Backups Jens Zimmermann zimmermmppmu mpg de MaxPlanckInstitut fr

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

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

k=3 out= k=4 out= 6 k=2 out= 4 3 0 1 2 k=5 out= # slides 5 k=1 out= x 10 k-Nearest-Neighbour 0 1 2 3 4 5 6 x 10 # formulas Regularization: Parameter k For every evaluation position the distances to each training position need to be determined! Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 3

Maximum Likelihood / Naive Bayes # formulas 0 2 4 # slides 6 x 10 0 2 4 31 6 x 10 32 out= Regularization: Binning Correlation gets lost completely by projection! Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 4

Linear Discriminant Analysis Fisher 1930 6 x 10 (-0. 49, 0. 87) out=1. 0 4 3 2 1 Only one separating hyperplane is usually not enough! Can we combine two or more? out=0. 0 0 # slides 5 out=0. 5 0 1 2 3 4 5 6 x 10 # formulas Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 5

Neural Networks 1 0 6 x 10 Construct Train NN with two hidden separating neuronshyperplanes: (gradient descent): +1. 1 -1. 1 +0. 1 # formulas +0. 2 # slides 4 2 +20 1 -50 3 +3. 6 0 +3. 6 5 -1. 8 0 1 2 3 4 5 Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 6 x 10 6

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

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 KKT: only SV have Only linear separation? No! Replace dot products: The mapping to feature space is hidden in a kernel Non-separable case: Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 8

Bagging – Procedure Draw with replacement Training events Resampled events 1 Dra ww ith r Dr aw Bootstrap aggregating wi th Around 63% of original events, rest are replications re pl epla c Classifier 1 eme nt Resampled events 2 ac em en Train Classifier 2 t Resampled events n • majority voting • (weighted) averaging Train Classifier n Combine to final decision Aim is to create strong classifiers which are as independent as possible. Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 9

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

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

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

L 2 Neural Network Trigger H 1 at HERA ep Collider, DESY Trigger Scheme Physics *00 78 Charged Current old 01 68 Phi K+K- 02 52, 54 J/Psi ee 03 83 Di. Jet 04 54 J/Psi µµ 05 32 D* untagged 06 40 Spacal back 2 back 50 Hz 07 78 Charged Current L 4 100 ms 08 33 J/Psi ee TC (1999) 09 41 DVCS 10 83 D* tagged 10 MHz L 1 2. 3 µs 500 Hz L 2 20 µs 10 Hz „L 2 NN“ new TE L 1 ST DVCS, J/Psi µµ, D*, Di. Jet CC, J/Psi ee TC *11 33 12 15 J/Psi ee TC (2004) J/Psi µµ inelastic Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 13

L 2 NN Rates and Efficiencies Last day before shutdown S 83 Di. Jets des=50% rej=50% S 32 D* des=94% rej=90% S 41 DVCS des=80% rej=80% S 78 CC des=58% rej=60% S 83 D* des=43% rej=50% S 33 J/Psi des=94% rej=90% S 15 J/Psi des=30% rej=30% Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen All measured rate-reductions match design. No wrong prediction for efficiency found. S 83 Di. Jets S 32 D* S 78 CC S 41 DVCS S 83 D* S 33 J/Psi ee S 15 J/Psi µµ 95% 58% 100% 97% 95% >95% 96% 14

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

Performance Measurement - Regression s²=<D>²+s. D² D=y-out(x) Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 16

From Classification to Regression 2 k-NN 4 3 5 5 2 RS 2 3 4 3 5 5 2 3 Fit Gauss NN a=s(-2. 1 x - 1) b=s(+2. 1 x - 1) out=s(-12. 7 a-12. 7 b+9. 4) Jens Zimmermann, MPI für Physik München, ACAT 2005 Zeuthen 17