Introduction
In biological and biomedical research, the identification of key variables in omics data—such as transcriptomes, proteomes, and methylomes—is generally accomplished using statistical tests like the t-test or correlation analysis. While these methods perform well for detecting classical mean differences, they often fail to capture more complex scenarios, such as non-Gaussian data distributions, interactions among multiple variables, or multimodal distributions.
To address these challenges, the scientific literature proposes to use the potential of explainable AI (XAI) to assist in the discovery of key features. Examples of these techniques can be found in the analysis of methylation and transcriptome data @Rajpal_2023, @Kumar_2023.
The XAItest package aims at proposing a versatile tool to run these types of analysis easily. It calculates various p-value based statistics, such as the t-test or correlation, depending on whether the target variable is categorical or numerical. It also computes different XAI matrics such as feature importance metrics, by default a built-in method from random forest, an implementation of SHAP and of LIME, and the possibility to integrate custom functions.
Establishing a significance level for a p-value is straightforward, often set at 0.05 or 0.01. However, determining thresholds for the feature importance is more complicated, and has to be computed at each experiment. Our package offers an integrated solution to this challenge by generating simulated data designed to meet selected p-value thresholds, thus setting significance thresholds for the feature importance.
Lastly, our package offers an intuitive visualization of results through color-coded tables, highlighting statistical metrics and their significance for easy interpretation.
Installation
if (!require("BiocManager")) {
install.packages("BiocManager")
}
BiocManager::install('XAItest')
Get feature importance of a SummarizedExperiment dataset
# Load the libraries
library(XAItest)
library(ggplot2)
library(ggforce)
library(gridExtra)
library(SummarizedExperiment)
We consider the RNA-seq data from the airway dataset, which contains read counts per gene for airway smooth muscles stored in a RangedSummarizedExperiment object. The metadata contains a column dex, which indicates whether the subjects are treated or untreated. The XAI.test function, by default, builds random forest models to predict a target, here the ‘dex’ treatment status, and calculates the associated gene feature importances.
data(airway, package="airway")
se <- airway
results <- XAI.test(se[1:100,], y = "dex", verbose = TRUE, simData = TRUE)
## Loading required package: lattice
##
## Attaching package: 'caret'
## The following object is masked from 'package:generics':
##
## train
results
## Metrics Table (first 5 rows):
## ttest_pval ttest_adjPval ebayes_pval ebayes_adjPval
## simFeat 0.0004442891 0.04487320 0.0002671305 0.02698018
## ENSG00000003096 0.0009195955 0.09287914 0.0001397020 0.01410990
## ENSG00000005189 0.0015221670 0.15373887 0.0009032689 0.09123016
## ENSG00000001626 0.0240899065 1.00000000 0.0954418912 1.00000000
## ENSG00000001036 0.0477152309 1.00000000 0.0363164951 1.00000000
## lm_coef lm_pval lm_adjPval RF_feat_imp SHAP_feat_imp
## simFeat NA NA NA 0.235 0.0020
## ENSG00000003096 NA NA NA 0.195 0.0070
## ENSG00000005189 NA NA NA 0.075 0.0045
## ENSG00000001626 NA NA NA 0.155 0.0030
## ENSG00000001036 0.0004872526 NaN NaN 0.000 0.0010
## LIME_feat_imp
## simFeat 0.042682296
## ENSG00000003096 0.052726825
## ENSG00000005189 0.031945838
## ENSG00000001626 0.008543779
## ENSG00000001036 0.012800245
Detect new key features on a classification dataset
On a toy dataset we will investigate which features can be identified using a t-test or linear modeling, and which can be detected through feature importance metrics.
