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On the statistical significance of communities from weighted graphs.

ABSTRACT: Community detection is a fundamental procedure in the analysis of network data. Despite decades of research, there is still no consensus on the definition of a community. To analytically test the realness of a candidate community in weighted networks, we present a general formulation from a significance testing perspective. In this new formulation, the edge-weight is modeled as a censored observation due to the noisy characteristics of real networks. In particular, the edge-weights of missing links are incorporated as well, which are specified to be zeros based on the assumption that they are truncated or unobserved. Thereafter, the community significance assessment issue is formulated as a two-sample test problem on censored data. More precisely, the Logrank test is employed to conduct the significance testing on two sets of augmented edge-weights: internal weight set and external weight set. The presented approach is evaluated on both weighted networks and un-weighted networks. The experimental results show that our method can outperform prior widely used evaluation metrics on the task of individual community validation.

SUBMITTER: He Z

PROVIDER: S-EPMC8514603 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundCausal graphs are an increasingly popular tool for the analysis of biological datasets. In particular, signed causal graphs--directed graphs whose edges additionally have a sign denoting upregulation or downregulation--can be used to model regulatory networks within a cell. Such models allow prediction of downstream effects of regulation of biological entities; conversely, they also enable inference of causative agents behind observed expression changes. However, due to their complex nature, signed causal graph models present special challenges with respect to assessing statistical significance. In this paper we frame and solve two fundamental computational problems that arise in practice when computing appropriate null distributions for hypothesis testing.ResultsFirst, we show how to compute a p-value for agreement between observed and model-predicted classifications of gene transcripts as upregulated, downregulated, or neither. Specifically, how likely are the classifications to agree to the same extent under the null distribution of the observed classification being randomized? This problem, which we call "Ternary Dot Product Distribution" owing to its mathematical form, can be viewed as a generalization of Fisher's exact test to ternary variables. We present two computationally efficient algorithms for computing the Ternary Dot Product Distribution and investigate its combinatorial structure analytically and numerically to establish computational complexity bounds.Second, we develop an algorithm for efficiently performing random sampling of causal graphs. This enables p-value computation under a different, equally important null distribution obtained by randomizing the graph topology but keeping fixed its basic structure: connectedness and the positive and negative in- and out-degrees of each vertex. We provide an algorithm for sampling a graph from this distribution uniformly at random. We also highlight theoretical challenges unique to signed causal graphs; previous work on graph randomization has studied undirected graphs and directed but unsigned graphs.ConclusionWe present algorithmic solutions to two statistical significance questions necessary to apply the causal graph methodology, a powerful tool for biological network analysis. The algorithms we present are both fast and provably correct. Our work may be of independent interest in non-biological contexts as well, as it generalizes mathematical results that have been studied extensively in other fields.

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On the statistical significance of communities from weighted graphs.

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