#Introduction
Extending results from the Cascade package: reverse engineering with selectboost to compute confidence indices for a fitted model. We first fit a model to a cascade network using the Cascade package inference function then we compute confidence indices for the inferred links using the Selecboost algorithm.
If you are a Linux/Unix or a Macos user, you can install a version of SelectBoost with support for doMC from github with:
devtools::install_github("fbertran/SelectBoost", ref = "doMC")Reference for the Cascade modelling: Vallat, L., Kemper, C. a., Jung, N., Maumy-Bertrand, M., Bertrand, F., Meyer, N., Pocheville, A., Fisher, J. W., Gribben, J. G. et Bahram, S. (2013). Reverse-engineering the genetic circuitry of a cancer cell with predicted intervention in chronic lymphocytic leukemia. Proceedings of the National Academy of Sciences of the United States of America, 110(2), 459-64.
Reference for the Cascade package: Jung, N., Bertrand, F., Bahram, S., Vallat, L. et Maumy-Bertrand, M. (2014). Cascade : A R package to study, predict and simulate the diffusion of a signal through a temporal gene network. Bioinformatics.
Code to reproduce the datasets saved with the package and some the figures of the article Bertrand et al. (2020), Bioinformatics. https://doi.org/10.1093/bioinformatics/btaa855
library(Cascade)We define the F array for the simulations.
T<-4
F<-array(0,c(T-1,T-1,T*(T-1)/2))
for(i in 1:(T*(T-1)/2)){diag(F[,,i])<-1}
F[,,2]<-F[,,2]*0.2
F[2,1,2]<-1
F[3,2,2]<-1
F[,,4]<-F[,,2]*0.3
F[3,1,4]<-1
F[,,5]<-F[,,2]We set the seed to make the results reproducible
set.seed(1)
Net<-Cascade::network_random(
nb=100,
time_label=rep(1:4,each=25),
exp=1,
init=1,
regul=round(rexp(100,1))+1,
min_expr=0.1,
max_expr=2,
casc.level=0.4
)
Net@F<-FWe simulate gene expression according to the network Net
M <- Cascade::gene_expr_simulation(
network=Net,
time_label=rep(1:4,each=25),
subject=5,
level_peak=200)We infer the new network.
Net_inf_C <- Cascade::inference(M,cv.subjects=TRUE)Heatmap of the coefficients of the Omega matrix of the network. Run the code to get the graph.
stats::heatmap(Net_inf_C@network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)Fab_inf_C <- Net_inf_C@Flibrary(SelectBoost)
set.seed(1)By default the crossvalidation is made subjectwise according to a leave one out scheme and the resampling analysis is made at the .95 c0 level. To pass CRAN tests, use.parallel = FALSE is required. Set use.parallel = TRUE and select the number of cores using ncores = 4.
net_pct_selected <- selectboost(M, Fab_inf_C, use.parallel = FALSE)net_pct_selected_.5 <- selectboost(M, Fab_inf_C, c0value = .5, use.parallel = FALSE)net_pct_selected_thr <- selectboost(M, Fab_inf_C, group = group_func_1, use.parallel = FALSE)Use cv.subject=FALSE to use default crossvalidation
net_pct_selected_cv <- selectboost(M, Fab_inf_C, cv.subject=FALSE, use.parallel = FALSE)Use plot to display the result of the confidence analysis.
plot(net_pct_selected)Run the code to plot the other results.
plot(net_pct_selected_.5)plot(net_pct_selected_thr)plot(net_pct_selected_cv)Run the code to plot the remaning graphs.
Distribution of non-zero (absolute value > 1e-5) coefficients
hist(Net_inf_C@network[abs(Net_inf_C@network)>1e-5])Plot of confidence at .95 resampling level versus coefficient value for non-zero (absolute value > 1e-5) coefficients
plot(Net_inf_C@network[abs(Net_inf_C@network)>1e-5],net_pct_selected@network.confidence[abs(Net_inf_C@network)>1e-5])hist(net_pct_selected@network.confidence[abs(Net_inf_C@network)>1e-5])Plot of confidence at .5 resampling level versus coefficient value for non-zero (absolute value > 1e-5) coefficients
plot(Net_inf_C@network[abs(Net_inf_C@network)>1e-5],net_pct_selected_.5@network.confidence[abs(Net_inf_C@network)>1e-5])hist(net_pct_selected_.5@network.confidence[abs(Net_inf_C@network)>1e-5])Plot of confidence at .95 resamling level with groups created by thresholding the correlation matrix versus coefficient value for non-zero (absolute value > 1e-5) coefficients.
plot(Net_inf_C@network[abs(Net_inf_C@network)>1e-5],net_pct_selected_thr@network.confidence[abs(Net_inf_C@network)>1e-5])hist(net_pct_selected_thr@network.confidence[abs(Net_inf_C@network)>1e-5])Plot of confidence at .95 resampling level versus coefficient value for non-zero (absolute value > 1e-5) coefficients using standard cross-validation.
plot(Net_inf_C@network[abs(Net_inf_C@network)>1e-5],net_pct_selected_cv@network.confidence[abs(Net_inf_C@network)>1e-5])hist(net_pct_selected_cv@network.confidence[abs(Net_inf_C@network)>1e-5])Either decrease percent selected or choose c0 as a quantile.