e/pi separation in CalDet and nue identification in MDC
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e/pi separation in CalDet and nue identification in MDC
T.J. Yang
Stanford University
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e/pi separation
Thanks to great help from Patricia Vahle and helpful discussion with Adam Para
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What do an electron and a pion look like in CalDet? P=1GeV/c
e
pi
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What do an electron and a pion look like in CalDet? P=2GeV/c
e
pi
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What do an electron and a pion look like in CalDet? P=3GeV/c
e
pi
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Information from CalDet data
EM shower is more compact than hadronic shower. And most of the EM showers have the same pattern regardless of energy: 4-5 planes long and 1-2 strip(s) wide.EM shower develops much faster than hadronic shower.Pions usually achieve the maximum energy lost later than electrons.
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Fractions of energy deposited in 1,2,3,4,5,6 consecutive plane(s) with the highest ph
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Fractions of energy deposited in 2,4,6,8,10,12 counters with the highest ph
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Fraction of energy in a narrow road
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Ratio of energy deposited in the first (second) plane to the second (third) plane
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Shower_max
Position (with respect to the first plane) of the plane with the highest energy lost in the event.
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Summary of discriminating variables (reference:NuMI-L-284)
Longitudinal features:Track lengthFractions of energy deposited in 1,2,3,4,5,6 consecutive plane(s) with the highest p.h.Ratio of energy deposited in plane 0 to plane 1Position of the maximum energy lost
Lateral features:Fraction of energy deposited in a narrow road
Others:Fractions of energy deposited in 2,4,6,8,10,12 strips with the highest p.h.
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Run numbers used for CalDet e/pi separation analysis
P(GeV/c) Run Numbers
1.0 40622,40624,40626
2.0 40715,40717,40722,40724
3.0 40924,40495,50497,50456
4.0 50531,50553
5.0 50533,50535,50555,50557,50559
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Results P(GeV/c) e pi/muon
1.0
before cuts 10613 59098
after cuts 2052 58
eff. & rej. 0.193 9.8e-4
2.0
before cuts 7444 176584
after cuts 781 20
eff. & rej. 0.105 1.1e-4
3.0
before cuts 27896 12555
after cuts 3376 0
eff. & rej. 0.121 0
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Results (continued)
P(1GeV/c) e pi/muon
4.0
before cuts 15913 46442
after cuts 2820 17
eff. & rej. 0.177 3.6e-4
5.0
before cuts 31166 128139
after cuts 6977 76
eff. & rej. 0.224 5.9e-4
Hadron rejection ~1e-4 – 1e-3 for e~10-20%
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nue identification
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Files used for nue analysis
beam files: f24100001_0000.sntp.R1.9.root
-f24100020_0000.sntp.R1.9.root (all)
nue files: f24110001_0000.sntp.R1.9.root – f24110009_0000.sntp.R1.9.root (all)
nutau files: f24130001_0000.sntp.R1.9.root – f24130020_0000.sntp.R1.9.root (half)
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Statistics and parameters
numu->nue: ~26,000 NC: ~33,000 CC: ~66,000
|Ue3|2 = 0.01
m2 = 2.5e-3eV2
assume a 2.5-yr run
pot/yr = 3.7e20
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Strategy
Making cuts on the variables from SR: total p.e. , track range, shower range and total number of strips
Calculating the same variables as I used in the CalDet e/pi separation analysis
Using neural network and boosted decision trees to get the optimal results
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Total pe (ph.pe)
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Track range (trk.ds)
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Shower range (shw.plane.n)
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Total number of strips (nstrip)
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Cuts on SR variables
200<ph.pe<700
trk.ds<0.9
5<shw.plane.n<14
14<nstrip<56
signal NC CC bnue Nutau FOM
all 28.6 1294 3371 68.4 33.9 0.41
survived 16.9 292 133 8.3 9.5 0.80
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Calculating variablesFractions of energy deposited in 1,2,3,4,5,6 consecutive plane(s) with the highest phFractions of energy which are deposited in 2,4,6,8,10,12 counters with the highest phFraction of energy in a narrow road
