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

Bounding probabilities of causation through the causal marginal problem

Probabilities of Causation play a fundamental role in decision making in law, health care and public policy. Nevertheless, their point identification is challenging, requiring strong assumptions such as monotonicity. In the absence of such assumptions, existing work requires multiple observations of datasets that contain the same treatment and outcome variables, in order to establish bounds on these probabilities. However, in many clinical trials and public policy evaluation cases, there exist independent datasets that examine the effect of a different treatment each on the same outcome variable. Here, we outline how to significantly tighten existing bounds on the probabilities of causation, by imposing counterfactual consistency between SCMs constructed from such independent datasets ('causal marginal problem'). Next, we describe a new information theoretic approach on falsification of counterfactual probabilities, using conditional mutual information to quantify counterfactual influence. The latter generalises to arbitrary discrete variables and number of treatments, and renders the causal marginal problem more interpretable. Since the question of 'tight enough' is left to the user, we provide an additional method of inference when the bounds are unsatisfactory: A maximum entropy based method that defines a metric for the space of plausible SCMs and proposes the entropy maximising SCM for inferring counterfactuals in the absence of more information

Toward Falsifying Causal Graphs Using a Permutation-Based Test

Understanding the causal relationships among the variables of a system is paramount to explain and control its behaviour. Inferring the causal graph from observational data without interventions, however, requires a lot of strong assumptions that are not always realistic. Even for domain experts it can be challenging to express the causal graph. Therefore, metrics that quantitatively assess the goodness of a causal graph provide helpful checks before using it in downstream tasks. Existing metrics provide an absolute number of inconsistencies between the graph and the observed data, and without a baseline, practitioners are left to answer the hard question of how many such inconsistencies are acceptable or expected. Here, we propose a novel consistency metric by constructing a surrogate baseline through node permutations. By comparing the number of inconsistencies with those on the surrogate baseline, we derive an interpretable metric that captures whether the DAG fits significantly better than random. Evaluating on both simulated and real data sets from various domains, including biology and cloud monitoring, we demonstrate that the true DAG is not falsified by our metric, whereas the wrong graphs given by a hypothetical user are likely to be falsified.Comment: 23 pages, 9 figure

Assumption violations in causal discovery and the robustness of score matching

When domain knowledge is limited and experimentation is restricted by ethical, financial, or time constraints, practitioners turn to observational causal discovery methods to recover the causal structure, exploiting the statistical properties of their data. Because causal discovery without further assumptions is an ill-posed problem, each algorithm comes with its own set of usually untestable assumptions, some of which are hard to meet in real datasets. Motivated by these considerations, this paper extensively benchmarks the empirical performance of recent causal discovery methods on observational i.i.d. data generated under different background conditions, allowing for violations of the critical assumptions required by each selected approach. Our experimental findings show that score matching-based methods demonstrate surprising performance in the false positive and false negative rate of the inferred graph in these challenging scenarios, and we provide theoretical insights into their performance. This work is also the first effort to benchmark the stability of causal discovery algorithms with respect to the values of their hyperparameters. Finally, we hope this paper will set a new standard for the evaluation of causal discovery methods and can serve as an accessible entry point for practitioners interested in the field, highlighting the empirical implications of different algorithm choices