整合學習

http://www.hmwu.idv.tw

吳漢銘 國立政治大學 統計學系

整合學習

Ensemble Learning

C05

本章大綱&學習目標

 Machine Learning

 Resampling methods

 Jackknife (leave-one-out)

 Bootstrapping

 Ensemble Learning

 bagging

 boosting

 Imbalanced Data Problem

 under-sampling

 over-sampling

2/29

Common Machine Learning Algorithms

Linear Regression, Logistic Regression,

Decision Tree, SVM, Naive Bayes, KNN,

K-Means, Random Forest, Dimensionality

Reduction, Boosting

Difference between

Machine Learning & Statistical Modeling

3/29

https://www.analyticsvidhya.com/blog/2015/07/difference-machine-learning-statistical-modeling/

機器學習和統計棤型的差異

http://vvar.pixnet.net/blog/post/242048881

為什麼統計學家、機器學習專家解決同一問題的方法差別那麼大?

https://read01.com/EBPPK7.html

深度| 機器學習與統計學是互補的嗎？

https://read01.com/ezQ3K.html

• Machine Learning is an algorithm that can learn from data without relying on rules-based programming.

• Statistical Modelling is the formalization of relationships between variables in the

form of mathematical equations.

Why Ensemble Learning? ^4/29

> prediction.accuracy.rate()

no.classifiers at.least.one.accuracy 1.0 0.5

> t(sapply(1:10, prediction.accuracy.rate)) no.classifiers at.least.one.accuracy [1,] 1 0.5000000 [2,] 2 0.7500000 [3,] 3 0.8750000 [4,] 4 0.9375000 [5,] 5 0.9687500 [6,] 6 0.9843750 [7,] 7 0.9921875 [8,] 8 0.9960938 [9,] 9 0.9980469 [10,] 10 0.9990234

prediction.accuracy.rate <- function(no.classifier=1, accuracy.rate=0.5){

c(no.classifiers=no.classifier,

at.least.one.accuracy=1-(1-accuracy.rate)^no.classifier) }

Training data

classifier 1

classifier 2

classifier k

y

y

y

ŷ

testing data y

replicates or

various algorithms

Why Resampling?



Resampling is any of a variety of methods for:



Estimating the precision of sample statistics (medians, variances, percentiles) by using subsets of available data (jackknifing) or drawing randomly with replacement from a set of data points (bootstrapping).



Exchanging labels on data points when performing significance tests (permutation tests, randomization tests)



Validating models by using random subsets (bootstrapping, cross validation)

https://en.wikipedia.org/wiki/Resampling_(statistics)



This single sample method can serve as a mini population, from which repeated small samples are drawn with replacement over and over again.



As well as saving time and money, bootstrapped samples can be

quite good approximations for population parameters.

Jackknife Resampling ^6/29

the calculated estimator of the parameter based on all n observations the average of these "leave-one-out" estimates

the resulting bias-corrected jackknife estimate

> # install.packages("bootstrap")

> library(bootstrap)

> jackknife

function (x, theta, ...) {

call <- match.call() n <- length(x)

u <- rep(0, n) for (i in 1:n) {

u[i] <- theta(x[-i], ...) }

thetahat <- theta(x, ...)

jack.bias <- (n - 1) * (mean(u) - thetahat)

jack.se <- sqrt(((n - 1)/n) * sum((u - mean(u))^2))

return(list(jack.se = jack.se, jack.bias = jack.bias, jack.values = u, call = call))

}

<environment: namespace:bootstrap>

Example: Jackknife Estimate the Coefficient of Variation

> set.seed(12345)

> x <- runif(30)

> n <- length(x)

> theta <- CV(x)

> CV <- function(x) sqrt(var(x))/mean(x)

> theta.i <- sapply(1:n, function(i) CV(x[-i]))

> theta.i

[1] 0.5497915 0.5442365 0.5489822 0.5436256 0.5448185 0.5195935 0.5359400 0.5472011 [9] 0.5496842 0.5357489 0.5011942 0.5178517 0.5495427 0.4958063 0.5409312 0.5451245 [17] 0.5407236 0.5416770 0.5211182 0.5390234 0.5446755 0.5360780 0.5378925 0.5499674 [25] 0.5501676 0.5408382 0.5500584 0.5484004 0.5265137 0.5461715

> theta.jack <- n*theta - (n-1)*mean(theta.i)

> theta.jack [1] 0.5356475

> plot(theta.i)

Jackknifing can be useful for analyzing

if influential observations are affecting

our estimates.