Load simulated classification dataset
The dataset contains 50 samples of A, and 50 samples of B, with 10 noise features et 3 key features:
- norm_noise01, norm_noise02 … 10 features of normal distribution noise
- diff_distrib01 different normal distributions between “A” and “B”
- diff_distrib02 different normal distributions between “A” and “B”
- bidistrib01 normal bidistribution for “A” and normal distribution for “B”
The t-test can detect diff_distrib01 and diff_distrib02 but not bidistrib01.
se_path <- system.file("extdata", "seClassif.rds", package="XAItest")
dataset_classif <- readRDS(se_path)
data_matrix <- assay(dataset_classif, "counts")
data_matrix <- t(data_matrix)
metadata <- as.data.frame(colData(dataset_classif))
df_simu_classif <- as.data.frame(cbind(data_matrix, y = metadata[['y']]))
for (col in names(df_simu_classif)) {
if (col != 'y') {
df_simu_classif[[col]] <- as.numeric(df_simu_classif[[col]])
}
}
Example with a dataframe.
df_path <- system.file("extdata", "dfClassif.txt", package="XAItest")
dataset_classif_df <- read.table(df_path)
df_simu_classif_df <- dataset_classif
We can see below how class A and class B are distributed accross the features: norm_noise01, norm_noise02, norm_noise03, norm_noise04, diff_distrib01, diff_distrib02 and biDistrib.
p1 <- ggplot(df_simu_classif, aes(x=norm_noise01, y=norm_noise02,
color=y)) +
geom_point() +
ggtitle("Noise features\nnorm_noise01 vs norm_noise02") +
theme_bw()
p2 <- ggplot(df_simu_classif, aes(x=diff_distrib01, y=diff_distrib02,
color=y)) +
geom_point() +
ggtitle("Normal distributions\ndiff_distrib01 vs diff_distrib02") +
theme_bw()
p3 <- ggplot(df_simu_classif, aes(x=norm_noise03, y=biDistrib, color=y)) +
geom_point() +
ggtitle("Normal bidistribution\nbidistrib01 vs norm_noise03") +
theme_bw()
grid.arrange(p1, p2, p3, ncol = 3, nrow = 1)
We employ the XAI.test function to evaluate the p-values and feature importance of each feature. The parameter simData is set to TRUE, which instructs the function to generate a new feature named simFeat, designed to achieve a specified p-value (column ttest_adjPval), set at simPvalTarget = 0.01. The purpose of simFeat is to establish a significance threshold for assessing feature importance values.
set.seed(123)
objXAI <- XAI.test(dataset_classif, "y", simData = TRUE, simPvalTarget = 0.01)
head(getMetricsTable(objXAI))
## ttest_pval ttest_adjPval ebayes_pval ebayes_adjPval
## diff_distrib02 1.017434e-43 1.424407e-42 8.037163e-48 1.125203e-46
## diff_distrib01 7.927938e-37 1.109911e-35 1.066684e-37 1.493358e-36
## simFeat 7.023057e-04 9.832280e-03 6.273684e-04 8.783158e-03
## norm_noise03 7.972660e-02 1.000000e+00 7.919121e-02 1.000000e+00
## norm_noise08 1.109098e-01 1.000000e+00 1.064060e-01 1.000000e+00
## norm_noise09 1.438542e-01 1.000000e+00 1.437854e-01 1.000000e+00
## lm_coef lm_pval lm_adjPval RF_feat_imp
## diff_distrib02 -0.0668305461 2.207235e-21 3.090129e-20 16.4114993
## diff_distrib01 -0.0312318926 1.235226e-11 1.729317e-10 19.4533855
## simFeat -0.0076745689 1.251399e-01 1.000000e+00 1.1936746
## norm_noise03 0.0027506413 6.054747e-01 1.000000e+00 1.1560764
## norm_noise08 0.0004548054 8.992620e-01 1.000000e+00 0.3780559
## norm_noise09 0.0035048925 5.214001e-01 1.000000e+00 0.7460329
## SHAP_feat_imp LIME_feat_imp
## diff_distrib02 0.2505628349 0.212450755
## diff_distrib01 0.2442789942 0.233883647
## simFeat 0.0003861862 0.014770319
## norm_noise03 0.0002316721 0.008099617
## norm_noise08 0.0002298521 0.008304666
## norm_noise09 0.0001920250 0.013512810
The mapPvalImportance function reveals the significance of the feature importance by comparison with the p-values.
