Introduction to XGboost

Introduction to XGBOOST

School of Computer Sicience and Engineering

Shuai Zhang, UNSW

1. Introduction

2. Boosted Tree

3. Tree Ensemble

4. Additive Training

5. Split Algorithm School of Computer Sicience and Engineering

1 Introduction• What Xgboost can do ?


Binary Classification

Multiclass Classification

Regression Learning to Rank

By 02. March.2017

Scalable, Portable and Distributed Gradient Boosting (GBDT, GBRT or GBM) Library

Support Language• Python• R• Java• Scala• C++ and more

Support Platform• Runs on single machine, • Hadoop• Spark• Flink• DataFlow

2 Boosted Tree• Variants:• GBDT: gradient boosted decision tree• GBRT: gradient boosted regression tree• MART: Multiple Additive Regression Trees• LambdaMART, for ranking task• ...


2.1 CART• CART: Classification and Regression Tree

• Classification• Three Classes• Two Variables


2.1 CARTPrediction• predicting price of 1993-model cars.• standardized (zero mean,unit variance)


partition

2.1 CART• Information Gain • Gain Ratio• Gini Index

• Pruning: prevent overfitting


Which variable to use for division

2.2 CART• Input: Age, gender, occupation • Goal: Does the person like computer games


3 Tree Ensemble• What is Tree Ensemble ?• Single Tree is not powerful enough

• Benifts of Tree Ensemble ?• Very widely used• Invariant to scaling of inputs• Learn higher order interaction between features• Scalable


Boosted Tree

Random Forest

Tree Ensemble

3 Tree Ensemble


Prediction of is sum of scores predicted by each of the tree

3 Tree Ensemble-Elements of Supervised Learning • Linear model


Optimizing training loss encourages predictive models

Opyimizing regularization encourages simple models

3 Tree Ensemble • Assuming we have k trees


• Parameters• Including structure of each tree, and the score in the leaf• Or simply use function as parameters

• Instead learning weights in R^d, we are learning functions ( trees)

3 Tree Ensemble • How can we learn functions?


The height in each segment

Splitting positions

• Training loss: How will the function fit on the points?

• Regularization: How do we define complexity of the function?

3 Tree Ensemble


Regularization

Number of splitting pointsL2 norm of the leaf weights

Training loss:error =

3 Tree Ensemble • We define tree by a vector of scores in leafs, and a leaf index mapping

function that maps an instance to a leaf


3 Tree Ensemble • Objective:

• Definiation of Complexity


4 Addictive Training (Boosting)• We can not use methods such as SGD, to find f ( since thet are trees,

instead of just numerical vectors)

• Start from constant prediction, add a new function each time.


4 Addictive Training (Boosting) • How do we decide which f to add ?

• The prediction at round t is

• Consider square loss


4 Addictive Training (Boosting) • Taylor expansion of the objective

• Objective after expansion


4 Addictive Training (Boosting) • Our new goal, with constants removed

• Benifits


4 Addictive Training (Boosting) • Define the instance set in leaf j as

• Regroup the objective by each leaf

• This is sum of T independent quadratic functions• Two facts about single variable quadratic function


4 Addictive Training (Boosting) • Let us define

• Results


There can be infinite possible tree structures

4 Addictive Training (Boosting) • Greedy Learning , we grow the tree greedily


5 Spliting algorithm• Efficeint finding of the best split

• What is the gain of a split rule xj < a ? say xj is age


All we need is sume of g and h in each side, and calculate

• Left to right linear scan over sorted instance is enough to decide the best split

5 Spliting algorithm


References• http://www.52cs.org/?p=429• http://www.stat.cmu.edu/~cshalizi/350-2006/lecture-10.pdf• http://www.sigkdd.org/node/362• http://homes.cs.washington.edu/~tqchen/pdf/BoostedTree.pdf• http://www.stat.wisc.edu/~loh/treeprogs/guide/wires11.pdf• https://github.com/dmlc/xgboost/blob/master/demo/README.md• http://datascience.la/xgboost-workshop-and-meetup-talk-with-tianqi-chen/• http://xgboost.readthedocs.io/en/latest/model.html• http://machinelearningmastery.com/gentle-introduction-xgboost-applied-machine-

learning/


Suplementary• Tree model, works very well on tabular data, easy to use,

and interpret and control

• It can not extrapolate

• Deep Forest: Towards An Alternative to Deep Neural Networks, Zhi-Hua Zhou, Ji Feng, Nanjing University• Submitted on 28 Feb 2017• Comparable performance and easy to train (less parameters)


Thank you!


Introduction to XGboost

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