Jackknife the Coefficients of a Linear Regression Model

8/29

> library(bootstrap)

> set.seed(12345)

> n <- 50; p <- 5

> mydata <- as.data.frame(matrix(rnorm(n*p), ncol=p))

> head(mydata, 3)

V1 V2 V3 V4 V5 1 0.5855288 -0.54038607 0.2239254 -1.6193283 -1.4361457 2 0.7094660 1.94769266 -1.1562233 0.5483979 -0.6292596 3 -0.1093033 0.05359027 0.4224185 0.1952822 0.2435218

> model.lm <- formula(V1 ~ V2 + V3 + V4)

> theta <- function(x, xdata, coefficient){

+ coef(lm(model.lm, data=xdata[x, ]))[coefficient]

+ }

> results <- jackknife(1:n, theta, xdata=mydata, coefficient="(Intercept)")

> results

$jack.se

[1] 0.1672309

$jack.bias (Intercept) 0.003368696

$jack.values

[1] 0.1412249 0.1570365 0.1723303 0.1703336 0.1529388 0.2038722 0.1620162 0.1754961 ...

[41] 0.1384219 0.2296432 0.1793121 0.1429386 0.1545121 0.1456370 0.2016571 0.1582340 [49] 0.1536307 0.2034109

$call

jackknife(x = 1:n, theta = theta, xdata = mydata, coefficient = "(Intercept)")

Bootstrap Methods



Bootstrapping is a statistical method for estimating the sampling distribution of an

estimator by sampling with replacement from the original sample, of the same size as the original sample.



The name "bootstrapping" comes from the phrase:

"To lift himself up by his bootstraps".



This refers to something that is preposterous and impossible.



Try as hard as you can, you cannot lift yourself into the air by tugging at pieces of leather on your boots.

Bradley Efron 1938~

Department of Statistics

Stanford University

Bootstrapping ^10/29

Original Data

.

Bootstrap Sample

Bootstrap Statistics Statistic 1

Statistic 2*

Statistic B*

Bootstrap Distribution sampling

with replacement

Sample

Statistic ..

• Types of bootstrap scheme: Case

resampling, Bayesian bootstrap, Smooth bootstrap, Parametric bootstrap,

Resampling residuals, Gaussian process regression bootstrap, Wild bootstrap, Block bootstrap.

• An empirical bootstrap sample is drawn from observations.

• A parametric bootstrap sample is drawn

from a parameterized distribution (e.g. a

normal distribution).

Example: Bootstrap Estimate the Coefficient of Variation

> set.seed(12345)

> x <- runif(30)

> CV <- function(x) sqrt(var(x))/mean(x)

> CV(x)

[1] 0.5380304

> CV(sample(x, replace=T)) # a single bootstrap sample [1] 0.5459389

> boot <- replicate(n=100, expr=CV(sample(x, replace=T)))

> boot

[1] 0.5044811 0.5286011 0.4634611 0.5605438 0.4835447 0.5374531 0.4857342 0.4342565 ...

[89] 0.5297020 0.5121274 0.4938053 0.5479498 0.5262306 0.6095145 0.5322045 0.6069263 [97] 0.5374840 0.4921430 0.4674226 0.4573680

> mean(boot) [1] 0.5251909

> var(boot) [1] 0.006107636

> hist(boot)

bootstrap Package ^12/29

> # install.packages("bootstrap")

> library(bootstrap)

> set.seed(12345)

> x <- rnorm(20)

> mean(x)

[1] 0.07651681

> (x.bootstrap.mean <- bootstrap(x, 50, theta=mean))

$thetastar

[1] 0.486197466 -0.160488357 0.274920990 0.398499864 -0.399967845 0.116086370 ...

[43] -0.348643786 0.185330636 -0.070823890 0.057609481 0.062067504 0.043716794 [49] -0.279597885 0.243843620

$func.thetastar NULL

$jack.boot.val NULL

$jack.boot.se NULL

$call

bootstrap(x = x, nboot = 50, theta = mean)

> mean(x.bootstrap.mean$thetastar) [1] 0.08647268

語法:

bootstrap(x, nboot, theta, ..., func=NULL) x:

a vector containing the data.

nboot:

the number of bootstrap samples.

theta:

function to be bootstrapped.

