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WW and WZ Analysis

发布时间:2013-11-30 16:01:32  

WW and WZ Analysis Based on Boosted Decision Trees

Hai-Jun YangUniversity of Michigan(contributed from Tiesheng Dai, Alan Wilson, Zhengguo Zhao, Bing Zhou)

ATLAS Trigger and Physics MeetingCERN, June 4-7, 2007

Outline

?Boosted Decision Trees (BDT)

?WW ?emX analysis based on BDT

?WZ ?ln ll analysis based on BDT

?BDT Applications and Free Softwares?Summary and Future Plan

June 4-7, 2007H.J. Yang -BDT for WW/WZ2

Boosted Decision Trees

Ref: B.P. Roe, H.J. Yang, J. Zhu, Y. Liu, I. Stancu, G. McGregor, ”Boosted decision trees as an alternative to

artificial neural networks for particle identification”, physics/0408124, NIM A543 (2005) 577-584.

June 4-7, 2007H.J. Yang -BDT for WW/WZ3

Weak ?

Powerful Classifier

?The advantage of using boosted decision

trees is that it combines many decision trees,

“weak” classifiers, to make a powerful classifier.

The performance of boosted decision trees is stable after a few hundred tree iterations.

?Boosted decision trees focus on the

misclassified events which usually have high

weights after hundreds of tree iterations. An

individual tree has a very weak discriminating

power; the weighted misclassified event rate

errmis about 0.4-0.45.

Ref1: H.J.Yang, B.P. Roe, J. Zhu, “Studies of Boosted Decision Trees for MiniBooNE Particle Identification”, physics/0508045, Nucl. Instum. & Meth. A 555(2005) 370-385.

Ref2: H.J. Yang, B. P. Roe, J. Zhu, " Studies of Stability and Robustness for Artificial Neural Networks and Boosted Decision Trees ", physics/0610276, Nucl. Instrum. & Meth. A574 (2007) 342-349.June 4-7, 2007H.J. Yang -BDT for WW/WZ4

Diboson analysis –Physics Motivation

WW Analysis

?W+W-?e+m-X, m+e-

X (CSC 11 Dataset)June 4-7, 2007H.J. Yang -BDT for WW/WZ6

WW analysis –datasets after precuts

Breakdown of MC samples for WW analysis after precuts

Event Selection for WW-> emXEvent Pre-selection

?At least one electron + one muon with Pt>10 GeV ?Missing Et > 15 GeV

?Signal efficiency is 39%

Final Selection

?Simple cutsbased on Rome sample studies?Boosted Decision Treeswith 15 input variables

June 4-7, 2007H.J. Yang -BDT for WW/WZ9

Select of WW -> em / me + Missing ETSimple cuts used in Rome studies

?Two isolated di-lepton PT> 20 GeV;

at least one PT > 25 GeV

?Missing ET > 30 GeV

?Mem > 30 GeV; Veto MZ (ee, mm)

?ET (had)=|Sum (lT)+ missing ET| < 60 GeV, Sum Et(jet) < 120 GeV;

?Number of jets < 2

?PT(l+l-) > 20 GeV

?Vertexbetween two leptons: DZ < 1mm, DA < 0.1 mmFor 1 fb-1, 189 signal and 168 backgroundZZ

June 4-7, 2007H.J. Yang -BDT for WW/WZ10

BDT Training Procedure?1ststep: use all 48 variables for BDT training, rank variables based on their gini index contributions or how often they were used as tree splitters.

?2ndstep: select 15 powerful variables?3rdstep: re-train BDT based on 15 selected good variables

June 4-7, 2007H.J. Yang -BDT for WW/WZ11

Variables after pre-selection used in BDTJune 4-7, 2007H.J. Yang -BDT for WW/WZ

12

Variable distributions after pre-selection

signalbackground

June 4-7, 2007H.J. Yang -BDT for WW/WZ13

Variable distributions after pre-selectionsignal

background

June 4-7, 2007H.J. Yang -BDT for WW/WZ14

Variable distributions after pre-selectionbackgroundsignal

June 4-7, 2007H.J. Yang -BDT for WW/WZ15

Variable distributions after pre-selectionsignal

background

June 4-7, 2007H.J. Yang -BDT for WW/WZ16

BDT Training Tips

?Epsilon-Boost (epsilon=0.01)

?exp(2*0.01) = 1.0207,I = 1 if training events are misclassified, otherwise I = 0?1000 tree iterations, 20 leaves/tree

?The MC samples are split into two halves, one for training, the other for test; then reverse the training and testing samples. The average of testing results

are regarded as the final results.

