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I am fitting an XGBoost model with this code on a grid of hyperparameters:
set.seed(20)
model_n <- xgb.train(data = xgb_trainval,
tree_method = "gpu_hist",
booster = "gbtree",
objective = "binary:logistic",
max_depth = parameters_df$max_depth[row],
eta = parameters_df$eta[row],
subsample = parameters_df$subsample[row],
colsample_bytree = parameters_df$colsample_bytree[row],
min_child_weight = parameters_df$min_child_weight[row],
nrounds = 1000,
eval_metric = "auc",
early_stopping_rounds = 30,
print_every_n = 1000,
watchlist = list(train = xgb_trainval, val = xgb_val)
)
xgb_trainval is the training data
xgb_val is the validation data
Next I have run the fitting again on the same traindata with the same hyperparameter-grid, although with different validation data (xgb_test):
set.seed(20)
model_n <- xgb.train(data = xgb_trainval,
tree_method = "gpu_hist",
booster = "gbtree",
objective = "binary:logistic",
max_depth = parameters_df$max_depth[row],
eta = parameters_df$eta[row],
subsample = parameters_df$subsample[row],
colsample_bytree = parameters_df$colsample_bytree[row],
min_child_weight = parameters_df$min_child_weight[row],
nrounds = 1000,
eval_metric = "auc",
early_stopping_rounds = 30,
print_every_n = 1000,
watchlist = list(train = xgb_trainval, val = xgb_test)
)
I notice this results in different auc values on the train data. I was expecting the same auc values on the train data since only my valuation data is different.
I also notice that the number of iterations is different for every hypertuning fit.
Does the different valuation data result in different number of iterations, resulting in different models, resulting in different auc values on the train data?
Thanks a lot!
I am learning to use the XGBoost package in R and I encountered some very weird behaviour that I'm not sure how to explain. Perhaps someone can give me some directions. I simplified the R code as much as possible:
rm(list = ls())
library(xgboost)
setwd("/home/my_username/Documents/R_files")
my_data <- read.csv("my_data.csv")
my_data$outcome_01 = ifelse(my_data$outcome_continuous > 0.0, 1, 0)
reg_features = c("feature_1", "feature_2")
class_features = c("feature_1", "feature_3")
set.seed(93571)
train_data = my_data[seq(1, nrow(my_data), 2), ]
mm_reg_train = model.matrix(~ . + 0, data = train_data[, reg_features])
train_DM_reg = xgb.DMatrix(data = mm_reg_train, label = train_data$outcome_continuous)
var_nrounds = 190
xgb_reg_model = xgb.train(data = train_DM_reg, booster = "gbtree", objective = "reg:squarederror",
nrounds = var_nrounds, eta = 0.07,
max_depth = 5, min_child_weight = 0.8, subsample = 0.6, colsample_bytree = 1.0,
verbose = F)
mm_class_train = model.matrix(~ . + 0, data = train_data[, class_features])
train_DM_class = xgb.DMatrix(data = mm_class_train, label = train_data$outcome_01)
xgb_class_model = xgb.train(data = train_DM_class, booster = "gbtree", objective = "binary:logistic",
eval_metric = 'auc', nrounds = 70, eta = 0.1,
max_depth = 3, min_child_weight = 0.5, subsample = 0.75, colsample_bytree = 0.5,
verbose = F)
probabilities = predict(xgb_class_model, newdata = train_DM_class, type = "response")
print(paste0("simple check: ", sum(probabilities)), quote = F)
Here is the problem: The outcome of sum(probabilities) depends on the value of var_nrounds!
How could that be? After all var_nrounds enters only in xgb_reg_model, while the probabilities are computed with the xgb_class_model that does (should) not know anything about the value of var_nrounds. The only thing that I change in this code is the value of var_nrounds and yet the sum of probabilities changes when I rerun it. It also changes deterministically, i.e., with var_nrounds = 190 I always get (with my data) 5324.3 and with var_nrounds = 285:5322.8. However, if I remove the line set.seed(93571), then the result changes non-deterministically every time I rerun the code.
Could it be that XGBoost has some sort of in-built stochastic behaviour that changes depending on the number of rounds run beforehand in another model and that also gets controlled by setting a seed somewhere in the code before training the XGBoost? Any ideas?
I'm using xgboost to build a model. The dataset only has 200 rows and 10000 cols.
