Date: 2025-09-13

# Benchmarking the SelectBoost Package for Network Reverse Engineering

#### Frédéric Bertrand and Myriam Maumy-Bertrand

#### 2025-09-13

# Overview

This vignette is a first benchmark of the use of the selectboost algorithm for stable and robust scale free network reverse engineering. It differs from the vignette Towards confidence estimates in Cascade Networks using the SelectBoost package where we compute confidence indices after the model was fitted. In this vignette, we use the Selecboost algorithm as a part of the inference algorithm in order to retrieve the most stable and robust links (against correlated resampling) between the genes of the network.

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")

Since the simulation time is quite large, we shipped the results with the package as an example dataset. We provide the code to rerun the simulations at the end of the vignette.

# Plots created for the article.

The following allows to reproduce some the figures of the article Aouadi et al. (2018), <arXiv:1810.01670>. The remaining code to create the datasets saved with the package is reproduced at the end of the vignette.

## Retrieve the results

Some simulation results were stored in the `results_simuls_reverse_engineering_v3` dataset provided with the package.

    library(SelectBoost)
    data(results_simuls_reverse_engineering_v3)
    colgrey=grey(.05,NULL)

## Compute graphs’ ranges

    rangeCPy_S=range(sensitivity_C,sensitivity_PL,sensitivity_PL2,sensitivity_PL2_W,sensitivity_PL2_tW,sensitivity_PSel,sensitivity_PSel_W,sensitivity_PSel.5,sensitivity_PSel.e2,sensitivity_PSel.5.e2,sensitivity_robust,sensitivity_PB,predictive_positive_value_PB_095_075,predictive_positive_value_PB_075_075,sensitivity_PB_W)
    rangeCPy_PPV=range(predictive_positive_value_C,predictive_positive_value_PL,predictive_positive_value_PL2,predictive_positive_value_PL2_W,predictive_positive_value_PL2_tW,predictive_positive_value_PSel,predictive_positive_value_PSel_W,predictive_positive_value_PSel.5,predictive_positive_value_PSel.e2,predictive_positive_value_PSel.5.e2,predictive_positive_value_robust,predictive_positive_value_PB,predictive_positive_value_PB_095_075,predictive_positive_value_PB_075_075,predictive_positive_value_PB_W)
    rangeCPy_F=range(F_score_C,F_score_PL,F_score_PL2,F_score_PL2_W,F_score_PL2_tW,F_score_PSel,F_score_PSel_W,F_score_PSel.5,F_score_PSel.e2,F_score_PSel.5.e2,F_score_PB,F_score_PB_095_075,F_score_PB_075_075,F_score_PB_W)
    rangeCPx=range(test.seq_C,test.seq_PL,test.seq_PL2,test.seq_PL2_W,test.seq_PL2_tW,test.seq_PSel,test.seq_PSel_W,test.seq_PSel.5,test.seq_PSel.e2,test.seq_PSel.5.e2,test.seq_robust,test.seq_PB,test.seq_PB_095_075,test.seq_PB_075_075,test.seq_PB_W)

## Sensitivity

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_PL2),t(sensitivity_PL2),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Lasso2",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PL2,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2_W),t(sensitivity_PL2_W),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Lasso2_W",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PL2_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel),t(sensitivity_PSel),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Stability_Selection",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel_W),t(sensitivity_PSel_W),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Stability_Selection_W",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PSel_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB),t(sensitivity_PB),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Select_Boost",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PB,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_W),t(sensitivity_PB_W),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Select_Boost_W",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PB_W,col=grey(.05,NULL),lty=3)

Run the code to plot the graph.

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_robust),t(sensitivity_robust),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Robust",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_robust,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB),t(sensitivity_PB),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Select_Boost",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PB,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_095_075),t(sensitivity_PB_095_075),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Select_Boost_095_075",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PB_095_075,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_075_075),t(sensitivity_PB_075_075),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Select_Boost_075_075",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PB_075_075,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_W),t(sensitivity_PB_W),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Select_Boost_W",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PB_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel),t(sensitivity_PSel),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Stability_Selection",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)

## Predictive positive value

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_PL2),t(predictive_positive_value_PL2),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Lasso2",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PL2,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2_W),t(predictive_positive_value_PL2_W),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Lasso2_W",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PL2_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel),t(predictive_positive_value_PSel),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Stability_Selection",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel_W),t(predictive_positive_value_PSel_W),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Stability_Selection_W",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PSel_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB),t(predictive_positive_value_PB),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Select_Boost",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PB,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_W),t(predictive_positive_value_PB_W),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Select_Boost_Weighted",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PB_W,col=grey(.05,NULL),lty=3)

Run the code to plot the graph.