June 4-7, 2007H.J. Yang -BDT for WW/WZ17

Boosted Decision Trees output

backgroundsignal

June 4-7, 2007H.J. Yang -BDT for WW/WZ18

Boosted Decision Trees output

backgroundsignal

June 4-7, 2007H.J. Yang -BDT for WW/WZ19

-1Signal (WW) and Backgrounds for 1 fb

June 4-7, 2007H.J. Yang -BDT for WW/WZ

20

MC breakdown with all cuts for 1 fb-1June 4-7, 2007H.J. Yang -BDT for WW/WZ

21

Summary for WW Analysis?Background event sample compared to Rome sample increased by a factor of ~10; compared to post Romesample increased by a factor of ~2.

?Simple Cuts: S/B ~ 1.1

?Boosted Decision Trees with 15 variables: S/B = 5.9?The major backgrounds are W-> mn(~50%), ttbar, WZ?W-> mn(event weight = 11.02)needs more statistics(x5)if possible.

June 4-7, 2007H.J. Yang -BDT for WW/WZ22

WZ?lnllanalyis

?Physics Goals

–Test of SM couplings

–Search for anomalous triple gauge boson couplings (TGCs) that could indicate new physics

–WZ final state would be a background to SUSY and technicolor signals.

?WZ event selection by two methods–Simple cuts

–Boosted Decision Trees

June 4-7, 2007H.J. Yang -BDT for WW/WZ23

WZ selection –Major backgrounds?Major backgrounds–pp ?t tbar?Pair of leptons fall in Z mass window?Jet produces lepton signal

?Fake missing ET?Jet produces third lepton signal

?Fake missing ETand third lepton

?

Lose a lepton–pp ?Z+jetsq’–pp ?Z/γ?ee, mm–pp ?ZZ?4 leptons

June 4-7, 2007H.J. Yang -BDT for WW/WZ24

Pre-selection for WZ analysis?Pre-selection–Identify leptons and require?pT > 5GeV, one with pT > 20GeV–Require missing ET > 15GeV–Find e+e-or m+m-pair with inv. mass closest to Z peak?must be within 91.18 ?20 GeV. –Third leptonwith pT > 15GeV and 10 < MT < 400GeV?Eff(W+Z) = 25.8%, Eff(W-Z) = 29.3%

?Compute additional variables(invariant masses, sums of jets, track isolations …), 67 variables in total

June 4-7, 2007H.J. Yang -BDT for WW/WZ25

WZ analysis –

datasets after precutsJune 4-7, 2007H.J. Yang -BDT for WW/WZ26

Final selection –simple cutsBased on pre-selected events, make further cuts–Lepton selection?????Isolation: leptons have tracks totaling < 8 GeV within DR<0.4 Z leptons have pT> 6 GeVW lepton pT> 25 GeVE ~ p for electrons: 0.7 < E/p < 1.3Hollow cone around leptons has little energy: [ET(DR<0.4) –ET(DR<0.2)] / ET< 0.1––––Leptons separated by DR > 0.2Exactly 3 leptonsMissing ET> 25 GeVFew jets??

?–Leptonic energy balanceNo more than one jet with ET> 30 GeV in |h| < 3Scalar sum of jet ET< 200 GeV

| Vector sum of leptons and missing ET| < 100 GeV–Z mass window: ?9 GeV for electrons and ?12 GeV for muons–W mass window: 40 GeV < MT(W) < 120 GeV

June 4-7, 2007H.J. Yang -BDT for WW/WZ27

Simple cuts –results (Alan)

June 4-7, 2007H.J. Yang -BDT for WW/WZ28

WZ –Boosted Decision Trees?Select 22 powerful variables out of 67 total available variables for BDT training.?Rank 22 variables based on the gini index contributions and the number of times used as tree splitters.?M(Z) and MT(W) are ranked highest.

June 4-7, 2007H.J. Yang -BDT for WW/WZ29

Input Variables(1-16)

June 4-7, 2007H.J. Yang -BDT for WW/WZ30

Input Variables(17-22)

June 4-7, 2007H.J. Yang -BDT for WW/WZ31

BDT Training Tips

?In the original BDT training program, all training events are set to have same weights in the beginning (the first tree). It works fine if all MC processes are produced based on their production rates.