I tried chi-2 to get 100 cols, but my confusion matrix looks like this:
1 0
1 190 0
0 10 0
I tried to use 10000 attributes, randomly select 100 attributes, select 100 attributes according to chi-2, but I never get 0 case predicted. Is it because of the dataset, or because the way I use xgboost?
My factor(pred.cv) is always showing only 1 level, while factor(y+1) has 1 or 2 as levels.
param <- list("objective" = "binary:logistic",
"eval_metric" = "error",
"nthread" = 2,
"max_depth" = 5,
"eta" = 0.3,
"gamma" = 0,
"subsample" = 0.8,
"colsample_bytree" = 0.8,
"min_child_weight" = 1,
"max_delta_step"= 5,
"learning_rate" =0.1,
"n_estimators" = 1000,
"seed"=27,
"scale_pos_weight" = 1
)
nfold=3
nrounds=200
pred.cv = matrix(bst.cv$pred, nrow=length(bst.cv$pred)/1, ncol=1)
pred.cv = max.col(pred.cv, "last")
factor(y+1) # this is the target in train, level 1 and 2
factor(pred.cv) # this is the issue, it is always only 1 level
I found caret to be slow and it is not able to tune all the parameters of xgboost models without building a custom model which is quite more complicated than using ones own custom function for evaluation.
However if you are doing some up/down sampling or smote/rose caret is the way to go since it incorporates them correctly in the model evaluating phase (during re-sampling). See: https://topepo.github.io/caret/subsampling-for-class-imbalances.html
However I found these techniques have a very small impact on the results and usually for the worse, at least in the models I trained.
scale_pos_weight gives a higher weight to a certain class, if the minority class is at 10% abundance then playing with scale_pos_weight around 5 - 10 should be beneficial.
Tuning regularization parameters can be quite beneficial for xgboost: here one has several parameters: alpha, beta and gamma - I found valid values to be 0 - 3. Other useful parameters that add direct regularization (by adding uncertainty) are subsample, colsample_bytree and colsample_bylevel. I found that playing with colsample_bylevel can also have a positive outcome on the model. subsample and colsample_bytree you are already utilizing.
I would test a much smaller eta and more trees to see if the model benefits. early_stopping_rounds rounds can speed up the process in that case.
Other eval_metric are probably going to be more beneficial than accuracy. Try logloss or auc and even map and ndcg
Here is a function for grid search of hyper-parameters. It uses auc as evaluation metric but one can change that easily
xgb.par.opt=function(train, seed){
require(xgboost)
ntrees=2000
searchGridSubCol <- expand.grid(subsample = c(0.5, 0.75, 1),
colsample_bytree = c(0.6, 0.8, 1),
gamma = c(0, 1, 2),
eta = c(0.01, 0.03),
max_depth = c(4,6,8,10))
aucErrorsHyperparameters <- apply(searchGridSubCol, 1, function(parameterList){
#Extract Parameters to test
currentSubsampleRate <- parameterList[["subsample"]]
currentColsampleRate <- parameterList[["colsample_bytree"]]
currentGamma <- parameterList[["gamma"]]
currentEta =parameterList[["eta"]]
currentMaxDepth =parameterList[["max_depth"]]
set.seed(seed)
xgboostModelCV <- xgb.cv(data = train,
nrounds = ntrees,
nfold = 5,
objective = "binary:logistic",
eval_metric= "auc",
metrics = "auc",
verbose = 1,
print_every_n = 50,
early_stopping_rounds = 200,
stratified = T,
scale_pos_weight=sum(all_data[train,1]==0)/sum(all_data[train,1]==1),
max_depth = currentMaxDepth,
eta = currentEta,
gamma = currentGamma,
colsample_bytree = currentColsampleRate,
min_child_weight = 1,
subsample = currentSubsampleRate
seed = seed)
xvalidationScores <- as.data.frame(xgboostModelCV$evaluation_log)
auc = xvalidationScores[xvalidationScores$iter==xgboostModelCV$best_iteration,c(1,4,5)]
auc = cbind(auc, currentSubsampleRate, currentColsampleRate, currentGamma, currentEta, currentMaxDepth)
names(auc) = c("iter", "test.auc.mean", "test.auc.std", "subsample", "colsample", "gamma", "eta", "max.depth")
print(auc)
return(auc)
})
return(aucErrorsHyperparameters)
}
One can add other parameters to the expand.grid call.