> mu.hat <- mean(x)

> n <- length(x)

> ja <- jackknife(x, mean)

> mu.hat.jack <- n*mu.hat - (n-1)*mean(ja$jack.values)

> # or

> mu.hat.jack <- mu.hat - ja$jack.bias

Bootstrap Estimation of

the Sample Mean

Bagging:

Bootstrap Aggregating

13/29

http://blog.csdn.net/bymaymay/article/details/77824574

• Breiman, L. (1996). Bagging predictors, Machine Learning, Vol. 26, pp. 123-140.

• Freund, Y. and Schapire, R. E. (1996). Experiments with a new boosting algorithm, Proceedings of

the Thirteenth International Conference, Machine Learning.

Boosting ^14/29

http://blog.csdn.net/bymaymay/article/details/77824574

Ad-Boost.M1 (Freund and Schapire, 1996)

Example: Apply rpart to Vehicle Data

> mfinal <- 10 #Defaults to mfinal=100 iterations

> maxdepth <- 5

> Vehicle.rpart <- rpart(Class ~ ., data = Vehicle.train, maxdepth = maxdepth)

> Vehicle.rpart.pred <- predict(Vehicle.rpart, newdata = Vehicle.test, type = "class")

> (tb <- table(Vehicle.rpart.pred, Observed.Class=Vehicle.test$Class)) Observed.Class

Vehicle.rpart.pred bus opel saab van bus 69 10 6 2 opel 1 25 13 3 saab 1 34 37 8 van 2 7 5 59

> (error.rpart <- 1 - (sum(diag(tb)) / sum(tb))) [1] 0.3262411

> library(rpart); library(mlbench); library(adabag)

> data(Vehicle)

> dim(Vehicle) [1] 846 19

> head(Vehicle)

Comp Circ D.Circ Rad.Ra Pr.Axis.Ra Max.L.Ra Scat.Ra Elong Pr.Axis.Rect Max.L.Rect Sc.Var.Maxis 1 95 48 83 178 72 10 162 42 20 159 176 ...

Sc.Var.maxis Ra.Gyr Skew.Maxis Skew.maxis Kurt.maxis Kurt.Maxis Holl.Ra Class 1 379 184 70 6 16 187 197 van ...

6 957 264 85 5 9 181 183 bus

> table(Vehicle$Class) bus opel saab van

218 212 217 199 > n <- nrow(Vehicle)

> sub <- sample(1:n, 2*n/3)

> Vehicle.train <- Vehicle[sub, ]

> Vehicle.test <- Vehicle[-sub, ]

adabag : An R Package for Classification with Boosting and Bagging

16/29

> library(adabag)

> Vehicle.adaboost <- boosting(Class ~., data = Vehicle.train, mfinal = mfinal, + control = rpart.control(maxdepth=maxdepth))

> Vehicle.adaboost.pred <- predict.boosting(Vehicle.adaboost, newdata = Vehicle.test)

> Vehicle.adaboost.pred$confusion Observed Class Predicted Class bus opel saab van

bus 69 2 3 1 opel 1 30 16 4 saab 1 38 39 1 van 2 6 3 66

> Vehicle.adaboost.pred$error [1] 0.2765957

> importanceplot(Vehicle.adaboost)

>

> # comparing error evolution in training and test set

> evol.train <- errorevol(Vehicle.adaboost, newdata = Vehicle.train)

> evol.test <- errorevol(Vehicle.adaboost, newdata = Vehicle.test)

> plot.errorevol(evol.test, evol.train)

> sort(Vehicle.adaboost$importance, dec=T)[1:5]

Max.L.Ra Sc.Var.maxis Max.L.Rect 29.623783 11.473254 9.956137

Elong Comp 7.570798 6.656360

Alfaro, E., Gamez, M. and Garcia, N. (2013): "adabag: An R Package for Classification with Boosting and Bagging".

Journal of Statistical Software, 54(2), 1–35.

Example: 10-fold CV adaboost.M1

> # 10-fold CV adaboost.M1

> Vehicle.boost.cv <- boosting.cv(Class ~., data = Vehicle, v = 10, mfinal = 5, + control = rpart.control(maxdepth=maxdepth)) i: 1 Tue Dec 05 09:36:37 2017

...

> Vehicle.boost.cv$confusion Observed Class Predicted Class bus opel saab van

bus 209 9 11 3 opel 1 101 72 2 saab 0 88 117 6 van 8 14 17 188

> Vehicle.boost.cv$error [1] 0.2730496

> Vehicle.bag.cv <- bagging.cv(Class ~., data = Vehicle, v = 10, mfinal = 5, + control = rpart.control(maxdepth=maxdepth))

> Vehicle.bag.cv$confusion Observed Class Predicted Class bus opel saab van

bus 208 20 24 2 opel 1 91 53 1 saab 1 81 116 5 van 8 20 24 191

> Vehicle.bag.cv$error [1] 0.2836879

# first tree

t1 <- adaboost$trees[[1]]

library(tree) plot(t1)

text(t1, pretty=0)

The Imbalanced Data Problem



A dataset is said to be unbalanced when the class of interest (minority class) is much rarer than normal behaviour (majority class).