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_robust),t(predictive_positive_value_robust),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Robust",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_robust,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB),t(predictive_positive_value_PB),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Select_Boost",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PB,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_095_075),t(predictive_positive_value_PB_095_075),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Select_Boost_095_075",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PB_095_075,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_075_075),t(predictive_positive_value_PB_075_075),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Select_Boost_075_075",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PB_075_075,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_W),t(predictive_positive_value_PB_W),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Select_Boost_Weighted",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PB_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel),t(predictive_positive_value_PSel),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Stability_Selection",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)

## F-score

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_PL2),t(F_score_PL2),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Lasso2",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PL2,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2_W),t(F_score_PL2_W),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Lasso2_W",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PL2_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel),t(F_score_PSel),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Stability_Selection",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel_W),t(F_score_PSel_W),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Stability_Selection_W",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PSel_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB),t(F_score_PB),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Select_Boost",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PB,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_W),t(F_score_PB_W),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Select_Boost_Weighted",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PB_W,col=grey(.05,NULL),lty=3)

Run the code to plot the graph.

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_robust),t(F_score_robust),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Robust",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_robust,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB),t(F_score_PB),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Select_Boost",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PB,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_095_075),t(F_score_PB_095_075),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Select_Boost_095_075",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PB_095_075,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_075_075),t(F_score_PB_075_075),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Select_Boost_075_075",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PB_075_075,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB_W),t(F_score_PB_W),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Select_Boost_Weighted",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PB_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel),t(F_score_PSel),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Stability_Selection",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)

# Additionnal plots

Run the code to get the graphics. ## Plot sensitivity results

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_C),t(sensitivity_C),type="l",xlab="cutoff",ylab="Sensitivity",main="Cascade",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_C,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL),t(sensitivity_PL),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Lasso",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PL,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2_W),t(sensitivity_PL2_W),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Lasso2_W",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PL2_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel),t(sensitivity_PSel),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Stability_Selection",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel_W),t(sensitivity_PSel_W),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Stability_Selection_W",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PSel_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2_tW),t(sensitivity_PL2_tW),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Lasso2_wrongW",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PL2_tW,col=grey(.05,NULL),lty=3)

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_PSel),t(sensitivity_PSel),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Stability_Selection",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel.5),t(sensitivity_PSel.5),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Stability_Selection_.5",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PSel.5,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel.e2),t(sensitivity_PSel.e2),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Stability_Selection.e2",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PSel.e2,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel.5.e2),t(sensitivity_PSel.5.e2),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Stability_Selection_.5.e2",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PSel.5.e2,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2),t(sensitivity_PL2),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Lasso2",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PL2,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB),t(sensitivity_PB),type="l",xlab="cutoff",ylab="Sensitivity",main="Patterns_Select_Boost",ylim=rangeCPy_S,col=grey(.05,NULL))
    abline(v=nv_PB,col=grey(.05,NULL),lty=3)

## Plot predictive positive value results

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_C),t(predictive_positive_value_C),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Cascade",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_C,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL),t(predictive_positive_value_PL),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Lasso",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PL,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2_W),t(predictive_positive_value_PL2_W),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Lasso2_W",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PL2_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel),t(predictive_positive_value_PSel),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Stability_Selection",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel_W),t(predictive_positive_value_PSel_W),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Stability_Selection_W",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PSel_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2_tW),t(predictive_positive_value_PL2_tW),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Lasso2_wrongW",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PL2_tW,col=grey(.05,NULL),lty=3)

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_PSel),t(predictive_positive_value_PSel),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Stability_Selection",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel.5),t(predictive_positive_value_PSel.5),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Stability_Selection.5",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PSel.5,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel.e2),t(predictive_positive_value_PSel.e2),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Stability_Selection",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel.5.e2),t(predictive_positive_value_PSel.5.e2),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Stability_Selection.5.e2",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PSel.5.e2,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2),t(predictive_positive_value_PL2),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Lasso2",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PL2,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB),t(predictive_positive_value_PB),type="l",xlab="cutoff",ylab="Predictive Positive Value",main="Patterns_Select_Boost",ylim=rangeCPy_PPV,col=grey(.05,NULL))
    abline(v=nv_PB,col=grey(.05,NULL),lty=3)