I usually train hyper-parameters on one CV repetition and evaluate them on additional repetitions with other seeds or on the validation set (but doing it on validation set should be used with caution to avoid over-fitting)
test
param <- list("objective" = "binary:logistic",
"eval_metric" = "error",
"nthread" = 2,
"max_depth" = 5,
"eta" = 0.3,
"gamma" = 0,
"subsample" = 0.8,
"colsample_bytree" = 0.8,
"min_child_weight" = 1,
"max_delta_step"= 5,
"learning_rate" =0.1,
"n_estimators" = 1000,
"seed"=27,
"scale_pos_weight" = 1
)
nfold=3
nrounds=200
pred.cv = matrix(bst.cv$pred, nrow=length(bst.cv$pred)/1, ncol=1)
pred.cv = max.col(pred.cv, "last")
factor(y+1) # this is the target in train, level 1 and 2
factor(pred.cv) # this is the issue, it is always only 1 level
I have the following R code that runs a simple xgboost model on a set of training and test data with the intention of predicting a binary outcome.
We start by
1) Reading in the relevant libraries.
library(xgboost)
library(readr)
library(caret)
2) Cleaning up the training and test data
train.raw = read.csv("train_data", header = TRUE, sep = ",")
drop = c('column')
train.df = train.raw[, !(names(train.raw) %in% drop)]
train.df[,'outcome'] = as.factor(train.df[,'outcome'])
test.raw = read.csv("test_data", header = TRUE, sep = ",")
drop = c('column')
test.df = test.raw[, !(names(test.raw) %in% drop)]
test.df[,'outcome'] = as.factor(test.df[,'outcome'])
train.c1 = subset(train.df , outcome == 1)
train.c0 = subset(train.df , outcome == 0)
3) Running XGBoost on the properly formatted data.
train_xgb = xgb.DMatrix(data.matrix(train.df [,1:124]), label = train.raw[, "outcome"])
test_xgb = xgb.DMatrix(data.matrix(test.df[,1:124]))
4) Running the model
model_xgb = xgboost(data = train_xgb, nrounds = 8, max_depth = 5, eta = .1, eval_metric = "logloss", objective = "binary:logistic", verbose = 5)
5) Making predicitions
pred_xgb <- predict(model_xgb, newdata = test_xgb)
My question is: How can I adjust this process so that I'm just pulling in / adjusting a single 'training' data set, and getting predictions on the hold-out sets of the cross-validated file?
To specify k-fold CV in the xgboost call one needs to call xgb.cv with nfold = some integer argument, to save the predictions for each resample use prediction = TRUE argument. For instance:
xgboostModelCV <- xgb.cv(data = dtrain,
nrounds = 1688,
nfold = 5,
objective = "binary:logistic",
eval_metric= "auc",
metrics = "auc",
verbose = 1,
print_every_n = 50,
stratified = T,
scale_pos_weight = 2
max_depth = 6,
eta = 0.01,
gamma=0,
colsample_bytree = 1 ,
min_child_weight = 1,
subsample= 0.5 ,
prediction = T)
xgboostModelCV$pred #contains predictions in the same order as in dtrain.