Problems:Distributions don’t look quite different between signal and backgroundsAfter the preliminary cuts, the distributions look almost the same
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Fraction of energy deposited in 3 consecutive planes
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Fraction of energy deposited in 3 counters with the highest ph
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Fraction of energy in a narrow road
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The use of neural network
Input variables: fract_1_cons, fract_2_cons, fract_3_cons, fract_4_cons, fract_5_cons, fract_6_cons, fract_1_count, fract_2_count, fract_3_count, fract_4_count, fract_6_count, fract_8_count, fract_ct, fract_ct_2, rms1u, rms1v
Structure: 17:14:1
Tried two different packages: Jetnet and TMultiLayerPerceptron(MLP) in ROOT
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Jetnet (training)
signal NC CC bnue Nutau FOM
8.8 58.4 19.4 4.2 3.0 0.95
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Jetnet (testing)
signal NC CC bnue Nutau FOM
8.9 59.9 20.9 5.8 3.4 0.94
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MLP (training)
signal NC CC bnue Nutau FOM
7.7 47.7 15.3 3.4 2.7 0.94
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MLP (testing)
signal NC CC bnue Nutau FOM
7.8 45.5 14.5 5.0 2.8 0.95
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Boosted Decision Trees
Jake Klamka
University of Toronto
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Boosted Decision TreesIn the past several years there has been a “revolution in the field of machine learning inspired by the extension of decision trees by boosting.” (J. Friedman -- PHYSTAT2003)BOOSTING: A procedure that combines the outputs of many “weak” classifiers to produce a powerful “committee”.Multiple decision trees are created using weighted versions of the training dataset. Final event classification is based on a linear combination of individual decision trees.
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Rough Outline of a Boosting Algorithm:
1. Weight all events in the data sample equally.
2. ** LOOP **:a) Train new decision tree with current event weig
hts.
b) Re-weight events, giving higher weight to events that were misclassified in (a).
3. Take the linear combination of all decision trees with most accurate decision trees given more weight.
AdaBoost.M1 (Freund and Schapire 1996)
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Software: See5 (C5)
Commercial decision tree software created by Ross Quinlan.New version allows for boosting. Previous version known as C4.5.Pros: 10 days free trial, easy to install and setup, very fast classification.Cons: Exact boosting algorithm used by See5 is unknown (proprietary), not easily customizable.
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Results with decision trees(no boosting)
no boosting, cost 1:1
no boosting, cost 1:2
signal NC CC bnue Nutau FOM
Training 9.3 57.1 21.2 3.9 2.7 1.00
Testing 9.0 67.7 25.1 5.6 3.3 0.89
signal NC CC bnue Nutau FOM
Training 4.7 13.6 3.9 2.0 0.8 1.04
Testing 4.5 15.1 5.0 2.9 1.6 0.89
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Results with boosted decision trees
boosting: 3 trials, cost 1:1
boosting: 3 trials, cost 1:2
signal NC CC bnue Nutau FOM
Training 9.0 56.4 19.3 3.8 2.7 1.00
Testing 9.0 64.3 22.5 5.3 3.2 0.92
signal NC CC bnue Nutau FOM
Training 4.3 10.8 2.7 1.9 0.9 1.06
Testing 4.3 13.6 3.2 3.0 1.2 0.94
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BOOSTING in NEUTRINO PHYSICS:The MiniBooNE collaboration is using boosted decision trees and has announced 20% to 80% improvements over their best results with neural networks. Their analysis is described in a recent preprint and their code is available online. (physics/0408124)
FUTURE PROSPECTS:Customized boosted decision tree code (use MiniBooNE code as prototype?)Try different boosting algorithms.Boosting algorithm can be applied to any classification technique, not just decision trees… “Boosted Neural Networks” may offer even better results.
More information and links:http://home.fnal.gov/~jklamka/
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Summary
signal NC CC bnue Nutau FOM
all 28.6 1294 3371 68.4 33.9 0.41
pre-sel 16.9 292 133 8.3 9.5 0.80
Jetnet 8.9 59.9 20.9 5.8 3.4 0.94
MLP 7.8 45.5 14.5 5.0 2.8 0.95
BDT 4.3 13.6 3.2 3.0 1.2 0.94
714 8.5 27.2 3.9 5.6 3.0 1.35
Ely 9.5 68.4 9.2 10.3 4.4 0.99
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Conclusion
For the CalDet e/pi separation study, we got the hadron rejection ~1e-4 – 1e-3 for e~10-20%
For the nue identification in MDC, we got FOM ~0.94
We will try to understand several issues and modify the variables to improve the FOM.