in a certain brain region, while not being a direct effect of the stimulus. The Python/Matlab implementation for all presented algorithms is available on https://github.com/sweichwald/MERLi

Beta Power May Mediate the Effect of Gamma-TACS on Motor Performance

Transcranial alternating current stimulation (tACS) is becoming an important method in the field of motor rehabilitation because of its ability to non-invasively influence ongoing brain oscillations at arbitrary frequencies. However, substantial variations in its effect across individuals are reported, making tACS a currently unreliable treatment tool. One reason for this variability is the lack of knowledge about the exact way tACS entrains and interacts with ongoing brain oscillations. The present crossover stimulation study on 20 healthy subjects contributes to the understanding of cross-frequency effects of gamma (70 Hz) tACS over the contralateral motor cortex by providing empirical evidence which is consistent with a role of low- (12~-20 Hz) and high- (20-~30 Hz) beta power as a mediator of gamma-tACS on motor performance.Comment: 7 pages, 5 figures, in Proceedings of IEEE Engineering in Medicine and Biology Conference, July 2019 (IEEE license notice

Quantifying causal influences

Many methods for causal inference generate directed acyclic graphs (DAGs) that formalize causal relations between $n$ variables. Given the joint distribution on all these variables, the DAG contains all information about how intervening on one variable changes the distribution of the other $n-1$ variables. However, quantifying the causal influence of one variable on another one remains a nontrivial question. Here we propose a set of natural, intuitive postulates that a measure of causal strength should satisfy. We then introduce a communication scenario, where edges in a DAG play the role of channels that can be locally corrupted by interventions. Causal strength is then the relative entropy distance between the old and the new distribution. Many other measures of causal strength have been proposed, including average causal effect, transfer entropy, directed information, and information flow. We explain how they fail to satisfy the postulates on simple DAGs of $\leq3$ nodes. Finally, we investigate the behavior of our measure on time-series, supporting our claims with experiments on simulated data.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1145 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Personalized Brain-Computer Interface Models for Motor Rehabilitation

We propose to fuse two currently separate research lines on novel therapies for stroke rehabilitation: brain-computer interface (BCI) training and transcranial electrical stimulation (TES). Specifically, we show that BCI technology can be used to learn personalized decoding models that relate the global configuration of brain rhythms in individual subjects (as measured by EEG) to their motor performance during 3D reaching movements. We demonstrate that our models capture substantial across-subject heterogeneity, and argue that this heterogeneity is a likely cause of limited effect sizes observed in TES for enhancing motor performance. We conclude by discussing how our personalized models can be used to derive optimal TES parameters, e.g., stimulation site and frequency, for individual patients.Comment: 6 pages, 6 figures, conference submissio