Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions.

Causality shapes how we view, understand, and react to the world around us.

We first present a topological sorting algorithm that leverages ancestral relationships in linear structural causal models to establish a compact top-down hierarchical ordering, encoding more causal information than linear orderings produced by existing methods.

X and R L sib ( X, G), the following three statements are equivalent.

Fair machine learning aims to avoid treating individuals or sub-populations unfavourably based on sensitive attributes, such as gender and race.

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Discovering causal structures in data is a challenging task. Ideally, we would like to input the data into an algorithm that outputs one or more plausible causal directed acyclic graphs (DAGs) linking the variables in the data. Such data driven approaches for estimating a causal DAG are known as causal discovery (or causal search, structure learning etc.). While algorithms for causal discovery were first developed in the field of computer science more than twenty years ago [1] and have, since then, continually been generalised and refined [2], their use with biomedical or epidemiological data is still rare (other than in genetics [3]). Exceptions are, for example, two applications of causal discovery to data from cohort studies finding that modifiable risk factors in early childhood or early life have mostly indirect, if any, causal relations with later health outcomes[4, 5]. Similarly, in an analysis of healthcare data considering cardiac surgery it was found that many of the known predictors were in fact only indirect causes of postoperative length of stay [6]. Also, it has been suggested to use causal discovery to improve the quality of care for hip replacement patients by investigating the complex clinical performance of implants with data from large patient registries [7]. Typical causal analyses often aim at causal effect estimation. In contrast to the above, such analyses typically assume the causal structure, i.e. the DAG, to be given, usually derived from domain

Learning the unique directed acyclic graph corresponding to an unknown causal model is a challenging task. Methods based on functional causal models can identify a unique graph, but either suffer from the curse of dimensionality or impose strong parametric assumptions. To address these challenges, we propose a novel hybrid approach for global causal discovery in observational data that leverages local causal substructures. We first present a topological sorting algorithm that leverages ancestral relationships in linear structural equation models to establish a compact top-down hierarchical ordering, encoding more causal information than linear orderings produced by existing methods. We demonstrate that this approach generalizes to nonlinear settings with arbitrary noise. We then introduce a nonparametric constraint-based algorithm that prunes spurious edges by searching for local conditioning sets, achieving greater accuracy than current methods. We provide theoretical guarantees for correctness and worst-case polynomial time complexities, with empirical validation on synthetic data.

Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in the independence information have been proposed recently. Though promising, existing approaches can still be greatly improved in terms of accuracy and scalability. We present a novel method that reduces the combinatorial explosion of the search space by using a more coarse-grained representation of causal information, drastically reducing computation time. Additionally, we propose a method to score causal predictions based on their confidence. Crucially, our implementation also allows one to easily combine observational and interventional data and to incorporate various types of available background knowledge. We prove soundness and asymptotic consistency of our method and demonstrate that it can outperform the state-ofthe-art on synthetic data, achieving a speedup of several orders of magnitude. We illustrate its practical feasibility by applying it to a challenging protein data set.