xgboostModelCV$folds #contains k-fold samples
Here's a decent function to pick hyperparams
function(train, seed){
require(xgboost)
ntrees=2000
searchGridSubCol <- expand.grid(subsample = c(0.5, 0.75, 1),
colsample_bytree = c(0.6, 0.8, 1),
gamma=c(0, 1, 2),
eta=c(0.01, 0.03),
max_depth=c(4,6,8,10))
aucErrorsHyperparameters <- apply(searchGridSubCol, 1, function(parameterList){
#Extract Parameters to test
currentSubsampleRate <- parameterList[["subsample"]]
currentColsampleRate <- parameterList[["colsample_bytree"]]
currentGamma <- parameterList[["gamma"]]
currentEta =parameterList[["eta"]]
currentMaxDepth =parameterList[["max_depth"]]
set.seed(seed)
xgboostModelCV <- xgb.cv(data = train,
nrounds = ntrees,
nfold = 5,
objective = "binary:logistic",
eval_metric= "auc",
metrics = "auc",
verbose = 1,
print_every_n = 50,
early_stopping_rounds = 200,
stratified = T,
scale_pos_weight=sum(all_data_nobad[index_no_bad,1]==0)/sum(all_data_nobad[index_no_bad,1]==1),
max_depth = currentMaxDepth,
eta = currentEta,
gamma=currentGamma,
colsample_bytree = currentColsampleRate,
min_child_weight = 1,
subsample= currentSubsampleRate)
xvalidationScores <- as.data.frame(xgboostModelCV$evaluation_log)
#Save rmse of the last iteration
auc=xvalidationScores[xvalidationScores$iter==xgboostModelCV$best_iteration,c(1,4,5)]
auc=cbind(auc, currentSubsampleRate, currentColsampleRate, currentGamma, currentEta, currentMaxDepth)
names(auc)=c("iter", "test.auc.mean", "test.auc.std", "subsample", "colsample", "gamma", "eta", "max.depth")
print(auc)
return(auc)
})
return(aucErrorsHyperparameters)
}
You can change the grid values and the params in the grid, as well as loss/evaluation metric. It is similar as provided by caret grid search, but caret does not provide the possibility to define alpha, lambda, colsample_bylevel, num_parallel_tree... hyper parameters in the grid search apart defining a custom function which I found cumbersome. Caret has the advantage of automatic preprocessing, automatic up/down sampling within CV etc.
setting the seed outside the xgb.cv call will pick the same folds for CV but not the same trees at each round so you will end up with a different model. Even if you set the seed inside the xgb.cv function call there is no guarantee you will end up with the same model but there's a much higher chance (depends on threads, type of model.. - I for one like the uncertainty and found it to have little impact on the result).
You can use xgb.cv and set prediction = TRUE.
I've been exploring the xgboost package in R and went through several demos as well as tutorials but this still confuses me: after using xgb.cv to do cross validation, how does the optimal parameters get passed to xgb.train? Or should I calculate the ideal parameters (such as nround, max.depth) based on the output of xgb.cv?
param <- list("objective" = "multi:softprob",
"eval_metric" = "mlogloss",
"num_class" = 12)
cv.nround <- 11
cv.nfold <- 5
mdcv <-xgb.cv(data=dtrain,params = param,nthread=6,nfold = cv.nfold,nrounds = cv.nround,verbose = T)
md <-xgb.train(data=dtrain,params = param,nround = 80,watchlist = list(train=dtrain,test=dtest),nthread=6)
Looks like you misunderstood xgb.cv, it is not a parameter searching function. It does k-folds cross validation, nothing more.
In your code, it does not change the value of param.
To find best parameters in R's XGBoost, there are some methods. These are 2 methods,
(1) Use mlr package, http://mlr-org.github.io/mlr-tutorial/release/html/
There is a XGBoost + mlr example code in the Kaggle's Prudential challenge,
But that code is for regression, not classification. As far as I know, there is no mlogloss metric yet in mlr package, so you must code the mlogloss measurement from scratch by yourself. CMIIW.
(2) Second method, by manually setting the parameters then repeat, example,
param <- list(objective = "multi:softprob",
eval_metric = "mlogloss",
num_class = 12,
max_depth = 8,
eta = 0.05,
gamma = 0.01,
subsample = 0.9,
colsample_bytree = 0.8,
min_child_weight = 4,
max_delta_step = 1
)
cv.nround = 1000
cv.nfold = 5
mdcv <- xgb.cv(data=dtrain, params = param, nthread=6,
nfold=cv.nfold, nrounds=cv.nround,
verbose = T)
Then, you find the best (minimum) mlogloss,
min_logloss = min(mdcv[, test.mlogloss.mean])
min_logloss_index = which.min(mdcv[, test.mlogloss.mean])
min_logloss is the minimum value of mlogloss, while min_logloss_index is the index (round).
You must repeat the process above several times, each time change the parameters manually (mlr does the repeat for you). Until finally you get best global minimum min_logloss.
Note: You can do it in a loop of 100 or 200 iterations, in which for each iteration you set the parameters value randomly. This way, you must save the best [parameters_list, min_logloss, min_logloss_index] in variables or in a file.
Note: better to set random seed by set.seed() for reproducible result. Different random seed yields different result. So, you must save [parameters_list, min_logloss, min_logloss_index, seednumber] in the variables or file.