?Our MCs are produced separately, the event weights vary from various backgrounds. e.g. assuming 1 fb-1wt (ZZ_llll) = 0.0024, wt (ttbar) = 0.7, wt(DY) = 1.8?We made two BDT trainings. One based on equal event weights for all training MC; the other based on their correct event weights for the 1sttree training.?BDT performance with correct event weights for training works better than that with equal weights.June 4-7, 2007H.J. Yang -BDT for WW/WZ32

BDT Tuning?

BDT with 22 and 67 variables have comparable performance?ANN and BDT training with correct event weights works significantlybetter than that with equal event weights

June 4-7, 2007H.J. Yang -BDT for WW/WZ33

ANN/BDT Tuning

June 4-7, 2007H.J. Yang -BDT for WW/WZ34

ANN/BDT Comparison

?Event weight training technique works better than equal weight training for both ANN(x5-7)and BDT(x6-10)

?BDT is better than ANNby reducing more background(x1.5-2)?Anote to describe the event weight training technique in detail

will be available shortly.

June 4-7, 2007H.J. Yang -BDT for WW/WZ35

Eff_bkgd/RMS vs Training EventsJune 4-7, 2007H.J. Yang -BDT for WW/WZ36

WZ –Boosted Decision TreesFor 1 fb-1 , BDT Results

?Nsignal= 150 to 60

?Significance (Nsignal/√Nbkg) ~ 40

?BDT, S/BG ~ 10 to 24

?Simple cuts

S/BG ~ 2-2.5

June 4-7, 2007H.J. Yang -BDT for WW/WZ37

ZW ?eee, eem, mme,

mmmJune 4-7, 2007H.J. Yang -BDT for WW/WZ38

MC breakdown with all cuts for 1 fb-1

June 4-7, 2007H.J. Yang -BDT for WW/WZ39

Summary for WZ Analysis?Simple CutsS/BG = 2 ~ 2.5

?Boosted Decision Trees with 22 variablesS/BG = 10 ~ 24

?The major backgrounds are (BDT>=200):ZZ -> 4ZJet -> 2l (47.8%)

ttbar (17.4%)mX (15.5%)

Drell-Yan -> 2l (12.4%)

June 4-7, 2007H.J. Yang -BDT for WW/WZ40

Applications of BDT in HEP?Boosted Decision Trees (BDT) has been applied for some major HEP experiments in the past few years.

–MiniBooNE data analysis (BDT reject 20-80% more background than ANN)?physics/0408124 (NIM A543, p577), physics/0508045 (NIM A555, p370), ?physics/0610276(NIM A574, p342), physics/0611267?“ A search for electron neutrino appearance at dm^2 ~ 1 eV^2 Scale”, hep-ex/0704150 (submitted to PRL)–ATLAS Di-Boson analysis, ww, wz, wg, zg–ATLAS SUSY analysis –hep-ph/0605106 (JHEP060740)–LHC B-tagging, physics/0702041, for 60% b-tagging eff, BDT has 35% more light jet rejection than that of ANN.–BaBar data analysis?“Measurement of CP-violating asymmetries in the B0->K+K-K0 dalitz plot”, hep-ex/0607112?physics/0507143, physics/0507157–D0 data analysis

–More are underway …

June 4-7, 2007?hep-ph/0606257, Fermilab-thesis-2006-15, ?“Evidence of single top quarks and first direct measurement of |Vtb|”, hep-ex/0612052 (to appear in PRL), BDT better than ANN, matrix-element likelihoodH.J. Yang -BDT for WW/WZ41

BDT Free Softwares

??TMVA toolkit, CERN Root V5.14/00June 4-7, 2007H.J. Yang -BDT for WW/WZ42

Summary and Future Plan?WW and WZ analysis results with Simple cuts and BDT are presented?BDT works better than ANN, it is a very powerful and promising data analysis tool?Redo WW/WZ analysis with CSC12 MC?BDT will be applied for WW->2mX, H->ZZ,WW and tautau etc.

June 4-7, 2007H.J. Yang -BDT for WW/WZ43

BACKUP SLIDESBoosted Decision Treesfor

June 4-7, 2007H.J. Yang -BDT for WW/WZ44

Decision Trees & Boosting Algorithms?Decision Trees have been available about two decades, they are known to be powerful but unstable, i.e., a small change in the training sample can give a large change in the tree and the results.