The cost of missing a minority class is typically much higher that missing a majority class. Most learning systems are not prepared to cope with unbalanced data and several techniques have been proposed.



Example: 5% of the target class represents fraudulent transactions, 95% of the target class represents legitimate transactions.

18/29

http://www.srutisj.in/blog/research/statisticalmodeling/balancing-techniques-for-unbalanced-datasets-in-python-r/

unbalanced

Racing for Unbalanced Methods Selection

Re-balance or remove noisy instances in unbalanced datasets.

ubBalance {unbalanced}

Usage

ubBalance(X, Y, type="ubSMOTE", positive=1, percOver=200, percUnder=200,

k=5, perc=50, method="percPos", w=NULL, verbose=FALSE)

Arguments

X: the input variables of the unbalanced dataset.

Y: the response variable of the unbalanced dataset.

type: the balancing technique to use (ubOver, ubUnder, ubSMOTE, ubOSS, ubCNN, ubENN, ubNCL, ubTomek).

positive: the majority class of the response variable.

percOver: parameter used in ubSMOTE percUnder: parameter used in ubSMOTE

k: parameter used in ubOver, ubSMOTE, ubCNN, ubENN, ubNCL perc: parameter used in ubUnder

method: parameter used in ubUnder w: parameter used in ubUnder

verbose: print extra information (TRUE/FALSE)

ubSMOTE {unbalanced}: synthetic minority over-sampling technique

Usage

ubSMOTE(X, Y, perc.over = 200, k = 5, perc.under = 200, verbose = TRUE)

NOTE: ^imbalance : Preprocessing Algorithms for Imbalanced Datasets, Imbalanced

Classification in R: ROSE (Random Over Sampling Examples) and DMwR (Data Mining with R).

The Balancing Technique



ubOver : replicates randomly some instances from the minority class in order to obtain a final dataset with the same number of instances from the two classes.



ubUnder : removes randomly some instances from the majority

(negative) class and keeps all instances in the minority (positive) class in order to obtain a more balanced dataset.



ubCNN : Condensed Nearest Neighbor selects the subset of instances that are able to correctly classifying the original datasets using a one- nearest neighbor rule.



ubENN : Edited Nearest Neighbor removes any example whose class label differs from the class of at least two of its three nearest neighbors.



ubNCL : Neighborhood Cleaning Rule modifies the Edited Nearest Neighbor method by increasing the role of data cleaning.



Firstly, NCL removes negatives examples which are misclassified by their 3- nearest neighbors.



Secondly, the neighbors of each positive examples are found and the ones belonging to the majority class are removed.

20/29

The Balancing Technique

 ubTomek : finds the points in the dataset that are tomek link using 1-NN and then removes only majority class instances that are tomek links.

 ubOSS : One Side Selection is an undersampling method resulting from the application of Tomek links followed by the application of Condensed Nearest Neighbor.

x's nearest neighbor is y y's nearest neighbor is x x and y are different classes

http://contrib.scikit-learn.org/imbalanced-learn/stable/auto_examples/under- sampling/plot_illustration_tomek_links.html

The Balancing Technique

 ubSMOTE : synthetic minority over-sampling technique

generates new examples by filling empty areas among the positive instances

 ubRacing : the Racing algorithm for selecting the best technique to re-balance or remove noisy instances in unbalanced datasets.

22/29

N. V. Chawla, K. W. Bowyer, L. O. Hall, W. P. Kegelmeyer, SMOTE: Synthetic Minority Over-sampling Technique, Journal Of Artificial Intelligence Research, Volume 16, pages 321-357, 2002.(由 NV Chawla 著作 - 2002 - 被引用 5161 次)

Ionosphere dataset

ubIonosphere {unbalanced}



The datasets is a modification of Ionosphere dataset contained in "mlbench" package.

