Causal network discovery by iterative conditioning: comparison of algorithms
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Estimating causal interactions in complex networks is an important problem encountered in many fields of current science. While a theoretical solution for detecting the graph of causal interactions has been previously formulated in the framework of prediction improvement, it generally requires the computation of high-dimensional information functionals -- a situation invoking the curse of dimensionality with increasing network size. Recently, several methods have been proposed to alleviate this problem, based on iterative procedures for assessment of conditional (in)dependences. In the current work, we bring a comparison of several such prominent approaches. This is done both by theoretical comparison of the algorithms using a formulation in a common framework, and by numerical simulations including realistic complex coupling patterns. The theoretical analysis shows that the algorithms are strongly related; including one algorithm being in particular situations equivalent to the first phase of another. Moreover, numerical simulations suggest that the accuracy of most of the algorithms is under suitable parameter choice almost indistinguishable. However, particularly for large networks there are substantial differences in their computational demands, suggesting some of the algorithms are relatively more efficient in the case of sparse networks, while other perform better in the case of dense networks. The most recent variant of the algorithm by Runge et al. then provides a promising speedup particularly for large sparse networks, albeit appears to lead to a substantial decrease in accuracy in some scenarios. Based on the analysis of the reviewed algorithms, we propose a hybrid approach that provides competitive results both concerning computational efficiency and accuracy.
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