Ref: L. Breiman, J.H. Friedman, R.A. Olshen, C.J.Stone, “Classification and Regression Trees”, Wadsworth, 1984.

?The boosting algorithm (AdaBoost) is a procedure that combines many “weak”classifiers to achieve a final powerful classifier.

Ref: Y. Freund, R.E. Schapire, “Experiments with a new boosting algorithm”, Proceedings of COLT, ACM Press, New York, 1996, pp. 209-217.

?Boosting algorithms can be applied to any classification method. Here, it is applied to decision trees, so called “Boosted Decision Trees”, for the MiniBooNE particle identification.

* Hai-Jun Yang, Byron P. Roe, Ji Zhu, " Studies of boosted decision trees for MiniBooNE particle identification", physics/0508045, NIM A 555:370,2005

* Byron P. Roe, Hai-Jun Yang, Ji Zhu, Yong Liu, Ion Stancu, Gordon McGregor," Boosted decision trees as an alternative to artificial neural networks for particle identification", NIM A 543:577,2005

* Hai-Jun Yang, Byron P. Roe, Ji Zhu, “Studies of Stability and Robustness of Artificial Neural Networks and Boosted Decision Trees”, NIM A574:342,2007

June 4-7, 2007H.J. Yang -BDT for WW/WZ45

June 4-7, 2007H.J. Yang -BDT for WW/WZ46

Criterion for “Best”Tree Split?Purity, P,is the fraction of the weight of a node (leaf) due to signal events.

?Gini Index: Note that Gini index is 0 for all signal or all background.

?The criterion is to minimize Gini_left_node+ Gini_right_node

.

June 4-7, 2007H.J. Yang -BDT for WW/WZ47

Criterion for Next Node to Split?Pick the node to maximize the change in Gini index.Criterion =

Giniparent_node–Giniright_child_node–Ginileft_child_node

?We can use Gini index contribution of tree split variables to sort the importance of input variables.

?We can also sort the importance of input variables based on how often they are used as tree splitters.

June 4-7, 2007H.J. Yang -BDT for WW/WZ48

Signal and Background Leaves?Assume an equal weight of signal and background training events.

?If event weight of signal is larger than ?of the total weight of a leaf, it is a signal leaf; otherwise it is a background leaf.

?Signal events on a background leaf or background events on a signal leaf are misclassified events.

June 4-7, 2007H.J. Yang -BDT for WW/WZ49

How to Boost Decision Trees ??For each tree iteration, same set of training events are

used but the weights of misclassified events in previous iteration are increased (boosted). Events with higher weights have larger impact on Gini index values and Criterion values. The use of boosted weights for

misclassified events makes them possible to be correctly classified in succeeding trees.

?Typically, one generates several hundred to thousand trees

until the performance is optimal.

?The score of a testing event is assigned as follows: If it

lands on a signal leaf, it is given a score of 1; otherwise -

1. The sum of scores (weighted) from all trees is the final score of the event.

June 4-7, 2007H.J. Yang -BDT for WW/WZ50

Weak ?

Powerful Classifier

?The advantage of using boosted

decision trees is that it combines

many decision trees, “weak”

classifiers, to make a powerful

classifier. The performance of BDT

is stable after few hundred tree

iterations.

?Boosted decision trees focus on the

misclassified events which usually have

high weights after hundreds of tree

iterations. An individual tree has a very

weak discriminating power; the

weighted misclassified event rate errmis about 0.4-0.45.

June 4-7, 2007H.J. Yang -BDT for WW/WZ51

Two Boosting Algorithms

June 4-7, 2007H.J. Yang -BDT for WW/WZ52

Example

?AdaBoost: the weight of misclassified events is increased by

–error rate=0.1 and b= 0.5, am= 1.1, exp(1.1) = 3

–error rate=0.4 and b= 0.5, am= 0.203, exp(0.203) = 1.225–Weight of a misclassified event is multiplied by a large factor which depends on the error rate.

?e-boost: the weight of misclassified events is increased by

–If e= 0.01, exp(2*0.01) = 1.02

–If e= 0.04, exp(2*0.04) = 1.083

–It changes event weight a little at a time.

?AdaBoost converges faster than e-boost. However, the performance of AdaBoost and e-boost are comparable with sufficient tree iterations.

June 4-7, 2007H.J. Yang -BDT for WW/WZ53

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