Say that finally you get 3 results in 3 iterations/repeats:
min_logloss = 2.1457, min_logloss_index = 840
min_logloss = 2.2293, min_logloss_index = 920
min_logloss = 1.9745, min_logloss_index = 780
Then you must use the third parameters (it has global minimum min_logloss of 1.9745). Your best index (nrounds) is 780.
Once you get best parameters, use it in the training,
# best_param is global best param with minimum min_logloss
# best_min_logloss_index is the global minimum logloss index
nround = 780
md <- xgb.train(data=dtrain, params=best_param, nrounds=nround, nthread=6)
I don't think you need watchlist in the training, because you have done the cross validation. But if you still want to use watchlist, it is just okay.
Even better you can use early stopping in xgb.cv.
mdcv <- xgb.cv(data=dtrain, params=param, nthread=6,
nfold=cv.nfold, nrounds=cv.nround,
verbose = T, early.stop.round=8, maximize=FALSE)
With this code, when mlogloss value is not decreasing in 8 steps, the xgb.cv will stop. You can save time. You must set maximize to FALSE, because you expect minimum mlogloss.
Here is an example code, with 100 iterations loop, and random chosen parameters.
best_param = list()
best_seednumber = 1234
best_logloss = Inf
best_logloss_index = 0
for (iter in 1:100) {
param <- list(objective = "multi:softprob",
eval_metric = "mlogloss",
num_class = 12,
max_depth = sample(6:10, 1),
eta = runif(1, .01, .3),
gamma = runif(1, 0.0, 0.2),
subsample = runif(1, .6, .9),
colsample_bytree = runif(1, .5, .8),
min_child_weight = sample(1:40, 1),
max_delta_step = sample(1:10, 1)
)
cv.nround = 1000
cv.nfold = 5
seed.number = sample.int(10000, 1)[[1]]
set.seed(seed.number)
mdcv <- xgb.cv(data=dtrain, params = param, nthread=6,
nfold=cv.nfold, nrounds=cv.nround,
verbose = T, early.stop.round=8, maximize=FALSE)
min_logloss = min(mdcv[, test.mlogloss.mean])
min_logloss_index = which.min(mdcv[, test.mlogloss.mean])
if (min_logloss < best_logloss) {
best_logloss = min_logloss
best_logloss_index = min_logloss_index
best_seednumber = seed.number
best_param = param
}
}
nround = best_logloss_index
set.seed(best_seednumber)
md <- xgb.train(data=dtrain, params=best_param, nrounds=nround, nthread=6)
With this code, you run cross validation 100 times, each time with random parameters. Then you get best parameter set, that is in the iteration with minimum min_logloss.
Increase the value of early.stop.round in case you find out that it's too small (too early stopping). You need also to change the random parameter values' limit based on your data characteristics.
And, for 100 or 200 iterations, I think you want to change verbose to FALSE.
Side note: That is example of random method, you can adjust it e.g. by Bayesian optimization for better method. If you have Python version of XGBoost, there is a good hyperparameter script for XGBoost, https://github.com/mpearmain/BayesBoost to search for best parameters set using Bayesian optimization.
Edit: I want to add 3rd manual method, posted by "Davut Polat" a Kaggle master, in the Kaggle forum.
Edit: If you know Python and sklearn, you can also use GridSearchCV along with xgboost.XGBClassifier or xgboost.XGBRegressor
This is a good question and great reply from silo with lots of details! I found it very helpful for someone new to xgboost like me. Thank you. The method to randomize and compared to boundary is very inspiring. Good to use and good to know. Now in 2018 some slight revise are needed, for example, early.stop.round should be early_stopping_rounds. The output mdcv is organized slightly differently:
min_rmse_index <- mdcv$best_iteration
min_rmse <- mdcv$evaluation_log[min_rmse_index]$test_rmse_mean
And depends on the application (linear, logistic,etc...), the objective, eval_metric and parameters shall be adjusted accordingly.
