Fig 1.
Example of Misleading Inference if Hidden Common Cause is Ignored.
The number on the link is the delay, and + or − is the sign of the effect.
Fig 2.
Overall Flow of the Algorithm.
The steps are 1) infer an initial GRN of the observed genes, 2) determine the genes with hidden common cause(s) by the variance of the error terms, 3) estimate the hidden common cause(s), 4) infer the parents and children of the hidden common causes.
Fig 3.
X and Y are independent. H is hidden.
Fig 4.
Illustration of Estimation of Hidden Common Cause from Un-aligned Time Series.
Fig 5.
Illustration of Handling Multiple Segments of Time Series.
Table 1.
Information of the Time Series Real Data.
Fig 6.
Example of Flipping Signs of Links and Shifting of Delays for Hidden Node.
The number on the link is the delay, and + or − is the sign of the effect. Consistently flipping the signs and shifting the delays results in equivalent predicted GRN, as the hidden node is not observed.
Fig 7.
There are p parents, c children and one hidden node.
Table 2.
Parameter Settings of Synthetic Data Generation.
Fig 8.
Profiles of F-scores of Links, Delays and Effects for Different Settings for Small Hidden Case.
The x-axis shows the records.
Fig 9.
Histogram of Absolute Difference of F-scores of Links and Effects for Small Hidden Case.
Fig 10.
Boxplot of Effect F-score with Different σ2 for Small Hidden Case.
Table 3.
Median Effects F-scores for One Segment Small Hidden Case with σ2 = 2.
Table 4.
Median Effects F-scores for Multiple Segments Small Hidden Case with σ2 = 2.
Table 5.
Median Effects F-scores for One Segment Small Non-Hidden Case with σ2 = 2.
Table 6.
Median Effects F-scores for Multiple Segments Small Non-Hidden Case with σ2 = 2.
Fig 11.
Each hidden node has up to 3 distinct parents, and up to 5 distinct children.
Fig 12.
Profiles of F-scores of Links, Delays and Effects for Different Settings for Large Case.
The x-axis shows the records.
Fig 13.
Profiles of Effects F-scores for Different σ2 for Different Settings for Large Case.
The x-axis shows the records.
Table 7.
Median Effects F-scores for One Segment Large Case with σ2 = 2.
Table 8.
Median Effects F-scores for Multiple Segments Large Case with σ2 = 2.
Table 9.
P-values of one-sided Wilcoxon signed-rank test on whether the medians Effects F-scores of hidden is better than hiddenCL for the One Segment Large Case with σ2 = 2.
Table 10.
P-values of one-sided Wilcoxon signed-rank test on whether the medians Effects F-scores of hidden is better than hiddenCL for the Multiple Segments Large Case with σ2 = 2.
Fig 14.
Median Effects F-scores for n = 50 with Different δ2 for One Segment Large Case.
complete is using CLINDE on the complete data. hidden is our proposed algorithm on the incomplete data. hiddenCL is CLINDE on the incomplete data. st used is 2.
Fig 15.
Median Effects F-scores for n = 100 with Different δ2 for One Segment Large Case.
complete is using CLINDE on the complete data. hidden is our proposed algorithm on the incomplete data. hiddenCL is CLINDE on the incomplete data. st used is 2.
Fig 16.
Median Effects F-scores for n = 50 with Different δ2 for Multiple Segments Large Case.
complete is using CLINDE on the complete data. hidden is our proposed algorithm on the incomplete data. hiddenCL is CLINDE on the incomplete data. st used is 2.
Fig 17.
Median Effects F-scores for n = 100 with Different δ2 for Multiple Segments Large Case.
complete is using CLINDE on the complete data. hidden is our proposed algorithm on the incomplete data. hiddenCL is CLINDE on the incomplete data. st used is 2.
Table 11.
P-values of one-sided Wilcoxon signed-rank test on whether the medians Effects F-scores of hidden is better than hiddenCL for the Heterogeneous Variance Large Case.
Table 12.
YEASTRACT Subnetworks.
Table 13.
Links F-scores for YEASTRACT Subnetworks.