Introduction
This vignette serves the purpose to reproduce the results shown in
the section “Real data example” of the manuscript describing
collaborative graphical lasso (Albanese, Kohlen
and Behrouzi, 2024). The computations carried out by the following
code are heavy and could take a considerable amount of time. On our
machine (RAM 48 Gb, CPU Intel(R) Xeon(R) W-2235 CPU @ 3.80GHz) it took
almost 3 hours. Hence, we refer the user who wants to get started with
the package to the introductory vignette:
vignette("coglasso"). Collaborative graphical
lasso is an algorithm to reconstruct multi-omics networks based on
graphical lasso (Friedman, Hastie and
Tibshirani, 2008) and collaborative regression (Gross and Tibshirani, 2015). The coglasso package
implements and R interface to this algorithm. We will use it to
reproduce the results obtained in the original manuscript.
Let us first attach coglasso.
We will use the multi-omics data set provided by the package, in its
largest version: multi_omics_sd. Let’s inspect its
description in the manual.
help(multi_omics_sd)We notice that this data set has 162 transcripts and 76 metabolites. For further information on the data set sources and generation, we refer the user to the script multi_omics_sd.R on the GitHub repository of the package.
Reproducing the results
For the multi-omics network reconstruction carried out in the manuscript we explored 30 automatically generated and values and 9 given values.
nlambda_w <- 30
nlambda_b <- 30
cs <- c(0.01, 0.05, 0.1, 0.2, 1, 5, 10, 20, 100)We can now build the networks, one per combination of the chosen
hyperparameters, with coglasso().
cg <- coglasso(multi_omics_sd,
p = 162,
nlambda_w = nlambda_w,
nlambda_b = nlambda_b,
c = cs
)We proceed now to select the most stable, yet sparse network, using
eXtended StARS (XStARS, Albanese,
Kohlen and Behrouzi, 2024), an adaptation to coglasso of
StARS (Liu, Roeder and Wasserman, 2010). The
function implementing XStARS is select_coglasso(),
when setting the argument method to “xstars” (which is the
default behaviour).
set.seed(42)
sel_cg <- select_coglasso(cg, method = "xstars")We display now the selected network using the package
igraph, reproducing the one displayed in Figure 3 of the
manuscript. The orientation of the network may vary.
plot(sel_cg)We now plot the subnetwork of the gene Cirbp and of its neighborhood. This reproduces the network displayed in Figure 4A.
igraph::V(sel_graph)$label<-colnames(sel_cg$data)
cirbp_index <- which(colnames(sel_cg$data) == "Cirbp")
subnetwork <- igraph::subgraph(
sel_graph,
c(cirbp_index, igraph::neighbors(sel_graph, cirbp_index))
)
plot(subnetwork)A useful way to extract information from a network is community
discovery. This technique allows to simplify a network by breaking it in
functional units where nodes share several connections, enough to be
recognized as separate communities. In the manuscript we used the greedy
algorithm described in Clauset, Newman and Moore,
2004, part of the igraph toolkit. We focused and
inspected the second largest community, shown in Figure 4B. Here is the
code to reproduce it.
communities <- igraph::cluster_fast_greedy(sel_graph)
community2 <- communities[[2]]
community2_graph<-igraph::subgraph(sel_graph, community2)
# Focusing on nodes of interest
fosjun_erg_AA <- c("Fos", "Fosb", "Junb", "Fosl2", "Egr1", "Egr2", "Egr3", "Ala", "Arg", "Asn","His","Ile","Leu","Lys","Met","Orn","Phe","Ser","Thr","Tyr","Val")
igraph::V(community2_igraph)[!(label %in% fosjun_erg_AA)]$color<-c(rep("#3bd8ff", 29), rep("#ffadad", 5))
igraph::V(community2_igraph)[!(label %in% fosjun_erg_AA)]$frame.color<-NA
igraph::V(community2_igraph)[!(label %in% fosjun_erg_AA)]$label<-NA
lo_community2 <- igraph::layout_with_fr(community2_graph)
plot(community2_graph, layout=lo_community2)References
Albanese, A., Kohlen, W., & Behrouzi, P. (2024). Collaborative graphical lasso (arXiv:2403.18602). arXiv https://doi.org/10.48550/arXiv.2403.18602
Friedman, J., Hastie, T., & Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3), 432–441. https://doi.org/10.1093/biostatistics/kxm045
Gross, S. M., & Tibshirani, R. (2015). Collaborative regression. Biostatistics, 16(2), 326–338. https://doi.org/10.1093/biostatistics/kxu047
Liu, H., Roeder, K., & Wasserman, L. (2010). Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models (arXiv:1006.3316). arXiv. https://doi.org/10.48550/arXiv.1006.3316
Clauset, A., Newman, M. E. J., & Moore, C. (2004). Finding community structure in very large networks. Physical Review E, 70(6), 066111. https://doi.org/10.1103/PhysRevE.70.066111