Display as a data.frame:
mpi <- mapPvalImportance(objXAI)
mpi$df
## ttest_pval isSign_ttest_pval ttest_adjPval isSign_ttest_adjPval
## diff_distrib02 1.02e-43 1 1.42e-42 1
## diff_distrib01 7.93e-37 1 1.11e-35 1
## simFeat 7.02e-04 1 9.83e-03 1
## norm_noise03 7.97e-02 0 1.00e+00 0
## norm_noise08 1.11e-01 0 1.00e+00 0
## norm_noise09 1.44e-01 0 1.00e+00 0
## norm_noise02 1.46e-01 0 1.00e+00 0
## biDistrib 2.08e-01 0 1.00e+00 0
## norm_noise06 2.20e-01 0 1.00e+00 0
## norm_noise10 5.21e-01 0 1.00e+00 0
## norm_noise04 5.25e-01 0 1.00e+00 0
## norm_noise05 5.87e-01 0 1.00e+00 0
## norm_noise01 6.78e-01 0 1.00e+00 0
## norm_noise07 8.92e-01 0 1.00e+00 0
## ebayes_pval isSign_ebayes_pval ebayes_adjPval
## diff_distrib02 8.04e-48 1 1.13e-46
## diff_distrib01 1.07e-37 1 1.49e-36
## simFeat 6.27e-04 1 8.78e-03
## norm_noise03 7.92e-02 0 1.00e+00
## norm_noise08 1.06e-01 0 1.00e+00
## norm_noise09 1.44e-01 0 1.00e+00
## norm_noise02 1.43e-01 0 1.00e+00
## biDistrib 1.99e-01 0 1.00e+00
## norm_noise06 2.22e-01 0 1.00e+00
## norm_noise10 5.54e-01 0 1.00e+00
## norm_noise04 5.18e-01 0 1.00e+00
## norm_noise05 5.83e-01 0 1.00e+00
## norm_noise01 6.74e-01 0 1.00e+00
## norm_noise07 8.91e-01 0 1.00e+00
## isSign_ebayes_adjPval lm_pval isSign_lm_pval lm_adjPval
## diff_distrib02 1 2.21e-21 1 3.09e-20
## diff_distrib01 1 1.24e-11 1 1.73e-10
## simFeat 1 1.25e-01 0 1.00e+00
## norm_noise03 0 6.05e-01 0 1.00e+00
## norm_noise08 0 8.99e-01 0 1.00e+00
## norm_noise09 0 5.21e-01 0 1.00e+00
## norm_noise02 0 3.05e-01 0 1.00e+00
## biDistrib 0 4.11e-01 0 1.00e+00
## norm_noise06 0 1.96e-01 0 1.00e+00
## norm_noise10 0 1.43e-01 0 1.00e+00
## norm_noise04 0 5.49e-03 1 7.69e-02
## norm_noise05 0 6.68e-01 0 1.00e+00
## norm_noise01 0 6.75e-01 0 1.00e+00
## norm_noise07 0 1.49e-01 0 1.00e+00
## isSign_lm_adjPval RF_feat_imp isSign_RF_feat_imp SHAP_feat_imp
## diff_distrib02 1 16.400 1.0 2.51e-01
## diff_distrib01 1 19.500 1.0 2.44e-01
## simFeat 0 1.190 0.5 3.86e-04
## norm_noise03 0 1.160 0.0 2.32e-04
## norm_noise08 0 0.378 0.0 2.30e-04
## norm_noise09 0 0.746 0.0 1.92e-04
## norm_noise02 0 0.565 0.0 1.18e-04
## biDistrib 0 8.250 1.0 6.69e-04
## norm_noise06 0 0.243 0.0 1.76e-04
## norm_noise10 0 0.245 0.0 1.09e-04
## norm_noise04 0 0.252 0.0 1.61e-04
## norm_noise05 0 0.113 0.0 1.98e-04
## norm_noise01 0 0.377 0.0 2.44e-04
## norm_noise07 0 0.174 0.0 6.05e-05
## isSign_SHAP_feat_imp LIME_feat_imp isSign_LIME_feat_imp
## diff_distrib02 1.0 0.21200 1.0
## diff_distrib01 1.0 0.23400 1.0
## simFeat 0.5 0.01480 0.5
## norm_noise03 0.0 0.00810 0.0
## norm_noise08 0.0 0.00830 0.0
## norm_noise09 0.0 0.01350 0.0
## norm_noise02 0.0 0.01700 0.5
## biDistrib 0.5 0.06450 1.0
## norm_noise06 0.0 0.00663 0.0
## norm_noise10 0.0 0.00676 0.0
## norm_noise04 0.0 0.00799 0.0
## norm_noise05 0.0 0.00743 0.0
## norm_noise01 0.0 0.00579 0.0
## norm_noise07 0.0 0.00572 0.0
Display as a datatable:
mpi$dt
We can see that the biDistrib feature is not detected by the p-values, but is detected by the feature importance metrics.