23/29

> # install.packages("unbalanced")

> library(unbalanced)

> p <- ncol(ubIonosphere)

> y <- ubIonosphere$Class

> x <- ubIonosphere[ ,-p]

> data <- ubBalance(X=x, Y=y, type="ubOver", k=0)

> overData <- data.frame(data$X, Class=data$Y)

> table(overData$Class) 0 1

225 225

> data <- ubBalance(X=x, Y=y, type="ubUnder", perc=50, method="percPos")

> underData <- data.frame(data$X, Class=data$Y)

> table(underData$Class) 0 1

126 126

> bdata <- ubBalance(X=x, Y=y, type="ubSMOTE", percOver=300, percUnder=150, verbose=TRUE) Proportion of positives after ubSMOTE : 47.06 % of 1071 observations

> str(bdata) List of 3

$ X :'data.frame': 1071 obs. of 32 variables:

..$ V3 : num [1:1071] -0.787 1 1 0.5 1 ...

...

..$ V34: num [1:1071] -0.576 0.714 -0.243 0.174 -0.892 ...

$ Y : Factor w/ 2 levels "0","1": 2 1 1 1 1 2 1 2 1 2 ...

$ id.rm: logi NA

> table(bdata$Y) 0 1

567 504

> data(ubIonosphere)

> dim(ubIonosphere) [1] 351 33

> head(ubIonosphere)

V3 V4 V34 Class 1 0.99539 -0.05889 ... -0.45300 0 ...

6 0.02337 -0.00592 ... 0.12011 1

> table(ubIonosphere$Class) 0 1

225 126

K=0: sample with replacement from the minority class until we have the same number of instances in each class.

If K>0: sample with replacement from the minority class until we have k-times the orginal number of minority instances per.over/100: number of new instances generated for each rare instance

perc.under/100: number of "normal" (majority class) instances that are randomly selected for each smoted observation.

Compare the Performances using SVM ^24/29

> set.seed(12345)

> n <- nrow(ubIonosphere) # 351

> no.train <- floor(0.5*n) # 175, keep half for training and half for testing

> id <- sample(1:n, no.train)

> x.train <- x[id, ] # 175 x 32

> y.train <- y[id]

> x.test <- x[-id, ] # 176 32

> y.test <- y[-id]

>

> library(e1071)

> model1 <- svm(x.train, y.train)

> y.pred1 <- predict(model1, x.test)

> table(y.pred1, y.test) y.test

y.pred1 0 1 0 113 10 1 4 49

>

> # rebalance the training set before building a model

> balancedData <- ubBalance(X=x.train, Y=y.train, type="ubSMOTE", percOver=200, percUnder=150)

> table(balancedData$Y) 0 1

201 201 > model2 <- svm(balancedData$X, balancedData$Y)

> y.pred2 <- predict(model2, x.test)

> table(y.pred2, y.test) y.test

y.pred2 0 1 0 112 8 1 5 51

ubRacing {unbalanced}

Racing for Strategy Selection

> set.seed(1234)

> # load(url("http://www.ulb.ac.be/di/map/adalpozz/data/creditcard.Rdata"))

> load("creditcard.Rdata")

> str(creditcard)

'data.frame': 284807 obs. of 31 variables:

$ Time : num 0 0 1 1 2 2 4 7 7 9 ...

$ V1 : num -1.36 1.192 -1.358 -0.966 -1.158 ...

...

$ V28 : num -0.0211 0.0147 -0.0598 0.0615 0.2152 ...

$ Amount: num 149.62 2.69 378.66 123.5 69.99 ...

$ Class : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...

> table(creditcard$Class) 0 1

284315 492

> # configuration of the sampling method used in the race

> ubConf <- list(percOver=200, percUnder=200, k=2, perc=50, method="percPos", w=NULL)

> # Race with 5 trees in the Random Forest

> results <- ubRacing(Class ~., creditcard, "randomForest",

+ positive=1, metric="auc", ubConf=ubConf, ntree=5)

Selecting the best technique to re-balance or remove noisy instances in unbalanced datasets.

ubRacing(formula, data, algo, positive=1, ncore=1, nFold=10, maxFold=10, maxExp=100, stat.test="friedman", metric="f1", ubConf, verbose=FALSE, ...)

Arguments

algo: the classification algorithm to use with the mlr package.

positive : label of the positive (minority) class.

ncore : the number of core (parallel execution) to use in the Race.

The function ubRacing

compares the 8 unbalanced

methods (ubUnder, ubOver,

ubSMOTE, ubOSS, ubCNN,

ubENN, ubNCL, ubTomek)

against the unbalanced

distribution.

Racing for Strategy Selection ^26/29

Racing for unbalanced methods selection in 10 fold CV

Number of candidates...9 Max number of folds in the CV...10 Max number of experiments...100 Statistical test...Friedman test

Markers:

x No test is performed.

