GBM package in r

Presentation Outline
• Algorithm Overview
• Basics
• How it solves problems
• Why to use it
• Deeper investigation while going through live code

What is GBM?
• Predictive modeling algorithm
• Classification & Regression
• Decision tree as a basis*
• Boosted
• Multiple weak models combined algorithmically
• Gradient boosted
• Iteratively solves residuals
• Stochastic
(some additional references on last slide)
* technically, GBM can take on other forms such as linear, but decision trees are the dominant usage,
Friedman specifically optimized for trees, and R’s implementation is internally represented as a tree

Predictive Modeling Landscape:
General Purpose Algorithms
(forillustrativepurposes only,nottoscale,precise,orcomprehensive;author’sperspective)
Linear Models Decision Trees Others
Linear Models
(lm)
Generalized
Linear Models (glm)
Regularized
Linear
Models
(glmnet)
Classification
And Regression
Trees (rpart)
Random
Forest
(randomForest)
Gradient
Boosted
Machines
(gbm)
Nearest Neighbor
(kNN)
Neural
Networks
(nnet)
Support
Vector
Machines
(kernlab)
complexity
Naïve Bayes
(klaR)
Splines
(earth)
More Comprehensive List: http://caret.r-forge.r-project.org/modelList.html

GBM’s decision tree structure

Why GBM?
• Characteristics
• Competitive Performance
• Robust
• Loss functions
• Fast (relatively)
• Usages
• Quick modeling
• Variable selection
• Final-stage precision modeling

Competitive Performance
• Competitive with high-end algorithms such as
RandomForest
• Reliable performance
• Avoids nonsensical predictions
• Rare to produce worse predictions than simpler models
• Often in winning Kaggle solutions
• Cited within winning solution descriptions in numerous
competitions, including $3M competition
• Many of the highest ranked competitors use it frequently
• Used in 4 of 5 personal top 20 finishes

Robust
• Explicitly handles NAs
• Scaling/normalization is unnecessary
• Handles more factor levels than random forest (1024 vs
32)
• Handles perfectly correlated independent variables
• No [known] limit to number of independent variables

Loss Functions
• Gaussian: squared loss
• Laplace: absolute loss
• Bernoulli: logistic, for 0/1
• Huberized: hinge, for 0/1
• Adaboost: exponential loss, for 0/1
• Multinomial: more than one class (produces probability matrix)
• Quantile: flexible alpha (e.g. optimize for 2 StDev threshold)
• Poisson: Poisson distribution, for counts
• CoxPH: Cox proportional hazard, for right-censored
• Tdist: t-distribution loss
• Pairwise: rankings (e.g. search result scoring)
• Concordant pairs
• Mean reciprocal rank
• Mean average precision
• Normalized discounted cumulative gain

Drawbacks
• Several hyper-parameters to tune
• I typically use roughly the same parameters to start, unless I
suspect the data set might have peculiar characteristics
• For creating a final model, tuning several parameters is advisable
• Still has capacity to overfit
• Despite internal cross-validation, it is still particularly prone to
overfit ID-like columns (suggestion: withhold them)
• Can have trouble with highly noisy data
• Black box
• However, GBM package does provide tools to analyze the resulting
models

Deeper Analysis via Walkthrough
• Hyper-parameter explanations (some, not all)
• Quickly analyze performance
• Analyze influence of variables
• Peek under the hood…then follow a toy problem
For those not attending the presentation, the code at the back is run at this
point and discussed. The remaining four slides were mainly to supplement
the discussion of the code and comments, and there was not sufficient
time.

Same analysis with a simpler data set
Note that one can recreate the
predictions of this first tree by finding the
terminal node for any prediction and
using the Prediction value (final column
in data frame). Those values for all
desired trees, plus the initial value (mean
for this) is the prediction.
Matches predictions 1 & 3
Matches predictions 2,4 & 5

Same analysis with a simpler data set
Explanation
1 tree built.
Tree has one decision only, node 0.
Node 0 indicates it split the 3rd field (SplitVar:2), to where values below 1.5
(ordered values 0 & 1 which are a & b) went to node 1; values above
1.5 (2/3 = c/d) went to node 2; missing (none) go to node 3.
Node 1 (X3=A/B) is a terminal node (SplitVar -1) and it predicts the mean plus -0.925.
Node 2 (X3=C/D) is a terminal node and it predicts the mean plus 1.01.
Node 3 (none) is a terminal node and it predicts the mean plus 0, effectively.
Later saw that gbm1$initF will show the intercept, which in this case is the mean.