## Plot F-score results

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_C),t(F_score_C),type="l",xlab="cutoff",ylab="Fscore",main="Cascade",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_C,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL),t(F_score_PL),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Lasso",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PL,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2_W),t(F_score_PL2_W),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Lasso2_W",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PL2_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel),t(F_score_PSel),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Stability_Selection",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PSel,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PSel_W),t(F_score_PSel_W),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Stability_Selection_W",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PSel_W,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PL2_tW),t(F_score_PL2_tW),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Lasso2_wrongW",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PL2_tW,col=grey(.05,NULL),lty=3)

    layout(matrix(1:6,nrow=2))
    matplot(t(test.seq_PSel),t(F_score_PSel),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Stability_Selection",ylim=rangeCPy_F,col=grey(.25,NULL))
    abline(v=nv_PSel,lty=3,col=grey(.05,NULL))
    matplot(t(test.seq_PSel.5),t(F_score_PSel.5),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Stability_Selection.5",ylim=rangeCPy_F,col=grey(.25,NULL))
    abline(v=nv_PSel.5,lty=3,col=grey(.05,NULL))
    matplot(t(test.seq_PSel.e2),t(F_score_PSel.e2),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Stability_Selection.e2",ylim=rangeCPy_F,col=grey(.25,NULL))
    abline(v=nv_PSel.e2,lty=3,col=grey(.05,NULL))
    matplot(t(test.seq_PSel.5.e2),t(F_score_PSel.5.e2),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Stability_Selection.5.e2",ylim=rangeCPy_F,col=grey(.25,NULL))
    abline(v=nv_PSel.5.e2,lty=3,col=grey(.05,NULL))
    matplot(t(test.seq_PL2),t(F_score_PL2),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Lasso2",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PL2,col=grey(.05,NULL),lty=3)
    matplot(t(test.seq_PB),t(F_score_PB),type="l",xlab="cutoff",ylab="Fscore",main="Patterns_Select_Boost",ylim=rangeCPy_F,col=grey(.05,NULL))
    abline(v=nv_PB,col=grey(.05,NULL),lty=3)

# Code

Set the working directory to a writable one since the simulated datasets and the results are saved during the simulation process.

    library(Cascade)
    if(exists("M")){rm(M)}
    BBB=1
    NNN=100
    {
      sensitivity_C<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PL<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PL2<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PL2_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PL2_tW<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PSel<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PSel_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PSel.5<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PSel.e2<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PSel.5.e2<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_robust<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PB<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PB_095_075<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PB_075_075<-matrix(rep(NA,200*NNN),nrow=NNN)
      sensitivity_PB_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_C<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PL<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PL2<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PL2_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PL2_tW<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PSel<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PSel_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PSel.5<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PSel.e2<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PSel.5.e2<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_robust<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PB<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PB_095_075<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PB_075_075<-matrix(rep(NA,200*NNN),nrow=NNN)
      predictive_positive_value_PB_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_C<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PL<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PL2<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PL2_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PL2_tW<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PSel<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PSel_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PSel.5<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PSel.e2<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PSel.5.e2<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_robust<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PB<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PB_095_075<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PB_075_075<-matrix(rep(NA,200*NNN),nrow=NNN)
      F_score_PB_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      #Here are the cutoff level tested
      test.seq_C<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PL<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PL2<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PL2_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PL2_tW<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PSel<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PSel_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PSel.5<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PSel.e2<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PSel.5.e2<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_robust<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PB<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PB_095_075<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PB_075_075<-matrix(rep(NA,200*NNN),nrow=NNN)
      test.seq_PB_W<-matrix(rep(NA,200*NNN),nrow=NNN)
      nv_C<-rep(0,NNN)
      nv_PL<-rep(0,NNN)
      nv_PL2<-rep(0,NNN)
      nv_PL2_W<-rep(0,NNN)
      nv_PL2_tW<-rep(0,NNN)
      nv_PSel<-rep(0,NNN)
      nv_PSel_W<-rep(0,NNN)
      nv_PSel.5<-rep(0,NNN)
      nv_PSel.e2<-rep(0,NNN)
      nv_PSel.5.e2<-rep(0,NNN)
      nv_robust<-rep(0,NNN)
      nv_PB<-rep(0,NNN)
      nv_PB_095_075<-rep(0,NNN)
      nv_PB_075_075<-rep(0,NNN)
      nv_PB_W<-rep(0,NNN)