For the convenience of anyone who is running a regression, here is the slightly adjusted version of code (most are the same as above).
library(xgboost)
# Matrix for xgb: dtrain and dtest, "label" is the dependent variable
dtrain <- xgb.DMatrix(X_train, label = Y_train)
dtest <- xgb.DMatrix(X_test, label = Y_test)
best_param <- list()
best_seednumber <- 1234
best_rmse <- Inf
best_rmse_index <- 0
set.seed(123)
for (iter in 1:100) {
param <- list(objective = "reg:linear",
eval_metric = "rmse",
max_depth = sample(6:10, 1),
eta = runif(1, .01, .3), # Learning rate, default: 0.3
subsample = runif(1, .6, .9),
colsample_bytree = runif(1, .5, .8),
min_child_weight = sample(1:40, 1),
max_delta_step = sample(1:10, 1)
)
cv.nround <- 1000
cv.nfold <- 5 # 5-fold cross-validation
seed.number <- sample.int(10000, 1) # set seed for the cv
set.seed(seed.number)
mdcv <- xgb.cv(data = dtrain, params = param,
nfold = cv.nfold, nrounds = cv.nround,
verbose = F, early_stopping_rounds = 8, maximize = FALSE)
min_rmse_index <- mdcv$best_iteration
min_rmse <- mdcv$evaluation_log[min_rmse_index]$test_rmse_mean
if (min_rmse < best_rmse) {
best_rmse <- min_rmse
best_rmse_index <- min_rmse_index
best_seednumber <- seed.number
best_param <- param
}
}
# The best index (min_rmse_index) is the best "nround" in the model
nround = best_rmse_index
set.seed(best_seednumber)
xg_mod <- xgboost(data = dtest, params = best_param, nround = nround, verbose = F)
# Check error in testing data
yhat_xg <- predict(xg_mod, dtest)
(MSE_xgb <- mean((yhat_xg - Y_test)^2))
I found silo's answer is very helpful.
In addition to his approach of random research, you may want to use Bayesian optimization to facilitate the process of hyperparameter search, e.g. rBayesianOptimization library.
The following is my code with rbayesianoptimization library.
cv_folds <- KFold(dataFTR$isPreIctalTrain, nfolds = 5, stratified = FALSE, seed = seedNum)
xgb_cv_bayes <- function(nround,max.depth, min_child_weight, subsample,eta,gamma,colsample_bytree,max_delta_step) {
param<-list(booster = "gbtree",
max_depth = max.depth,
min_child_weight = min_child_weight,
eta=eta,gamma=gamma,
subsample = subsample, colsample_bytree = colsample_bytree,
max_delta_step=max_delta_step,
lambda = 1, alpha = 0,
objective = "binary:logistic",
eval_metric = "auc")
cv <- xgb.cv(params = param, data = dtrain, folds = cv_folds,nrounds = 1000,early_stopping_rounds = 10, maximize = TRUE, verbose = verbose)
list(Score = cv$evaluation_log$test_auc_mean[cv$best_iteration],
Pred=cv$best_iteration)
# we don't need cross-validation prediction and we need the number of rounds.
# a workaround is to pass the number of rounds(best_iteration) to the Pred, which is a default parameter in the rbayesianoptimization library.
}
OPT_Res <- BayesianOptimization(xgb_cv_bayes,
bounds = list(max.depth =c(3L, 10L),min_child_weight = c(1L, 40L),
subsample = c(0.6, 0.9),
eta=c(0.01,0.3),gamma = c(0.0, 0.2),
colsample_bytree=c(0.5,0.8),max_delta_step=c(1L,10L)),
init_grid_dt = NULL, init_points = 10, n_iter = 10,
acq = "ucb", kappa = 2.576, eps = 0.0,
verbose = verbose)
best_param <- list(
booster = "gbtree",
eval.metric = "auc",
objective = "binary:logistic",
max_depth = OPT_Res$Best_Par["max.depth"],
eta = OPT_Res$Best_Par["eta"],
gamma = OPT_Res$Best_Par["gamma"],
subsample = OPT_Res$Best_Par["subsample"],
colsample_bytree = OPT_Res$Best_Par["colsample_bytree"],
min_child_weight = OPT_Res$Best_Par["min_child_weight"],
max_delta_step = OPT_Res$Best_Par["max_delta_step"])
# number of rounds should be tuned using CV
#https://www.hackerearth.com/practice/machine-learning/machine-learning-algorithms/beginners-tutorial-on-xgboost-parameter-tuning-r/tutorial/
# However, nrounds can not be directly derivied from the bayesianoptimization function
# Here, OPT_Res$Pred, which was supposed to be used for cross-validation, is used to record the number of rounds
nrounds=OPT_Res$Pred[[which.max(OPT_Res$History$Value)]]
xgb_model <- xgb.train (params = best_param, data = dtrain, nrounds = nrounds)