GBM predict: fit a GBM to data
• gbm(formula = formula(data),
• distribution = "bernoulli",
• n.trees = 100,
• interaction.depth = 1,
• n.minobsinnode = 10,
• shrinkage = 0.001,
• bag.fraction = 0.5,
• train.fraction = 1.0,
• cv.folds=0,
• weights,
• data = list(),
• var.monotone = NULL,
• keep.data = TRUE,
• verbose = "CV",
• class.stratify.cv=NULL,
• n.cores = NULL)

Effect of shrinkage & trees
Source: https://www.youtube.com/watch?v=IXZKgIsZRm0 (GBM explanation by SciKit author)

Code Dump
• The code has been copied from a text R script into PowerPoint, so
the format isn’t great, but it should look OK if copying and pasting
back out to a text file. If not, here it is on Github.
• The code shown uses a competition data set that is comparable to
real world data and uses a simple GBM to predict sale prices of
construction equipment at auction.
• A GBM model was fit against 100k rows with 45-50 variables in about
2-4 minutes during the presentation. It improves the RMSE of
prediction against the mean from ~24.5k to ~9.7k, when scored on
data the model had not seen (and future dates, so the 100k/50k splits
should be valid), with fairly stable train:test performance.
• After predictions are made and scored, some GBM utilities are used
to see which variables the model found most influential, see how the
top 2 variables are used (per factor for one; throughout a continuous
distribution for the other), and see interaction effects of specific
variable pairs.
• Note: GBM was used by my teammate and I to finish 12th out of 476
in this competition (albeit a complex ensemble of GBMs)

Code Dump: Page1
library(Metrics) ##load evaluation package
setwd("C:/Users/Mark_Landry/Documents/K/dozer/")
##Done in advance to speed up loading of data set
train<-read.csv("Train.csv")
## Kaggle data set: http://www.kaggle.com/c/bluebook-for-bulldozers/data
train$saleTransform<-strptime(train$saledate,"%m/%d/%Y %H:%M")
train<-train[order(train$saleTransform),]
save(train,file="rTrain.Rdata")
load("rTrain.Rdata")
xTrain<-train[(nrow(train)-149999):(nrow(train)-50000),5:ncol(train)]
xTest<-train[(nrow(train)-49999):nrow(train),5:ncol(train)]
yTrain<-train[(nrow(train)-149999):(nrow(train)-50000),2]
yTest<-train[(nrow(train)-49999):nrow(train),2]
dim(xTrain); dim(xTest)
sapply(xTrain,function(x) length(levels(x)))
## check levels; gbm is robust, but still has a limit of 1024 per factor; for initial model, remove
## after iterating through model, would want to go back and compress these factors to investigate
## their usefulness (or other information analysis)
xTrain$saledate<-NULL; xTest$saledate<-NULL
xTrain$fiModelDesc<-NULL; xTest$fiModelDesc<-NULL
xTrain$fiBaseModel<-NULL; xTest$fiBaseModel<-NULL
xTrain$saleTransform<-NULL; xTest$saleTransform<-NULL