      #We change F matrices
      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]

      TFshape=Patterns::CascadeFshape(ngrp = 4,sqF = 4)
      TF=Patterns::CascadeFinit(ngrp = 4,sqF = 4)
      #    TF[,,1]
      TF[,,2]<-cbind(rbind(rep(0,3),F[,,1]),rep(0,4))
      TF[,,3]<-cbind(rbind(rep(0,3),F[,,2]),rep(0,4))
      TF[,,4]<-cbind(rbind(rep(0,3),F[,,3]),rep(0,4))
      #    TF[,,5]
      #    TF[,,6]
      TF[,,7]<-cbind(rbind(rep(0,3),F[,,4]),rep(0,4))
      TF[,,8]<-cbind(rbind(rep(0,3),F[,,5]),rep(0,4))
      #    TF[,,9]
      #    TF[,,10]
      #    TF[,,11]
      TF[,,12]<-cbind(rbind(rep(0,3),F[,,6]),rep(0,4))
      #    TF[,,13]
      #    TF[,,14]
      #    TF[,,15]
      #    TF[,,16]
    }

    #We set the seed to make the results reproducible
    set.seed(1)
    for(iii in BBB:NNN){
      #We create a random scale free network
      if(!file.exists(paste(paste("Net",iii,sep="_"),".RData",sep=""))){
        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<-F
        assign(paste("Net",iii,sep="_"),Net);rm(Net)
        save(list=paste("Net",iii,sep="_"),file=paste(paste("Net",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net",iii,sep="_"),".RData",sep=""))
      }

      #We simulate gene expression according to the network Net
      if(!file.exists(paste(paste("M",iii,sep="_"),".RData",sep=""))){
        assign(paste("M",iii,sep="_"),Cascade::gene_expr_simulation(
          network=get(paste("Net",iii,sep="_")),
          time_label=rep(1:4,each=25),
          subject=5,
          level_peak=200))
        save(list=paste("M",iii,sep="_"),file=paste(paste("M",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("M",iii,sep="_"),".RData",sep=""))
      }
    }

