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

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease with substantial heterogeneity in its clinical presentation. This makes diagnosis and effective treatment difficult, so better tools for estimating disease progression are needed. Here, we report results from the DREAM-Phil Bowen ALS Prediction Prize4Life challenge. In this crowdsourcing competition, competitors developed algorithms for the prediction of disease progression of 1,822 ALS patients from standardized, anonymized phase 2/3 clinical trials. The two best algorithms outperformed a method designed by the challenge organizers as well as predictions by ALS clinicians. We estimate that using both winning algorithms in future trial designs could reduce the required number of patients by at least 20%. The DREAM-Phil Bowen ALS Prediction Prize4Life challenge also identified several potential nonstandard predictors of disease progression including uric acid, creatinine and surprisingly, blood pressure, shedding light on ALS pathobiology. This analysis reveals the potential of a crowdsourcing competition that uses clinical trial data for accelerating ALS research and development

We address two shortcomings of the common spatial patterns (CSP) algorithm for spatial filtering in the context of brain--computer interfaces (BCIs) based on electroencephalography/magnetoencephalography (EEG/MEG): First, the question of optimality of CSP in terms of the minimal achievable classification error remains unsolved. Second, CSP has been initially proposed for two-class paradigms. Extensions to multiclass paradigms have been suggested, but are based on heuristics. We address these shortcomings in the framework of information theoretic feature extraction (ITFE). We show that for two-class paradigms, CSP maximizes an approximation of mutual information of extracted EEG/MEG components and class labels. This establishes a link between CSP and the minimal classification error. For multiclass paradigms, we point out that CSP by joint approximate diagonalization (JAD) is equivalent to independent component analysis (ICA), and provide a method to choose those independent components (ICs) that approximately maximize mutual information of ICs and class labels. This eliminates the need for heuristics in multiclass CSP, and allows incorporating prior class probabilities. The proposed method is applied to the dataset IIIa of the third BCI competition, and is shown to increase the mean classification accuracy by 23.4% in comparison to multiclass CSP.

Analyzing neural signals and providing feedback in realtime is one of the core characteristics of a brain–computer interface (BCI). As this feature may be employed to induce neural plasticity, utilizing BCI technology for therapeutic purposes is increasingly gaining popularity in the BCI community. In this paper, we discuss the state-of-the-art of research on this topic, address the principles of and challenges in inducing neural plasticity by means of a BCI, and delineate the problems of study design and outcome evaluation arising in this context. We conclude with a list of open questions and recommendations for future research in this field.