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Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 1
Backups
Jens Zimmermannzimmerm@mppmu.mpg.de
Max-Planck-Institut für Physik, München
Forschungszentrum Jülich GmbH
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 2
Check Behaviour
determine efficiency by theprinciple of orthogonal triggers
Determine efficiencyin dependence of
important quantities
DVCS dataset
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 3
k-Nearest-Neighbour
0 1 2 3 4 5 6 x10# formulas
# s
lide
s
0
1
2
3
4
5
6 x
10
k=1out=
k=2out=
k=3out=
k=4out=
k=5out=
For every evaluation position the distances to eachtraining position need to be determined!
Regularization:Parameter k
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 4
Maximum Likelihood / Naive Bayes
0 2 4 6 x10 0 2 4 6 x10
# formulas # slides
31 32
24.05
3
5
2Thp
04.05
1
5
1Expp
out=
Correlation gets lost completely by projection! Regularization:Binning
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 5
Linear Discriminant Analysis
slides
formulasout
021.0
012.03.0
(-0.49,0.87)
out=0.0
out=1.0
out=0.5
YAAAγ TT 1)(ˆ
Only one separating hyperplaneis usually not enough!
Can we combine two or more?
nkvxxy kdkdkk 1,1,10 Fisher
dnn
d
xx
xx
A
,1,
,11,1
1
1
AγY
0 1 2 3 4 5 6 x10# formulas
# s
lide
s
0
1
2
3
4
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6 x
10
1930
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 6
Neural Networks
aeaσ
1
1)(
0 1 2 3 4 5 6 x10
0
1
2
3
4
5
6 x
10
-50
+0.1+1.1 -1.1
+20
+0.2
+3.6 +3.6
-1.8
# formulas # slides
sxwσy ii 0
1
Construct NN with two separating hyperplanes:Train NN with two hidden neurons (gradient descent):
N
iii xouty
NE
1
2)(1
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 7
NN Training
N
iii xouty
NE
1
2)(1
8 hidden neurons = 8 separating lines
Test-Error
Train-Error
signal
background
Training Epochs
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 8
Support Vector Machines
Separating hyperplane with maximum distance to each datapoint: Maximum margin classifier
Found by setting up condition for correct classficationand minimizing which leads to the Lagrangian
1)( bxwy ii
2
w
1)(2
1 2 bxwyαwL iii
Necessary condition for a minimum is
So the output becomes
iii xyαw
bxxyαout iii sgn
Only linear separation?
The mapping to feature spaceis hidden in a kernel
FRd :)()(),( yxyxK
No! Replace dot products: )()( yxyx
KKT: only SV have 0iα
Non-separable case: iξCww
22
2
1
2
1
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 9
Bagging – Procedure
Training eventsDraw with replacement
Draw with replacementDraw with replacement
Resampled events 1
Resampled events 2
Resampled events n
Train
Train
Train
Classifier1
Classifier2
Classifiern
Combine tofinal decision
• majority voting• (weighted) averaging
Around 63% oforiginal events,
rest are replications
Bootstrap aggregating
Aim is to create strong classifiers which are as independent as possible.
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 10
Random Forests
Modification:At each node of the tree:Search only through arandomly selected subsetof all features
Tree, Randomness, Combination
RF
Use Bagging on this classifier
1 – 2,1 2 – 2,1 1 – 1,2
Training:
Testing/Evaluation:
final output =
final output =
Basis:Decision Tree (CART)without pruning
Create3 trees
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 11
Boosting – Procedure
Training eventsnormal weights
Train Classifier1
Raise weights ofmisclassified events Training events
weight config 1
TrainClassifier2
Raise weights ofmisclassified eventsTraining events
weight config 2
Train Classifiern
i i iE out true
1
1 N
i ii
E E wN
1 E
E
iEi iw w
Weight classifiers withtheir performance andcombine to final decision
Misclassified eventsget higher weights,are learned better.
Boosting tries to equalizemisclassification ratesfor each event.
?
!
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 12
Theory of Communication: Minimum Description Length Principle
)()|()()()|( HPHDPDHPDPDHP
)(
)|()()|(
DP
HDPHPDHP
)|()( maximize HDPHP)|(log)( log maximize HDPHP
Bayes
Hypothesis H and Data D
)|( maximize DHPOur hypothesis should have the maximum probability given the data:
)(log)( XPXI Shannon
)|()( minimize HDIHI MDLP Rissanen
18th century
1948
1990
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 13
L2 Neural Network Trigger
L1 2.3 µs
L2 20 µs
L4 100 ms
10 MHz
500 Hz
50 Hz
10 Hz
DVCS, J/Psi µµ, D*, DiJetCC, J/Psi ee TC
Trigger Scheme
H1 at HERA ep Collider, DESY
„L2NN“
new
TE L1ST Physics
*00 78 Charged Current old
01 68 Phi K+K-
02 52,54 J/Psi ee
03 83 DiJet
04 54 J/Psi µµ
05 32 D* untagged
06 40 Spacal back2back
07 78 Charged Current
08 33 J/Psi ee TC (1999)
09 41 DVCS
10 83 D* tagged
*11 33 J/Psi ee TC (2004)
12 15 J/Psi µµ inelastic
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 14
L2NN Rates and Efficiencies
Last daybefore
shutdownS83 DiJets
des=50%rej=50%
S32 D*des=94%rej=90%
S78 CCdes=58%rej=60%
S41 DVCSdes=80%rej=80%
S83 D*des=43%rej=50%
S33 J/Psides=94%rej=90%
S15 J/Psides=30%rej=30%
All measuredrate-reductionsmatch design.
No wrong prediction for efficiency found.
S83 DiJetsS32 D*S78 CCS41 DVCSS83 D*S33 J/Psi eeS15 J/Psi µµ
95%58%
100%97%95%
>95%96%
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 15
Performance Measurement - Classification
Eff@Rej = xx%Rej@Eff = xx%
0 output 1
signal
background
Misclassification =200%-Eff-Rej
Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 16
Performance Measurement - Regression
=y-out(x)
²=<>²+²
N
iii xouty
NE
1
2)(1
2
1
( )1 Ni i
i i
y out xE
N y
22 2
i i
i i
m y out x
s y out x m
0
5
10
15
20
25
-15.0 -7.5 0 7.5 15.0
=y-out(x)
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