Plot each model
The XAI.test function builds several predictive models. In order to provide a p-value, linear regression (lm) builds a model that we can access. Similarly, to give feature importances, methods like the random forest, SHAP, and LIME also build models that are accessible
The plotModel function is used to visualize the results of these predictive models. This visualization helps determine which classes are well-predicted by which model. This function aids in more effectively interpreting the model’s performance in each situation.
In this section, we aim to evaluate the performance of each model after removing the diff_distrib01 and diff_distrib02 features from the dataset, leaving only noise and the biDistrib features.
set.seed(123)
objXAI <- XAI.test(df_simu_classif[,setdiff(colnames(df_simu_classif),
c("diff_distrib01", "diff_distrib02"))],
simData=TRUE)
head(getMetricsTable(objXAI))
## ttest_pval ttest_adjPval ebayes_pval ebayes_adjPval lm_coef
## simFeat 0.00373774 0.04485288 0.003572831 0.04287397 -0.048072126
## norm_noise03 0.07972660 0.95671925 0.079812024 0.95774429 0.026051579
## norm_noise08 0.11090980 1.00000000 0.106582213 1.00000000 -0.015024728
## norm_noise09 0.14385418 1.00000000 0.144698338 1.00000000 0.029296030
## norm_noise02 0.14626421 1.00000000 0.143893819 1.00000000 0.023104227
## biDistrib 0.20818373 1.00000000 0.199417829 1.00000000 0.004796583
## lm_pval lm_adjPval RF_feat_imp SHAP_feat_imp LIME_feat_imp
## simFeat 0.01789724 0.2147668 3.864181 0.011120655 0.009946593
## norm_noise03 0.18885965 1.0000000 4.310358 0.019611018 0.011494790
## norm_noise08 0.25933766 1.0000000 1.282664 0.004310561 0.010515326
## norm_noise09 0.15050988 1.0000000 3.879493 0.001379714 0.012126513
## norm_noise02 0.16579352 1.0000000 2.694503 0.006493732 0.010868020
## biDistrib 0.74233539 1.0000000 22.104365 0.415727705 0.596812724
We can see below that the linear model predictions contain many errors, while the random forest, along with the models used for SHAP and LIME, are much more precise.