    #We infer the new network
    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_C",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_C",iii,sep="_"),Cascade::inference(get(paste("M",iii,sep="_"))))
        save(list=paste("Net_inf_C",iii,sep="_"),file=paste(paste("Net_inf_C",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_C",iii,sep="_"),".RData",sep=""))
      }
    }
    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_PL",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PL",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="LASSO"))
        save(list=paste("Net_inf_PL",iii,sep="_"),file=paste(paste("Net_inf_PL",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PL",iii,sep="_"),".RData",sep=""))
      }
    }
    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_PL2",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PL2",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="LASSO2"))
        save(list=paste("Net_inf_PL2",iii,sep="_"),file=paste(paste("Net_inf_PL2",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PL2",iii,sep="_"),".RData",sep=""))
      }
    }
    for(iii in BBB:NNN){
      Temp_Weights_Net<-slot(get(paste("Net",iii,sep="_")),"network")
      Temp_Weights_Net[Temp_Weights_Net!=0]=.1
      Temp_Weights_Net[Temp_Weights_Net==0]=1000
      assign(paste("Weights_Net",iii,sep="_"),Temp_Weights_Net)
      if(!file.exists(paste(paste("Net_inf_PL2_W",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PL2_W",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="LASSO2",priors=get(paste("Weights_Net",iii,sep="_"))))
        save(list=c(paste("Net_inf_PL2_W",iii,sep="_"),paste("Weights_Net",iii,sep="_")),file=paste(paste("Net_inf_PL2_W",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PL2_W",iii,sep="_"),".RData",sep=""))
      }
      rm(Temp_Weights_Net)
    }
    for(iii in BBB:NNN){
      Temp_Weights_Net<-slot(get(paste("Net",iii,sep="_")),"network")
      Temp_Weights_Net[Temp_Weights_Net!=0]=.1
      Temp_Weights_Net[Temp_Weights_Net==0]=1000
      assign(paste("Weights_Net",iii,sep="_"),Temp_Weights_Net)
      if(!file.exists(paste(paste("Net_inf_PL2_tW",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PL2_tW",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="LASSO2",priors=t(get(paste("Weights_Net",iii,sep="_")))))
        save(list=c(paste("Net_inf_PL2_tW",iii,sep="_"),paste("Weights_Net",iii,sep="_")),file=paste(paste("Net_inf_PL2_tW",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PL2_tW",iii,sep="_"),".RData",sep=""))
      }
      rm(Temp_Weights_Net)
    }
    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_PSel",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PSel",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="stability.c060",use.Gram=FALSE,error.stabsel=0.05,pi_thr.stabsel=0.9,mc.cores=1,intercept.stabpath=FALSE))
        save(list=paste("Net_inf_PSel",iii,sep="_"),file=paste(paste("Net_inf_PSel",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PSel",iii,sep="_"),".RData",sep=""))
      }
    }
    for(iii in BBB:NNN){
      Temp_Weights_Net<-slot(get(paste("Net",iii,sep="_")),"network")
      Temp_Weights_Net[Temp_Weights_Net!=0]=.1
      Temp_Weights_Net[Temp_Weights_Net==0]=1000
      assign(paste("Weights_Net",iii,sep="_"),Temp_Weights_Net)
      if(!file.exists(paste(paste("Net_inf_PSel_W",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PSel_W",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="stability.c060.weighted",use.Gram=FALSE,error.stabsel=0.05,pi_thr.stabsel=0.9,mc.cores=2,intercept.stabpath=FALSE,priors=get(paste("Weights_Net",iii,sep="_"))))
        save(list=c(paste("Net_inf_PSel_W",iii,sep="_"),paste("Weights_Net",iii,sep="_")),file=paste(paste("Net_inf_PSel_W",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PSel_W",iii,sep="_"),".RData",sep=""))
      }
    }
    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_PSel.5",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PSel.5",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="stability.c060",use.Gram=FALSE,error.stabsel=0.05,pi_thr.stabsel=0.51,mc.cores=1,intercept.stabpath=FALSE))
        save(list=paste("Net_inf_PSel.5",iii,sep="_"),file=paste(paste("Net_inf_PSel.5",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PSel.5",iii,sep="_"),".RData",sep=""))
      }
    }
    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_PSel.e2",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PSel.e2",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="stability.c060",use.Gram=FALSE,error.stabsel=0.2,pi_thr.stabsel=0.9,mc.cores=1,intercept.stabpath=FALSE))
        save(list=paste("Net_inf_PSel.e2",iii,sep="_"),file=paste(paste("Net_inf_PSel.e2",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PSel.e2",iii,sep="_"),".RData",sep=""))
      }
    }
    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_PSel.5.e2",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PSel.5.e2",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="stability.c060",use.Gram=FALSE,error.stabsel=0.2,pi_thr.stabsel=0.51,mc.cores=1,intercept.stabpath=FALSE))
        save(list=paste("Net_inf_PSel.5.e2",iii,sep="_"),file=paste(paste("Net_inf_PSel.5.e2",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PSel.5.e2",iii,sep="_"),".RData",sep=""))
      }
    }
    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_robust",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_robust",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="robust"))
        save(list=paste("Net_inf_robust",iii,sep="_"),file=paste(paste("Net_inf_robust",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_robust",iii,sep="_"),".RData",sep=""))
      }
    }

    # vmf.lme<-function (x, tol = 1e-07)
    # {
    #   dm <- dim(x)
    #   p <- dm[2]
    #   n <- dm[1]
    #   Apk <- function(p, k) besselI(k, p/2, expon.scaled = TRUE)/besselI(k, p/2 - 1, expon.scaled = TRUE)
    #   m1 <- Rfast::colsums(x)
    #   R <- sqrt(sum(m1^2))/n
    #   m <- m1/n/R
    #   k1 <- R * (p - R^2)/(1 - R^2)
    #   if (k1 < 1e+05) {
    #     apk <- Apk(p, k1)
    #     k2 <- k1 - (apk - R)/(1 - apk^2 - (p - 1)/k1 * apk)
    #     while (abs(k2 - k1) > tol) {
    #       k1 <- k2
    #       if (k1 < 1e+05) {apk <- Apk(p, k1)} else {k2<-k1;break}
    #       k2 <- k1 - (apk - R)/(1 - apk^2 - (p - 1)/k1 * apk)
    #     }
    #     k <- k2
    #   }
    #   else k <- k1
    #   loglik <- n * (p/2 - 1) * log(k) - 0.5 * n * p * log(2 * pi) - n * (log(besselI(k, p/2 - 1, expon.scaled = TRUE)) + k) + k * n * R
    #   list(loglik = loglik, mu = m, kappa = k)
    # }