Code Dump: Page2
library(gbm)
## Set up parameters to pass in; there are many more hyper-parameters available, but these are the most common to
control
GBM_NTREES = 400
## 400 trees in the model; can scale back later for predictions, if desired or overfitting is suspected
GBM_SHRINKAGE = 0.05
## shrinkage is a regularization parameter dictating how fast/aggressive the algorithm moves across
the loss gradient
## 0.05 is somewhat aggressive; default is 0.001, values below 0.1 tend to produce good results
## decreasing shrinkage generally improves results, but requires more trees, so the two
should be adjusted in tandem
GBM_DEPTH = 4
## depth 4 means each tree will evaluate four decisions;
## will always yield [3*depth + 1] nodes and [2*depth + 1] terminal nodes (depth 4 = 9)
## because each decision yields 3 nodes, but each decision will come from a prior node
GBM_MINOBS = 30
## regularization parameter to dictate how many observations must be present to yield a terminal node
## higher number means more conservative fit; 30 is fairly high, but good for exploratory fits; default is
10
## Fit model
g<-gbm.fit(x=xTrain,y=yTrain,distribution = "gaussian",n.trees = GBM_NTREES,shrinkage = GBM_SHRINKAGE,
interaction.depth = GBM_DEPTH,n.minobsinnode = GBM_MINOBS)
## gbm fit; provide all remaining independent variables in xTrain; provide targets as yTrain;
## gaussian distribution will optimize squared loss;

Code Dump: Page3
## get predictions; first on train set, then on unseen test data
tP1 <- predict.gbm(object = g,newdata = xTrain,GBM_NTREES)
hP1 <- predict.gbm(object = g,newdata = xTest,GBM_NTREES)
## compare model performance to default (overall mean)
rmse(yTrain,tP1) ## 9452.742 on data used for training
rmse(yTest,hP1) ## 9740.559 ~3% drop on unseen data; does not seem
to be overfit
rmse(yTest,mean(yTrain)) ## 24481.08 overall mean; cut error rate (from perfection) by 60%
## look at variables
summary(g) ## summary will plot and then show the relative influence of each variable to the entire GBM model (all trees)
## test dominant variable mean
library(sqldf)
trainProdClass<-as.data.frame(cbind(as.character(xTrain$fiProductClassDesc),yTrain))
testProdClass<-as.data.frame(cbind(as.character(xTest$fiProductClassDesc),yTest))
colnames(trainProdClass)<-c("fiProductClassDesc","y"); colnames(testProdClass)<-c("fiProductClassDesc","y")
ProdClassMeans<-sqldf("SELECT fiProductClassDesc,avg(y) avg, COUNT(*) n FROM trainProdClass GROUP BY
fiProductClassDesc")
ProdClassPredictions<-sqldf("SELECT case when n > 30 then avg ELSE 31348.63 end avg
FROM ProdClassMeans P LEFT JOIN testProdClass t ON t.fiProductClassDesc = P.fiProductClassDesc")
rmse(yTest,ProdClassPredictions$avg) ## 29082.64 ? peculiar result on the fiProductClassDesc means, which seemed
fairly stable and useful
##seems to say that the primary factor alone is not helpful; full tree needed

Code Dump: Page4
## Investigate actual GBM model
pretty.gbm.tree(g,1) ## show underlying model for the first decision tree
summary(xTrain[,10]) ## underlying model showed variable 9 to be first point in tree (9 with 0 index = 10th
column)
g$initF ## view what is effectively the "y intercept"
mean(yTrain) ## equivalence shows gaussian y intercept is the mean
t(g$c.splits[1][[1]]) ## show whether each factor level should go left or right
plot(g,10) ## plot fiProductClassDesc, the variable with the highest
rel.inf
plot(g,3) ## plot YearMade, continuous variable with 2nd highest
rel.inf
interact.gbm(g,xTrain,c(10,3))
## compute H statistic to
show interaction; integrates
interact.gbm(g,xTrain,c(10,3))
## example of uninteresting
interaction

Selected References
• CRAN
• Documentation
• vignette
• Algorithm publications:
• Greedy function approximation: A gradient boosting machine
Friedman 2/99
• Stochastic Gradient Boosting; Friedman 3/99
• Overviews
• Gradient boosting machines, a tutorial: Frontiers (4/13)
• Wikipedia (pretty good article, really)
• Video of author of GBM in Python: Gradient Boosted Regression
Trees in scikit-learn
• Very helpful, but the implementation is not decision “stumps” in R, so
some things are different in R (e.g. number of trees need not be so high)

GBM package in r

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