p1 <- plotModel(objXAI, "lm_pval", "biDistrib", "simFeat")
p2 <- plotModel(objXAI, "RF_feat_imp", "biDistrib", "simFeat")
p3 <- plotModel(objXAI, "SHAP_feat_imp", "biDistrib", "simFeat")
p4 <- plotModel(objXAI, "LIME_feat_imp", "biDistrib", "simFeat")
grid.arrange(p1, p2, p3, p4, ncol = 2, nrow = 2)
Display as a data.frame:
mpi <- mapPvalImportance(objXAI)
head(mpi$df)
## ttest_pval isSign_ttest_pval ttest_adjPval isSign_ttest_adjPval
## simFeat 0.00374 1 0.0449 1
## norm_noise03 0.07970 0 0.9570 0
## norm_noise08 0.11100 0 1.0000 0
## norm_noise09 0.14400 0 1.0000 0
## norm_noise02 0.14600 0 1.0000 0
## biDistrib 0.20800 0 1.0000 0
## ebayes_pval isSign_ebayes_pval ebayes_adjPval
## simFeat 0.00357 1 0.0429
## norm_noise03 0.07980 0 0.9580
## norm_noise08 0.10700 0 1.0000
## norm_noise09 0.14500 0 1.0000
## norm_noise02 0.14400 0 1.0000
## biDistrib 0.19900 0 1.0000
## isSign_ebayes_adjPval lm_pval isSign_lm_pval lm_adjPval
## simFeat 1 0.0179 1 0.215
## norm_noise03 0 0.1890 0 1.000
## norm_noise08 0 0.2590 0 1.000
## norm_noise09 0 0.1510 0 1.000
## norm_noise02 0 0.1660 0 1.000
## biDistrib 0 0.7420 0 1.000
## isSign_lm_adjPval RF_feat_imp isSign_RF_feat_imp SHAP_feat_imp
## simFeat 0 3.86 0.5 0.01110
## norm_noise03 0 4.31 0.5 0.01960
## norm_noise08 0 1.28 0.0 0.00431
## norm_noise09 0 3.88 0.5 0.00138
## norm_noise02 0 2.69 0.0 0.00649
## biDistrib 0 22.10 1.0 0.41600
## isSign_SHAP_feat_imp LIME_feat_imp isSign_LIME_feat_imp
## simFeat 0.5 0.00995 0.5
## norm_noise03 0.5 0.01150 0.5
## norm_noise08 0.0 0.01050 0.5
## norm_noise09 0.0 0.01210 0.5
## norm_noise02 0.0 0.01090 0.5
## biDistrib 1.0 0.59700 1.0
Display as a datatable:
mpi$dt
Detect new key features on a regression dataset
First, we load a regression toy example of 100 samples, with 5 noise features, and a y feature computed from one of the noise feature. We will investigate if the feature used to compute y can be identified using correlation, linear modeling, or feature importance metrics.
Load regression simulated dataset
- norm_noise1, norm_noise2: normal distribution noise features
- unif_noise1, unif_noise2 and unif_noise3: uniform distribution noise features
- y feature is aparabole computed from the norm_noise2 values.
Function of parabole
This function is invisible to the correlation test and is used to create the
output df_simu_regr$y <- transfo_parab(df_simu_regr$norm_noise2).
transfo_parab <- function(xs){
x1 <- min(xs)
x2 <- max(xs)
h <- (x1 + x2) / 2
k <- max(xs)/2
a <- k / ((h - x1) * (h - x2))
y <- a * (xs - x1) * (xs - x2)
return (y)
}
se_path <- system.file("extdata", "seRegress.rds", package="XAItest")
dataset_regress <- readRDS(se_path)
data_matrix <- assay(dataset_regress, "counts")
data_matrix <- t(data_matrix)
metadata <- as.data.frame(colData(dataset_regress))
df_simu_regr <- as.data.frame(cbind(data_matrix, y = metadata[['y']]))
for (col in names(df_simu_regr)) {
if (col != 'y') {
df_simu_regr[[col]] <- as.numeric(df_simu_regr[[col]])
}
}
Example with a dataframe.
df_path <- system.file("extdata", "dfRegress.txt", package="XAItest")
dataset_regress_df <- read.table(df_path)
df_simu_regr_df <- dataset_regress
ggplot(df_simu_regr, aes(x=norm_noise2, y=y)) + geom_point() + theme_bw()
We employ the XAI.test function to evaluate the p-values and feature importance of each feature. The parameter simData is set to TRUE, which instructs the function to generate a new feature named simFeat, which is designed to achieve a specified p-value (column ttest_adjPval), set at simPvalTarget = 0.01. The purpose of simFeat is to establish a significance threshold for assessing feature importance values.
