![](bg7.png)
0 20 40 60 80 100
top x%
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
AUPR
Figure 5: Average AUPR for inferred networks of reliable
top x% edges.
posed method can translate a problem to use other es-
timators of residuals ε, η and independence measures
instead of HKRR and J. The score of p-value offered
by the permutation test can be interpreted as the sig-
nificance level, and this threshold is easier to deter-
mine than other scores such as the conditional mutual
information. Additionally, the reliability of p-value is
defined.
The proposed method was applied to inferring
artificial gene networks from the Dream4 challenge
datasets, and had the better performance in terms of
AUROC and AUPR. Although the proposed method
infers an part of network by omitting low reliable
p-values, there an advantage to find unknown asso-
ciations. Furthermore, merging parts of network of
high reliable p-values inferred by various estimators
would be a promising strategy to identify whole net-
work structure.
The proposed method would be basically ex-
tended to the inference of associative networks in case
that the dataset is many-dimensional, that is, X and
Y can be multidimensional. This method may prove
useful, for instance, in the examination of associations
between layers or pathways in transomics datasets.
The HKRR method is employed to infer ε and η in
the method proposed above. However, if p(x|Z) or
p(y|Z) can have a multi-modal distribution for some
fixed Z, HKRR is no longer suitable. The appropriate
method for inferring ε and η depends on the distri-
bution of the data in question, and demands further
study.
ACKNOWLEDGEMENTS
This work was supported by the Creating informa-
tion utilization platform by integrating mathemati-
cal and information sciences, and development to so-
ciety, CREST (JPMJCR1912) from the Japan Sci-
ence and Technology Agency (JST) and by the Japan
Society for the Promotion of Science (JSPS) KAK-
ENHI Grant Number (JP18H04801, JP18H02431)
and Kayamori Foundation of Informational Science
Advancement.
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