ASP-based Discovery of Semi-Markovian Causal Models under Weaker Assumptions

In recent years the possibility of relaxing the so-called Faithfulness assumption in automated causal discovery has been investigated. The investigation showed (1) that the Faithfulness assumption can be weakened in various ways that in an important sense preserve its power, and (2) that weakening of Faithfulness may help to speed up methods based on Answer Set Programming. However, this line of work has so far only considered the discovery of causal models without latent variables. In this paper, we study weakenings of Faithfulness for constraint-based discovery of semi-Markovian causal models, which accommodate the possibility of latent variables, and show that both (1) and (2) remain the case in this more realistic setting

Learning high-dimensional directed acyclic graphs with latent and selection variables

We consider the problem of learning causal information between random variables in directed acyclic graphs (DAGs) when allowing arbitrarily many latent and selection variables. The FCI (Fast Causal Inference) algorithm has been explicitly designed to infer conditional independence and causal information in such settings. However, FCI is computationally infeasible for large graphs. We therefore propose the new RFCI algorithm, which is much faster than FCI. In some situations the output of RFCI is slightly less informative, in particular with respect to conditional independence information. However, we prove that any causal information in the output of RFCI is correct in the asymptotic limit. We also define a class of graphs on which the outputs of FCI and RFCI are identical. We prove consistency of FCI and RFCI in sparse high-dimensional settings, and demonstrate in simulations that the estimation performances of the algorithms are very similar. All software is implemented in the R-package pcalg.Comment: Published in at http://dx.doi.org/10.1214/11-AOS940 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Geometry of the faithfulness assumption in causal inference

Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or high-dimensional consistency. In contrast to the plain faithfulness assumption, the set of distributions that is not strong-faithful has nonzero Lebesgue measure and in fact, can be surprisingly large as we show in this paper. We study the strong-faithfulness condition from a geometric and combinatorial point of view and give upper and lower bounds on the Lebesgue measure of strong-faithful distributions for various classes of directed acyclic graphs. Our results imply fundamental limitations for the PC-algorithm and potentially also for other algorithms based on partial correlation testing in the Gaussian case.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1080 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Three algorithms for causal learning

The field of causal learning has grown in the past decade, establishing itself as a major focus in artificial intelligence research. Traditionally, approaches to causal learning are split into two areas. One area involves the learning of structures from observational data alone and the second, involves the methodologies of conducting and learning from experiments. In this dissertation, I investigate three different aspects of causal learning, all of which are based on the causal Bayesian network framework. Constraint based structure search algorithms that learn partially directed acyclic graphs as causal models from observational data rely on the faithfulness assumption, which is often violated due to inaccurate statistical tests on finite datasets. My first contribution is a modification of the traditional approaches to achieving greater robustness in the light of these faults. Secondly, I present a new algorithm to infer the parent set of a variable when a specific type of experiment called a `hard intervention\u27 is performed. I also present an auxiliary result of this effort, a fast algorithm to estimate the Kullback Leibler divergence of high dimensional distributions from datasets. Thirdly, I introduce a fast heuristic algorithm to optimize the number and sequence of experiments required towards complete causal discovery for different classes of causal graphs and provide suggestions for implementing an interactive version. Finally, I provide numerical simulation results for each algorithm discussed and present some directions for future research