set.seed(123)
regr_results <- XAI.test(dataset_regress, "y",
simData=TRUE, simPvalTarget = 0.01)
getMetricsTable(regr_results)
## cor cor_pval cor_adjPval lm_coef lm_pval
## simFeat 0.31120805 0.001623763 0.009742579 0.092081676 0.00113489
## unif_noise1 0.20779578 0.038029687 0.228178121 0.349840416 0.03174897
## unif_noise2 0.14747642 0.143127825 0.858766953 0.127425571 0.12148391
## unif_noise3 0.12517231 0.214652757 1.000000000 0.016799254 0.53806117
## norm_noise1 0.06115865 0.545535487 1.000000000 0.002523175 0.91762120
## norm_noise2 -0.01119237 0.911996996 1.000000000 -0.008511977 0.60820434
## lm_adjPval RF_feat_imp SHAP_feat_imp LIME_feat_imp
## simFeat 0.006809342 2.483707 0.002641477 0.01215317
## unif_noise1 0.190493842 1.954692 0.002873977 0.01452009
## unif_noise2 0.728903433 1.536527 0.003131702 0.01629232
## unif_noise3 1.000000000 1.415226 0.005048025 0.01241457
## norm_noise1 1.000000000 1.651757 0.001689609 0.01227430
## norm_noise2 1.000000000 12.932198 0.380749615 0.55671653
Display as a data.frame:
mpi <- mapPvalImportance(regr_results, refPvalColumn = "cor_adjPval", refPval = 0.01)
head(mpi$df)
## cor_pval isSign_cor_pval cor_adjPval isSign_cor_adjPval lm_pval
## simFeat 0.00162 1 0.00974 1 0.00113
## unif_noise1 0.03800 0 0.22800 0 0.03170
## unif_noise2 0.14300 0 0.85900 0 0.12100
## unif_noise3 0.21500 0 1.00000 0 0.53800
## norm_noise1 0.54600 0 1.00000 0 0.91800
## norm_noise2 0.91200 0 1.00000 0 0.60800
## isSign_lm_pval lm_adjPval isSign_lm_adjPval RF_feat_imp
## simFeat 1 0.00681 1 2.48
## unif_noise1 0 0.19000 0 1.95
## unif_noise2 0 0.72900 0 1.54
## unif_noise3 0 1.00000 0 1.42
## norm_noise1 0 1.00000 0 1.65
## norm_noise2 0 1.00000 0 12.90
## isSign_RF_feat_imp SHAP_feat_imp isSign_SHAP_feat_imp LIME_feat_imp
## simFeat 0.5 0.00264 0.5 0.0122
## unif_noise1 0.0 0.00287 0.5 0.0145
## unif_noise2 0.0 0.00313 0.5 0.0163
## unif_noise3 0.0 0.00505 0.5 0.0124
## norm_noise1 0.0 0.00169 0.0 0.0123
## norm_noise2 1.0 0.38100 1.0 0.5570
## isSign_LIME_feat_imp
## simFeat 0.5
## unif_noise1 0.5
## unif_noise2 0.5
## unif_noise3 0.5
## norm_noise1 0.5
## norm_noise2 1.0
Display as a datatable:
mpi$dt
The relationship between the norm_noise2 and y features is not apparent through correlation and linear modeling statistical tests, but is revealed by the Random Forest built-in feature importance, as well as its SHAP and LIME values.