    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_PB",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PB",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="selectboost.weighted"))
        save(list=paste("Net_inf_PB",iii,sep="_"),file=paste(paste("Net_inf_PB",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PB",iii,sep="_"),".RData",sep=""))
      }
    }
    #Default values
    #,steps.seq=.95
    #,limselect=.75
    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_PB_c095_limsel075",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PB_c095_limsel075",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="selectboost.weighted"
                                                                   ,steps.seq=.95
                                                                   ,limselect=.75
        ))
        save(list=paste("Net_inf_PB_c095_limsel075",iii,sep="_"),file=paste(paste("Net_inf_PB_c095_limsel075",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PB_c095_limsel075",iii,sep="_"),".RData",sep=""))
      }
    }
    for(iii in BBB:NNN){
      if(!file.exists(paste(paste("Net_inf_PB_c075_limsel075",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PB_c075_limsel075",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="selectboost.weighted"
                                                                   ,steps.seq=.75
                                                                   ,limselect=.75
        ))
        save(list=paste("Net_inf_PB_c075_limsel075",iii,sep="_"),file=paste(paste("Net_inf_PB_c075_limsel075",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PB_c075_limsel075",iii,sep="_"),".RData",sep=""))
      }
    }
    for(iii in BBB:NNN){
      Temp_Weights_Net<-slot(get(paste("Net",iii,sep="_")),"network")
      Temp_Weights_Net[Temp_Weights_Net!=0]=.1
      Temp_Weights_Net[Temp_Weights_Net==0]=1000
      assign(paste("Weights_Net",iii,sep="_"),Temp_Weights_Net)
      if(!file.exists(paste(paste("Net_inf_PB_W",iii,sep="_"),".RData",sep=""))){
        assign(paste("Net_inf_PB_W",iii,sep="_"),Patterns::inference(get(paste("M",iii,sep="_")),Finit=TF,Fshape=TFshape,fitfun="selectboost.weighted",priors=get(paste("Weights_Net",iii,sep="_"))))
        save(list=paste("Net_inf_PB_W",iii,sep="_"),file=paste(paste("Net_inf_PB_W",iii,sep="_"),".RData",sep=""))
      } else {
        load(file=paste(paste("Net_inf_PB_W",iii,sep="_"),".RData",sep=""))
      }
    }

    #      ,fitfun="stability.c060.weighted"
    #      ,fitfun="LASSO2.weighted"

    #Comparing true and inferred networks
    #Here are the cutoff level tested
    for(iii in BBB:NNN){
      test.seq_C[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_C",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PL[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PL",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PL2[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PL2",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PL2_W[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PL2_W",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PL2_tW[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PL2_tW",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PSel[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PSel",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PSel_W[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PSel_W",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PSel.5[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PSel.5",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PSel.e2[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PSel.e2",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PSel.5.e2[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PSel.5.e2",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_robust[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_robust",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PB[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PB",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PB_095_075[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PB_c095_limsel075",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PB_075_075[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PB_c075_limsel075",iii,sep="_")),"network")*0.9)),length.out=200)
      test.seq_PB_W[iii,]<-seq(0,max(abs(slot(get(paste("Net_inf_PB_W",iii,sep="_")),"network")*0.9)),length.out=200)
    }

