1. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen1 Backups Jens Zimmermann zimmerm@mppmu.mpg.de Max-Planck-Institut für Physik, München Forschungszentrum Jülich GmbH

2. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen2 Check Behaviour determine efficiency by the principle of orthogonal triggers Determine efficiency in dependence of important quantities DVCS dataset

3. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen3 k-Nearest-Neighbour 0 1 2 3 4 5 6 x10 # formulas # slides 0 1 2 3 4 5 6 x10 k=1 out= k=2 out= k=3 out= k=4 out= k=5 out= For every evaluation position the distances to each training position need to be determined! Regularization: Parameter k

4. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen4 Maximum Likelihood / Naive Bayes 0 2 4 6 x10 # formulas# slides 3132 out= Correlation gets lost completely by projection! Regularization: Binning

5. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen5 Linear Discriminant Analysis (-0.49,0.87) out=0.0 out=1.0 out=0.5 Only one separating hyperplane is usually not enough! Can we combine two or more? Fisher 0 1 2 3 4 5 6 x10 # formulas # slides 0 1 2 3 4 5 6 x10 1930

6. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen6 Neural Networks 0 1 2 3 4 5 6 x10 -50 +0.1 +1.1-1.1 +20 +0.2 +3.6 -1.8 # formulas# slides 0 1 Construct NN with two separating hyperplanes:Train NN with two hidden neurons (gradient descent):

7. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen7 NN Training 8 hidden neurons = 8 separating lines Test-Error Train-Error signal background Training Epochs

8. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen8 Support Vector Machines Separating hyperplane with maximum distance to each datapoint: Maximum margin classifier Found by setting up condition for correct classfication and minimizing which leads to the Lagrangian Necessary condition for a minimum is So the output becomes Only linear separation? The mapping to feature space is hidden in a kernel No! Replace dot products: KKT: only SV have Non-separable case:

9. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen9 Bagging – Procedure Training events Draw with replacement Resampled events 1 Resampled events 2 Resampled events n Train Classifier 1 Classifier 2 Classifier n Combine to final decision majority voting (weighted) averaging Around 63% of original events, rest are replications Bootstrap aggregating Aim is to create strong classifiers which are as independent as possible.

10. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen10 Random Forests Modification: At each node of the tree: Search only through a randomly selected subset of all features Tree, Randomness, Combination RF Use Bagging on this classifier 1 – 2,12 – 2,11 – 1,2 Training: Testing/Evaluation: final output = Basis: Decision Tree (CART) without pruning Create 3 trees

11. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen11 Boosting – Procedure Training events normal weights Train Classifier 1 Raise weights of misclassified events Training events weight config 1 Train Classifier 2 Raise weights of misclassified events Training events weight config 2 Train Classifier n Weight classifiers with their performance  and combine to final decision Misclassified events get higher weights, are learned better. Boosting tries to equalize misclassification rates for each event. ? !

12. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen12 Theory of Communication: Minimum Description Length Principle Bayes Hypothesis H and Data D Our hypothesis should have the maximum probability given the data: Shannon MDLP Rissanen 18 th century 1948 1990

13. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen13 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*, DiJet CC, J/Psi ee TC Trigger Scheme H1 at HERA ep Collider, DESY „L2NN“ new TEL1STPhysics *0078Charged Current old 0168Phi K+K- 0252,54J/Psi ee 0383DiJet 0454J/Psi µµ 0532D* untagged 0640Spacal back2back 0778Charged Current 0833J/Psi ee TC (1999) 0941DVCS 1083D* tagged *1133J/Psi ee TC (2004) 1215J/Psi µµ inelastic

14. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen14 L2NN Rates and Efficiencies Last day before shutdown S83 DiJets des=50% rej=50% S32 D* des=94% rej=90% S78 CC des=58% rej=60% S41 DVCS des=80% rej=80% S83 D* des=43% rej=50% S33 J/Psi des=94% rej=90% S15 J/Psi des=30% rej=30% All measured rate-reductions match design. No wrong prediction for efficiency found. S83 DiJets S32 D* S78 CC S41 DVCS S83 D* S33 J/Psi ee S15 J/Psi µµ 95% 58% 100% 97% 95% >95% 96%

15. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen15 Performance Measurement - Classification Eff@Rej = xx% Rej@Eff = xx% 0 output 1 signal background Misclassification = 200%-Eff-Rej

16. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen16 Performance Measurement - Regression  =y-out(x)  ²= ²+   ²  =y-out(x)

17. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen17 From Classification to Regression k-NN 3 4 5 3 2 2 5 RS 3 4 5 3 2 2 5 NN Fit Gauss a=  (-2.1x - 1) b=  (+2.1x - 1)out=  (-12.7a-12.7b+9.4)