Plot each model
Similar to the classification case, the use of the XAI.test function creates predictive models that we can visualize with the plotModel function. This provides insights into why the norm_noise2 feature was detected by feature importance metrics and not by linear modeling.
regr_results@args$modelType
## [1] "regression"
p1 <- plotModel(regr_results, "lm_pval", "norm_noise2")
p2 <- plotModel(regr_results, "SHAP_feat_imp", "norm_noise2")
grid.arrange(p1, p2, ncol = 2, nrow = 1)
Use the modelsOverview function to quickly review the performance of the models.
modelsOverview(regr_results)
## lm_pval RF_feat_imp SHAP_feat_imp LIME_feat_imp
## mse 0.2000662 0.01346611 0.01391434 0.002154499
## rmse 0.4472877 0.11604358 0.11795904 0.046416576
## mae 0.3347928 0.07164813 0.05904951 0.019892683
## r2 0.1736793 0.94438178 0.94253052 0.991101414
sessionInfo()
## R Under development (unstable) (2025-01-20 r87609)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.21-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0 LAPACK version 3.12.0
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB LC_COLLATE=C
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## time zone: America/New_York
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats4 stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] caret_7.0-1 lattice_0.22-6
## [3] SummarizedExperiment_1.37.0 Biobase_2.67.0
## [5] GenomicRanges_1.59.1 GenomeInfoDb_1.43.4
## [7] IRanges_2.41.2 S4Vectors_0.45.2
## [9] BiocGenerics_0.53.6 generics_0.1.3
## [11] MatrixGenerics_1.19.1 matrixStats_1.5.0
## [13] gridExtra_2.3 ggforce_0.4.2
## [15] ggplot2_3.5.1 XAItest_0.99.24
##
## loaded via a namespace (and not attached):
## [1] pROC_1.18.5 rlang_1.1.5 magrittr_2.0.3
## [4] e1071_1.7-16 compiler_4.5.0 lime_0.5.3
## [7] vctrs_0.6.5 reshape2_1.4.4 stringr_1.5.1
## [10] fastmap_1.2.0 pkgconfig_2.0.3 shape_1.4.6.1
## [13] crayon_1.5.3 XVector_0.47.2 labeling_0.4.3
## [16] prodlim_2024.06.25 UCSC.utils_1.3.1 purrr_1.0.2
## [19] xfun_0.50 glmnet_4.1-8 cachem_1.1.0
## [22] randomForest_4.7-1.2 jsonlite_1.8.9 recipes_1.1.0
## [25] DelayedArray_0.33.4 tweenr_2.0.3 parallel_4.5.0
## [28] R6_2.5.1 bslib_0.9.0 stringi_1.8.4
## [31] limma_3.63.3 parallelly_1.42.0 rpart_4.1.24
## [34] jquerylib_0.1.4 lubridate_1.9.4 Rcpp_1.0.14
## [37] assertthat_0.2.1 iterators_1.0.14 knitr_1.49
## [40] future.apply_1.11.3 Matrix_1.7-2 splines_4.5.0
## [43] nnet_7.3-20 timechange_0.3.0 tidyselect_1.2.1
## [46] abind_1.4-8 timeDate_4041.110 codetools_0.2-20
## [49] listenv_0.9.1 tibble_3.2.1 plyr_1.8.9
## [52] withr_3.0.2 evaluate_1.0.3 future_1.34.0
## [55] survival_3.8-3 proxy_0.4-27 polyclip_1.10-7
## [58] pillar_1.10.1 kernelshap_0.7.0 DT_0.33
## [61] foreach_1.5.2 munsell_0.5.1 scales_1.3.0
## [64] globals_0.16.3 class_7.3-23 glue_1.8.0
## [67] tools_4.5.0 data.table_1.16.4 ModelMetrics_1.2.2.2
## [70] gower_1.0.2 grid_4.5.0 crosstalk_1.2.1
## [73] ipred_0.9-15 colorspace_2.1-1 nlme_3.1-167
## [76] GenomeInfoDbData_1.2.13 cli_3.6.3 S4Arrays_1.7.1
## [79] lava_1.8.1 dplyr_1.1.4 gtable_0.3.6
## [82] sass_0.4.9 digest_0.6.37 SparseArray_1.7.4
## [85] htmlwidgets_1.6.4 farver_2.1.2 htmltools_0.5.8.1
## [88] lifecycle_1.0.4 hardhat_1.4.1 httr_1.4.7
## [91] statmod_1.5.0 MASS_7.3-64