Abstract
For many data analysis tasks, obtaining the causal relationships between interacting objects is of crucial interest. Here, the case of modelling causal relationships via causal orderings is considered. Triplet ordering preferences are used to perform Monte Carlo sampling of the posterior causal orderings originating from the analysis of experiments involving observation as well as, usually few, interventions, like knockouts in case of gene expression. The performance of this sampling approach is compared to a previously used sampling via pairwise ordering preference as well as to the sampling of the full posterior distribution. This is performed for artificially generated causal, i.e. directed acyclic graphs (DAGs) with a scale-free structure, i.e. a power-law distribution for the out-degree. The sampling using the triplets ordering turns out to be superior to both other approaches, similar to our previous work, where the less-realistic case of Erdős-R é nyi random graphs was considered.
Highlights
When analysing large sets of data, on important task is to identify causal relationships [1] between the objects described by the data
As explained in Ref. [9] estimating the underlying directed acyclic graphs (DAGs) (Directed Acyclic Graph) structure of a causal Bayesian network is equivalent to finding of the so-called causal ordering between the genes of interest
We show how pair- and triplet-approximations are used to speed up the sampling procedure
Summary
When analysing large sets of data, on important task is to identify causal relationships [1] between the objects described by the data. [9] estimating the underlying DAG (Directed Acyclic Graph) structure of a causal Bayesian network is equivalent to finding of the so-called causal ordering between the genes of interest. Given that for practical applications one only has a finite amount of computational resources available, only small networks can be treated in this way For this reason, an approximation based solely on pairwise probabilities of ordering preference has recently been introduced [11]. For real systems the underlying graphs usually have a more complicated structure, [14] often resulting in a scale-free, i.e. power-law, degree distribution For this reason, we have applied the pair- and triplet-based approaches to scale-free graphs.
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