Graph reconstruction using covariance-based methods
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ABSTRACT
Methods based on correlation and partial correlation are today employed in the reconstruction of a statistical interaction graph from high-throughput omics data. These dedicated methods work well even for the case when the number of variables exceeds the number of samples. In this study, we investigate how the graphs extracted from covariance and concentration matrix estimates are related by using Neumann series and transitive closure and through discussing concrete small examples. Considering the ideal case where the true graph is available, we also compare correlation and partial correlation methods for large realistic graphs. In particular, we perform the comparisons with optimally selected parameters based on the true underlying graph and with data-driven approaches where the parameters are directly estimated from the data. Electronic supplementary material: The online version of this article (doi:10.1186/s13637-016-0052-y) contains supplementary material, which is available to authorized users. No MeSH data available. |
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Mentions: In the following, we investigate how this scaling parameter affects indirect edges of different order with numerical simulations. For this purpose, we choose a six-node chain graph, generate synthetic data using the workflow illustrated in Fig. 4, and compute the correlation matrix. The covariance graph reconstructed from the correlation matrix is accordingly fully connected and has five direct and ten indirect edges, where edges of the same order were assigned the same weight. |
View Article: PubMed Central - PubMed
Methods based on correlation and partial correlation are today employed in the reconstruction of a statistical interaction graph from high-throughput omics data. These dedicated methods work well even for the case when the number of variables exceeds the number of samples. In this study, we investigate how the graphs extracted from covariance and concentration matrix estimates are related by using Neumann series and transitive closure and through discussing concrete small examples. Considering the ideal case where the true graph is available, we also compare correlation and partial correlation methods for large realistic graphs. In particular, we perform the comparisons with optimally selected parameters based on the true underlying graph and with data-driven approaches where the parameters are directly estimated from the data.
Electronic supplementary material: The online version of this article (doi:10.1186/s13637-016-0052-y) contains supplementary material, which is available to authorized users.
No MeSH data available.