    for(iii in BBB:NNN){
      cat(iii,"\n")
      u<-0
      cat("Net_inf_C")
      for(i in test.seq_C[iii,]){
        u<-u+1
        sensitivity_C[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_C",iii,sep="_")),i)[1]
        predictive_positive_value_C[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_C",iii,sep="_")),i)[2]
        F_score_C[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_C",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PL")
      for(i in test.seq_PL[iii,]){
        u<-u+1
        sensitivity_PL[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL",iii,sep="_")),i)[1]
        predictive_positive_value_PL[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL",iii,sep="_")),i)[2]
        F_score_PL[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PL2")
      for(i in test.seq_PL2[iii,]){
        u<-u+1
        sensitivity_PL2[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL2",iii,sep="_")),i)[1]
        predictive_positive_value_PL2[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL2",iii,sep="_")),i)[2]
        F_score_PL2[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL2",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PL2_W")
      for(i in test.seq_PL2_W[iii,]){
        u<-u+1
        sensitivity_PL2_W[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL2_W",iii,sep="_")),i)[1]
        predictive_positive_value_PL2_W[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL2_W",iii,sep="_")),i)[2]
        F_score_PL2_W[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL2_W",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PL2_tW")
      for(i in test.seq_PL2_tW[iii,]){
        u<-u+1
        sensitivity_PL2_tW[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL2_tW",iii,sep="_")),i)[1]
        predictive_positive_value_PL2_tW[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL2_tW",iii,sep="_")),i)[2]
        F_score_PL2_tW[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PL2_tW",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PSel")
      for(i in test.seq_PSel[iii,]){
        u<-u+1
        sensitivity_PSel[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel",iii,sep="_")),i)[1]
        predictive_positive_value_PSel[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel",iii,sep="_")),i)[2]
        F_score_PSel[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PSel_W")
      for(i in test.seq_PSel_W[iii,]){
        u<-u+1
        sensitivity_PSel_W[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel_W",iii,sep="_")),i)[1]
        predictive_positive_value_PSel_W[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel_W",iii,sep="_")),i)[2]
        F_score_PSel_W[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel_W",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PSel.5")
      for(i in test.seq_PSel.5[iii,]){
        u<-u+1
        sensitivity_PSel.5[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel.5",iii,sep="_")),i)[1]
        predictive_positive_value_PSel.5[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel.5",iii,sep="_")),i)[2]
        F_score_PSel.5[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel.5",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PSel.e2")
      for(i in test.seq_PSel.e2[iii,]){
        u<-u+1
        sensitivity_PSel.e2[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel.e2",iii,sep="_")),i)[1]
        predictive_positive_value_PSel.e2[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel.e2",iii,sep="_")),i)[2]
        F_score_PSel.e2[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel.e2",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PSel.5.e2")
      for(i in test.seq_PSel.5.e2[iii,]){
        u<-u+1
        sensitivity_PSel.5.e2[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel.5.e2",iii,sep="_")),i)[1]
        predictive_positive_value_PSel.5.e2[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel.5.e2",iii,sep="_")),i)[2]
        F_score_PSel.5.e2[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PSel.5.e2",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_robust")
      for(i in test.seq_robust[iii,]){
        u<-u+1
        sensitivity_robust[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_robust",iii,sep="_")),i)[1]
        predictive_positive_value_robust[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_robust",iii,sep="_")),i)[2]
        F_score_robust[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_robust",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PB")
      for(i in test.seq_PB[iii,]){
        u<-u+1
        sensitivity_PB[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB",iii,sep="_")),i)[1]
        predictive_positive_value_PB[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB",iii,sep="_")),i)[2]
        F_score_PB[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PB_095_075")
      for(i in test.seq_PB_095_075[iii,]){
        u<-u+1
        sensitivity_PB_095_075[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB_c095_limsel075",iii,sep="_")),i)[1]
        predictive_positive_value_PB_095_075[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB_c095_limsel075",iii,sep="_")),i)[2]
        F_score_PB_095_075[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB_c095_limsel075",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PB_075_075")
      for(i in test.seq_PB[iii,]){
        u<-u+1
        sensitivity_PB_075_075[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB_c075_limsel075",iii,sep="_")),i)[1]
        predictive_positive_value_PB_075_075[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB_c075_limsel075",iii,sep="_")),i)[2]
        F_score_PB_075_075[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB_c075_limsel075",iii,sep="_")),i)[3]
      }
      u<-0
      cat("Net_inf_PB_W\n")
      for(i in test.seq_PB_W[iii,]){
        u<-u+1
        sensitivity_PB_W[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB_W",iii,sep="_")),i)[1]
        predictive_positive_value_PB_W[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB_W",iii,sep="_")),i)[2]
        F_score_PB_W[iii,u]<-Cascade::compare(get(paste("Net",iii,sep="_")),get(paste("Net_inf_PB_W",iii,sep="_")),i)[3]
      }
      #Corresponding Fscore evolution
      nv_C[iii]=test.seq_C[iii,which.max(F_score_C[iii,])]
      nv_PL[iii]=test.seq_PL[iii,which.max(F_score_PL[iii,])]
      nv_PL2[iii]=test.seq_PL2[iii,which.max(F_score_PL2[iii,])]
      nv_PL2_W[iii]=test.seq_PL2[iii,which.max(F_score_PL2_W[iii,])]
      nv_PL2_tW[iii]=test.seq_PL2[iii,which.max(F_score_PL2_tW[iii,])]
      nv_PSel[iii]=test.seq_PSel[iii,which.max(F_score_PSel[iii,])]
      nv_PSel_W[iii]=test.seq_PSel[iii,which.max(F_score_PSel_W[iii,])]
      nv_PSel.5[iii]=test.seq_PSel.5[iii,which.max(F_score_PSel.5[iii,])]
      nv_PSel.e2[iii]=test.seq_PSel.e2[iii,which.max(F_score_PSel.e2[iii,])]
      nv_PSel.5.e2[iii]=test.seq_PSel.5.e2[iii,which.max(F_score_PSel.5.e2[iii,])]
      nv_robust[iii]=test.seq_robust[iii,which.max(F_score_robust[iii,])]
      nv_PB[iii]=test.seq_PB[iii,which.max(F_score_PB[iii,])]
      nv_PB_095_075[iii]=test.seq_PB_095_075[iii,which.max(F_score_PB_095_075[iii,])]
      nv_PB_075_075[iii]=test.seq_PB_075_075[iii,which.max(F_score_PB_075_075[iii,])]
      nv_PB_W[iii]=test.seq_PB_W[iii,which.max(F_score_PB_W[iii,])]
    }

