Multivariate techniques for identifying diffractive interactions at the LHC

Transcription

1 Multivariate techniques for identifying diffractive interactions at the LHC Mikael Kuusela,,, Eric Malmi,,, Risto Orava,,, Tommi Vatanen,, Helsinki Institute of Physics University of Helsinki CERN Aalto University DIFFRACTION 2010 International Workshop on Diffraction in High-Energy Physics September 15, / 18

2 Motivation Diffraction is usually identified based on rapidity gaps How to define the characteristics of the gap? Fluctuations in QCD background may create rapidity gaps Low gap survival probability at LHC energies With a multivariate approach, one utilizes the full event topology Figure: Probability of finding a rapidity gap larger than η in a non-diffractive inclusive QCD sample generated with SHERPA using cluster hadronization and p T,cut = 500 MeV. (V.A. Khoze et al., arxiv: ) 2 / 18

3 Multivariate Classification of Diffraction Identify different diffractive event classes using several well-understood low-level variables The use of machine learning algorithms allows for automatic determination of optimal event signatures Two approaches Hard classification: each event is exclusively assigned to a certain class Soft classification: each event belongs with some probability to all the event classes We have performed dedicated feasibility studies of both approaches 3 / 18

4 Hard Classification of Diffraction Classification of a diffractive sample generated with Pythia6 and Phojet at 14 TeV Four event classes: SD, DD, CD, ND ND defined as the Pythia6 low-p T production Use forward and central multiplicity and energy flows Corresponding to the CMS (including FSC) and TOTEM detectors Simulated using a Geant3-based model of the forward region of IP5 by Jerry Lämsä Each event is described using 23 variables No explicit information about the rapidity gap or the leading protons Comparison of three hard classification algorithms Multi-layer perceptron neural networks Gene expression programming Support vector machines 4 / 18

5 Classification Results Table: Confusion matrix for neural network, rows correspond to correct event classes and columns to classification results Predicted Class DD SD CD ND Actual DD SD CD ND Purities / 18

6 Findings Table: Average efficiencies of the different algorithms Method <Efficiency> Gene Expression Programming Support Vector Machine Neural Network All algorithms achieved over 90% average efficiencies Diffraction can be efficiently identified using multiplicity and energy flows No need to explicitly look for rapidity gaps For more details, see Kuusela et al. Multivariate techniques for identifying diffractive interactions at the LHC. International Journal of Modern Physics A, 25(8): , / 18

7 Motivation for Soft Classification There are areas of data space where different classes overlap Hard classification produces inevitable classification errors Take a probabilistic approach Estimate the posterior probabilities p(c i x) of an event x to belong to a certain class C i Posterior probabilities can be used to weigh event contributions to physical observables Soft classification is more consistent with the underlying probabilistic quantum mechanics 7 / 18

8 Details of the Study Use a generator level Pythia6 minimum bias sample at 7 TeV (CMS D6T tune) Four event classes: SDL, SDR, DD, ND ND includes also the hard QCD processes Want to estimate the probabilities p(sdl x), p(sdr x), p(dd x), p(nd x) Variables based on geometrical acceptance of detectors at IP5 Charged particle multiplicities in central tracker, T1 and T2 Energy deposits in central, HF, Castor and ZDC calorimeters p T and invariant mass for charged particles within η < 2.5 Each event described by 24 variables Soft classification with the k nearest neightbours (knn) algorithm Dimensionality reduction with linear discriminant analysis (LDA) Comparison to hard classification with neural networks 8 / 18

9 k Nearest Neighbours Algorithm (knn) The knn algorithm: for each event x 1. Find the k nearest neighbours in the training set 2. Count the number of instances k i from each class C i 3. Estimate the posterior probabilities p(c i x) k i k The error rate is guaranteed to approach the Bayes error rate (optimal error rate for known distributions) for some k Soft classification: use probabilities p(c i x) as weights Hard classification: select class based on the highest probability Figure: Illustration of knn classification. For k = 5, p(blue x) = 3/5 and p(red x) = 2/5. 9 / 18

10 Dimensionality Reduction with Linear Discriminant Analysis (LDA) The performance of the knn classifier descreases with increasing dimensionality d (curse of dimensionality) Reduce dimensionality with mapping z = W T x LDA: choose W to maximize between-class distances and to minimize within-class spreads Figure: Illustration of LDA for two classes (Alpaydin, Intoduction to Machine Learning, 2010) 10 / 18

11 Visualization of the Training Sample 4 2 ND DD SDR SDL LDA LDA1 Figure: A two-dimensional visualization of the training sample after dimensionality reduction using LDA. The DD events overlap with both SD and ND events. 11 / 18

12 Multiplicity (DD) DD Multiplicity Count Classified - Pythia Pythia6 Soft knn (k=16) Hard knn (k=16) Neural Network Pythia6 Soft knn (k=16) Hard knn (k=16) Neural Network η η Figure: Left: Charged particle multiplicity distribution for double diffractive (DD) events. Right: Distributions after subtraction of MC truth. Comparison of soft classification (soft knn) and hard classification (hard knn & neural network). 12 / 18

13 Multiplicity (SDL) SDL Multiplicity Count Pythia6 Soft knn (k=16) Hard knn (k=16) Neural Network Classified - Pythia Pythia6 Soft knn (k=16) Hard knn (k=16) Neural Network η η Figure: Left: Charged particle multiplicity distribution for single diffractive events with the diffractive system on the left side (SDL). Right: Distributions after subtraction of MC truth. Comparison of soft classification (soft knn) and hard classification (hard knn & neural network). 13 / 18

14 Multiplicity (ND) ND Multiplicity Count Classified - Pythia Pythia6 Soft knn (k=16) Hard knn (k=16) Neural Network Pythia6 Soft knn (k=16) Hard knn (k=16) Neural Network η η Figure: Left: Charged particle multiplicity distribution for non-diffractive (ND) events. Right: Distributions after subtraction of MC truth. Comparison of soft classification (soft knn) and hard classification (hard knn & neural network). 14 / 18

15 Relative Event Rates Table: Relative event rates of the different categories. Soft knn is able to estimate the rates with high accuracy. Hard classification overestimates the non-diffractive contribution and underestimates all the diffractive classes. ND DD SDR SDL Pythia Soft knn Hard knn Neural Network / 18

16 Train with Pythia, test with Phojet Table: Confusion matrix for soft knn trained and tested with Pythia Predicted Class ND DD SDR SDL Actual ND DD SDR SDL Table: Confusion matrix for soft knn trained with Pythia and tested with Phojet Predicted Class ND DD SDR SDL Actual ND DD SDR SDL / 18

17 Findings Soft classification is able to accurately reconstruct physical distributions Very accurate estimates for relative cross sections Although a really simple algorithm, knn is able to classify diffraction with great efficiency Little dependence on the selection of k Crucial to use dimensionality reduction More advanced soft classification methods (kernel density estimation, non-linear discriminant analysis) did not seem to give advantage over knn 17 / 18

18 Conclusions Multivariate classification methods are a viable alternative to the rapidity gap method Produce very accurate results Use all the available information in an optimal manner Need to select the traning sample carefully Weighting of events based on soft classification seems to improve measurement of physical observables compared to hard classification A natural way to accommodate the DD events which represent a non-reducible physics background 18 / 18