By aggregating data for complex traits in a biologically meaningful way, gene and gene-set analysis constitute a valuable addition to single-marker analysis. However, although various methods for gene and gene-set analysis currently exist, they generally suffer from a number of issues. Statistical power for most methods is strongly affected by linkage disequilibrium between markers, multi-marker associations are often hard to detect, and the reliance on permutation to compute p-values tends to make the analysis computationally very expensive. To address these issues we have developed MAGMA, a novel tool for gene and gene-set analysis. The gene analysis is based on a multiple regression model, to provide better statistical performance. The gene-set analysis is built as a separate layer around the gene analysis for additional flexibility. This gene-set analysis also uses a regression structure to allow generalization to analysis of continuous properties of genes and simultaneous analysis of multiple gene sets and other gene properties. Simulations and an analysis of Crohn’s Disease data are used to evaluate the performance of MAGMA and to compare it to a number of other gene and gene-set analysis tools. The results show that MAGMA has significantly more power than other tools for both the gene and the gene-set analysis, identifying more genes and gene sets associated with Crohn’s Disease while maintaining a correct type 1 error rate. Moreover, the MAGMA analysis of the Crohn’s Disease data was found to be considerably faster as well.

While conventional approaches to causal inference are mainly based on conditional (in)dependences, recent methods also account for the shape of (conditional) distributions. The idea is that the causal hypothesis “X causes Y” imposes that the marginal distribution PX and the conditional distribution PY|X represent independent mechanisms of nature. Recently it has been postulated that the shortest description of the joint distribution PX,Y should therefore be given by separate descriptions of PX and PY|X. Since description length in the sense of Kolmogorov complexity is uncomputable, practical implementations rely on other notions of independence. Here we define independence via orthogonality in information space. This way, we can explicitly describe the kind of dependence that occurs between PY and PX|Y making the causal hypothesis “Y causes X” implausible. Remarkably, this asymmetry between cause and effect becomes particularly simple if X and Y are deterministically related. We present an inference method that works in this case. We also discuss some theoretical results for the non-deterministic case although it is not clear how to employ them for a more general inference method

We derive novel conditions that guarantee convergence of the Sum-Product algorithm (also known as Loopy Belief Propagation or simply Belief Propagation) to a unique fixed point, irrespective of the initial messages. The computational complexity of the conditions is polynomial in the number of variables. In contrast with previously existing conditions, our results are directly applicable to arbitrary factor graphs (with discrete variables) and are shown to be valid also in the case of factors containing zeros, under some additional conditions. We compare our bounds with existing ones, numerically and, if possible, analytically. For binary variables with pairwise interactions, we derive sufficient conditions that take into account local evidence (i.e. single variable factors) and the type of pair interactions (attractive or repulsive). It is shown empirically that this bound outperforms existing bounds.

Inferring causal effects from observational and interventional data is a highly desirable but ambitious goal. Many of the computational and statistical methods are plagued by fundamental identifiability issues, instability, and unreliable performance, especially for largescale systems with many measured variables. We present software and provide some validation of a recently developed methodology based on an invariance principle, called invariant causal prediction (ICP). The ICP method quantifies confidence probabilities for inferring causal structures and thus leads to more reliable and confirmatory statements for causal relations and predictions of external intervention effects. We validate the ICP method and some other procedures using large-scale genome-wide gene perturbation experiments in Saccharomyces cerevisiae. The results suggest that prediction and prioritization of future experimental interventions, such as gene deletions, can be improved by using our statistical inference techniques.interventional-observational data | invariant causal prediction | genome database validation | graphical models I n this article, we discuss statistical methods for causal inference from perturbation experiments. As this is a rather general topic, we focus on the following problem: based on data from observational and perturbation settings, we want to predict the effect and outcome of an unseen and new intervention or perturbation. Taking applications in genomics as an example, a typical task is as follows: based on observational data from wild-type organisms and interventional data from gene knockout or knockdown experiments, we want to predict the effect of a new gene knockout or knockdown on a phenotype of interest. For example, the organism is the model plant Arabidopsis thaliana, the gene knockouts correspond to mutant plants, and the phenotype of interest is the time it takes until the plant is flowering (1).From a methodological viewpoint, the prediction of unseen future interventions belongs to the area of causal inference where one aims to quantify presence and strength of causal effects among various variables. Loosely speaking, a causal effect is the effect of an external intervention (or say the response to a "What if I do?" question). The corresponding theory, e.g., using Pearl's do-operator (2), provides a link between causal effects and perturbations or randomized experiments. We mostly assume here that all of the variables in the causal model (for inferring causal effects) are observed: the case with hidden variables is mentioned only briefly in a later section, although it is an important theme in causal inference (due to the problem of hidden confounding variables) (cf. refs. 2 and 3).A popular and powerful route for causal modeling is given by structural equation models (SEMs) (2, 4). We consider a set of random variables X 1 , . . . , X p , X p+1 , and we often denote by Y = X 1 , emphasizing that Y is our response variable of interest (e.g., a phenotype of interest). The main building blocks of a SEM...

Motivated by causal inference problems, we propose a novel method for regression that minimizes the statistical dependence between regressors and residuals. The key advantage of this approach to regression is that it does not assume a particular distribution of the noise, i.e., it is non-parametric with respect to the noise distribution. We argue that the proposed regression method is well suited to the task of causal inference in additive noise models. A practical disadvantage is that the resulting optimization problem is generally non-convex and can be difficult to solve. Nevertheless, we report good results on one of the tasks of the NIPS 2008 Causality Challenge, where the goal is to distinguish causes from effects in pairs of statistically dependent variables. In addition, we propose an algorithm for efficiently inferring causal models from observational data for more than two variables. The required number of regressions and independence tests is quadratic in the number of variables, which is a significant improvement over the simple method that tests all possible DAGs