    save(
      sensitivity_C,
      sensitivity_PL,
      sensitivity_PL2,
      sensitivity_PL2_W,
      sensitivity_PL2_tW,
      sensitivity_PSel,
      sensitivity_PSel_W,
      sensitivity_PSel.5,
      sensitivity_PSel.e2,
      sensitivity_PSel.5.e2,
      sensitivity_robust,
      sensitivity_PB,
      sensitivity_PB_095_075,
      sensitivity_PB_075_075,
      sensitivity_PB_W,
      predictive_positive_value_C,
      predictive_positive_value_PL,
      predictive_positive_value_PL2,
      predictive_positive_value_PL2_W,
      predictive_positive_value_PL2_tW,
      predictive_positive_value_PSel,
      predictive_positive_value_PSel_W,
      predictive_positive_value_PSel.5,
      predictive_positive_value_PSel.e2,
      predictive_positive_value_PSel.5.e2,
      predictive_positive_value_robust,
      predictive_positive_value_PB,
      predictive_positive_value_PB_095_075,
      predictive_positive_value_PB_075_075,
      predictive_positive_value_PB_W,
      F_score_C,
      F_score_PL,
      F_score_PL2,
      F_score_PL2_W,
      F_score_PL2_tW,
      F_score_PSel,
      F_score_PSel_W,
      F_score_PSel.5,
      F_score_PSel.e2,
      F_score_PSel.5.e2,
      F_score_robust,
      F_score_PB,
      F_score_PB_095_075,
      F_score_PB_075_075,
      F_score_PB_W,
      #Here are the cutoff level tested
      test.seq_C,
      test.seq_PL,
      test.seq_PL2,
      test.seq_PL2_W,
      test.seq_PL2_tW,
      test.seq_PSel,
      test.seq_PSel_W,
      test.seq_PSel.5,
      test.seq_PSel.e2,
      test.seq_PSel.5.e2,
      test.seq_robust,
      test.seq_PB,
      test.seq_PB_095_075,
      test.seq_PB_075_075,
      test.seq_PB_W,
      nv_C,
      nv_PL,
      nv_PL2,
      nv_PL2_W,
      nv_PL2_tW,
      nv_PSel,
      nv_PSel_W,
      nv_PSel.5,
      nv_PSel.e2,
      nv_PSel.5.e2,
      nv_robust,
      nv_PB,
      nv_PB_095_075,
      nv_PB_075_075,
      nv_PB_W,file="results_simuls_reverse_engineering_v3.RData",
      compress = "xz")