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Analysing causal structures with entropy.

ABSTRACT: A central question for causal inference is to decide whether a set of correlations fits a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for certificates of compatibility. Here, we review several such approaches based on entropy. We bring together the key aspects of these entropic techniques with unified terminology, filling several gaps and establishing new connections, all illustrated with examples. We consider cases where unobserved causes are classical, quantum and post-quantum, and discuss what entropic analyses tell us about the difference. This difference has applications to quantum cryptography, where it can be crucial to eliminate the possibility of classical causes. We discuss the achievements and limitations of the entropic approach in comparison to other techniques and point out the main open problems.

SUBMITTER: Weilenmann M

PROVIDER: S-EPMC5719630 | biostudies-literature | 2017 Nov

REPOSITORIES: biostudies-literature

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Analysing causal structures with entropy.

Weilenmann Mirjam M Colbeck Roger R

Proceedings. Mathematical, physical, and engineering sciences 20171101 2207

A central question for causal inference is to decide whether a set of correlations fits a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for certificates of compatibility. Here, we review several such approaches based on entropy. We bring together the key aspects of these entropic techniques with unified terminology, filling several gaps and establishing new connections, all illustrated with examples. We ...[more]

PMID: 29225499

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Project description:BackgroundOne of the core issues of forest community ecology is the exploration of how ecological processes affect community structure. The relative importance of different processes is still under debate. This study addresses four questions: (1) how is the taxonomic structure of a forest community affected by spatial scale? (2) does the taxonomic structure reveal effects of local processes such as environmental filtering, dispersal limitation or interspecific competition at a local scale? (3) does the effect of local processes on the taxonomic structure vary with the spatial scale? (4) does the analysis based on taxonomic structures provide similar insights when compared with the use of phylogenetic information? Based on the data collected in two large forest observational field studies, the taxonomic structures of the plant communities were analyzed at different sampling scales using taxonomic ratios (number of genera/number of species, number of families/number of species), and the relationship between the number of higher taxa and the number of species. Two random null models were used and the "standardized effect size" (SES) of taxonomic ratios was calculated, to assess possible differences between the observed and simulated taxonomic structures, which may be caused by specific ecological processes. We further applied a phylogeny-based method to compare results with those of the taxonomic approach.ResultsAs expected, the taxonomic ratios decline with increasing grain size. The quantitative relationship between genera/families and species, described by a linearized power function, showed a good fit. With the exception of the family-species relationship in the Jiaohe study area, the exponents of the genus/family-species relationships did not show any scale dependent effects. The taxonomic ratios of the observed communities had significantly lower values than those of the simulated random community under the test of two null models at almost all scales. Null Model 2 which considered the spatial dispersion of species generated a taxonomic structure which proved to be more consistent with that in the observed community. As sampling sizes increased from 20 m × 20 m to 50 m × 50 m, the magnitudes of SESs of taxonomic ratios increased. Based on the phylogenetic analysis, we found that the Jiaohe plot was phylogenetically clustered at almost all scales. We detected significant phylogenetically overdispersion at the 20 m × 20 m and 30 m × 30 m scales in the Liangshui plot.ConclusionsThe results suggest that the effect of abiotic filtering is greater than the effects of interspecific competition in shaping the local community at almost all scales. Local processes influence the taxonomic structures, but their combined effects vary with the spatial scale. The taxonomic approach provides similar insights as the phylogenetic approach, especially when we applied a more conservative null model. Analysing taxonomic structure may be a useful tool for communities where well-resolved phylogenetic data are not available.

Dataset Information

Analysing causal structures with entropy.

Publications

Analysing causal structures with entropy.

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