A
Bayesian approach to reconstructing genetic regulatory networks with hidden
factors
Matthew J. Beal,
Francesco Falciani, Zoubin Ghahramani, Claudia Rangel and David L. Wild
(Bioinformatics 2004)
Graph
(PDF version) representing gene-gene interactions
that are present in at least 80% of the VB state-space models from 10 random
initialisations and k=14 hidden states at a confidence level of 99.8%. The
number inside each node is the gene identity, with gene symbols given. Numbers
on the edges represent the number of models from 10 different random seeds in
which the interaction is supported at this confidence level. Dotted lined are
negative interactions, continuous lines represent positive interactions.
Genes without parents or self-feedback arcs have no direct or indirect
influence from genes at the previous time step; note that these genes may still
be driven by the hidden state dynamics via the C matrix, and therefore
influenced by genes at earlier time steps.
Figure showing the averaged inverses of the precisions of b which are summaries of the variances of the entries in each of the columns of the B matrix. In both plots, the columns refer to the corresponding gene, and each row corresponds to a model with a different number of hidden states, k=1..20. If a gene has a large component in the inverse precision b-1this implies that it plays an important role in determining the hidden state at the following time step. We see that for small simple models, most genes are directly involved in the hidden state dynamics; but for larger models the influence of almost all the genes decays, suggesting that the modeling load is being sharedacross several dimensions of the hidden state, or that the hidden state's dynamics becomes self-sustaining.
Figure showing the averaged inverses
of the precisions of d, which are summaries of the variances of the entries in
each of the columns of the D matrix. In
the plot of d-1we see that, with the
exception of a few genes, all remain useful in predicting at least one gene
(possibly itself) at the following time step.