- The test is performed and some candidates are discarded.

= The test is performed but no candidate is discarded.

+-+---+---+---+---+---+

| | Fold| Alive| Best| Mean best| Exp so far|

+-+---+---+---+---+---+

|x| 1| 9| 4| 0.9543| 9|

|=| 2| 9| 3| 0.9433| 18|

|-| 3| 3| 4| 0.9567| 27|

|-| 4| 2| 4| 0.9566| 30|

|=| 5| 2| 4| 0.9582| 32|

|=| 6| 2| 4| 0.9546| 34|

|=| 7| 2| 4| 0.9531| 36|

|=| 8| 2| 4| 0.9539| 38|

|=| 9| 2| 4| 0.9531| 40|

|=| 10| 2| 4| 0.9529| 42|

+-+---+---+---+---+---+

Selected candidate: ubSMOTE metric: auc mean value: 0.9529

Racing for Strategy Selection

> results

$best

[1] "ubSMOTE"

$avg

[1] 0.9529177

$sd

[1] 0.009049014

$N.test [1] 42

$Gain [1] 53

$Race

unbal ubOver ubUnder ubSMOTE ubOSS ubCNN ubENN ubNCL ubTomek [1,] 0.8844582 0.9138946 0.9354739 0.9543104 0.8957273 0.9139340 0.9024656 0.9014143 0.9048642 [2,] 0.9116642 0.9104928 0.9511485 0.9507221 0.9037491 0.9104840 0.9139047 0.9094542 0.9105558 [3,] 0.8979478 0.9013642 0.9502417 0.9649361 0.9092505 0.9081796 0.9103668 0.9036617 0.9058917 [4,] NA NA 0.9503782 0.9564226 NA NA 0.8999928 NA NA [5,] NA NA 0.9537802 0.9647722 NA NA NA NA NA [6,] NA NA 0.9494913 0.9362763 NA NA NA NA NA [7,] NA NA 0.9411979 0.9440379 NA NA NA NA NA [8,] NA NA 0.9576971 0.9594249 NA NA NA NA NA [9,] NA NA 0.9530119 0.9473722 NA NA NA NA NA [10,] NA NA 0.9633438 0.9509024 NA NA NA NA NA

> # Race using 4 cores and 500 trees (default)

> results <- ubRacing(Class ~., creditcard, "randomForest",

positive=1, metric="auc", ubConf=ubConf, ncore=4)

> library(e1071)

> results <- ubRacing(Class ~., creditcard, "svm", positive=1, ubConf=ubConf)

> library(rpart)

> results <- ubRacing(Class ~., creditcard, "rpart", positive=1, ubConf=ubConf)

Useful R Packages ^28/29

mlr: Machine Learning in R

https://cran.r-project.org/web/packages/mlr/vignettes/mlr.html

DMwR: Functions and data for "Data Mining with R"

https://cran.r-project.org/web/packages/DMwR/index.html

XGBoost: eXtreme Gradient Boosting

(used for supervised learning tasks such as Regression, Classification, and Ranking)

https://github.com/dmlc/xgboost

http://xgboost.readthedocs.io/en/latest/

How to use XGBoost algorithm in R in easy steps

https://www.analyticsvidhya.com/blog/2016/01/xgboost-algorithm-easy-steps/

Kaggle 神器 XGBoost 入門：為什麼要用它?怎麼用?

https://weiwenku.net/d/100778240

imbalance

https://cran.r-project.org/web/packages/imbalance/vignettes/imbalance.pdf

Reference



Chawla, Nitesh V. (2010) Data Mining for Imbalanced Datasets: An Overview, In: Maimon, Oded; Rokach, Lior (Eds) Data Mining and

Knowledge Discovery Handbook, Springer ISBN 978-0-387-09823-4 (pages 875–886)



Dealing with unbalanced data in machine learning

https://shiring.github.io/machine_learning/2017/04/02/unbalanced



Dealing with imbalanced data: undersampling, oversampling and proper cross-validation

https://www.marcoaltini.com/blog/dealing-with-imbalanced-data-undersampling- oversampling-and-proper-cross-validation



Practical Guide to deal with Imbalanced Classification Problems in R

https://www.analyticsvidhya.com/blog/2016/03/practical-guide-deal-imbalanced- classification-problems/



How to handle Imbalanced Classification Problems in machine learning?

https://www.analyticsvidhya.com/blog/2017/03/imbalanced-classification-

problem/