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New Directions in Data Analysis

New Directions in Data Analysis. Pushpalatha Bhat Fermilab. DPF2000 Columbus, Ohio August 11, 2000. “A reasonable man adapts himself to the world. An unreasonable man tries to adapt the world to himself. So, all progress depends on the unreasonable one.”. Outline.

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New Directions in Data Analysis

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  1. New Directions in Data Analysis Pushpalatha Bhat Fermilab DPF2000 Columbus, Ohio August 11, 2000 “A reasonable man adapts himself to the world. An unreasonable man tries to adapt the world to himself. So, all progress depends on the unreasonable one.”

  2. Outline • Intelligent Detectors • Moving intelligence closer to action • Multivariate Methods • Neural Networks: The “New” Paradigm • New Searches & Precision Measurements: Some Examples • Measuring the Top Quark Mass • Discovery Reach for the Higgs • More Sophisticated Approaches • Probabilistic Approach to Analysis: Exploring Models • Summary DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  3. World After Experiment/ Analysis World before Experiment/ Analysis Transformation Feature Extraction Global Decision Data Collection Data Interpretation Data Organization Reduction Analysis DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  4. Intelligent Detectors • Data analysis starts when a high energy collision/event occurs • Transform electronic data into useful “physics” information in real-time • Move intelligence closer to action! • Algorithm-specific hardware • Neural Network chips, for example • Configurable hardware • FPGAs, DSPs • Innovative data management on-line + “smart” algorithms in hardware • Data in RAM disk & AI algorithms in FPGAs • Expert systems for control & monitoring • Trouble-shooting, diagnosis and fix DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  5. 27.5 GeV 920 GeV e- p+ hardwired logic Neural Nets Smart Triggers • There are already Success Stories! H1 Level-2 Trigger • Trigger on rare ep collisions in an overwhelming beam-gas background • NN Hardware: the CNAPS 1064 chip • 12 Independent neural nets each one trained for a specific physics process in a total of 960 digital processors • Successful operations since 1996 DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  6. Multivariate Methods Keep it simple As simple as possible Not any simpler Einstein

  7. Multivariate Methods • The measurements being multivariate, the optimal methods of analyses are necessarily multivariate • Many Applications: • Particle Identification • e-ID, t-ID, b-ID, e/g , q/g • Signal/Background Event Classification • New physics • Signals of new physics are rare and small (Finding a “jewel” in a hay-stack) • Parameter Estimation • t mass, H mass, track parameters, for example • Function Approximation • Parametric methods: • Fisher discriminant, Kernel methods • Non-parametric Methods • Adaptive/AI methods DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  8. B = r(x,y) = constant defines an optimal decision boundary S = Feature space Optimal Event Selection Conventional cuts DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  9. Discriminant Approximation with Neural Networks Output of a feed forward neural network can approximate the Bayesian posterior probability p(s|x,y). DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  10. Calculating the Discriminant Consider the sum Where di = 1 for signal = 0 for background  = vector of parameters Then in the limit of large data samples and provided that the function n(x,y,) is flexible enough. DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  11. x1 x2 DNN x3 x4 Neural Networks The “New” Paradigm • Neural Networks (NN) are mathematical, adaptive systems (algorithms). • The “hidden” transformation functions, g, adapt themselves to the data as part of the training process. The number of such functions need to grow only as the complexity of the problem grows. • NN estimates a mapping function without requiring a mathematical description of how the output formally depends on the input. DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  12. Measuring the Top Quark Mass Discriminant variables shaded = top The Discriminants DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  13. NN Discriminant(DNN vs mfit ) Background Signal (170 GeV/c2) DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  14. Measuring the Top Quark Mass DØ Lepton+jets Background-rich Signal-rich mt = 173.3 ± 5.6(stat.) ± 6.2 (syst.) GeV/c2 DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  15. Strategy for Discovering the Higgs Boson at the Tevatron P.C. Bhat, R. Gilmartin, H. Prosper, PRD 62 (2000) hep-ph/0001152

  16. Hints from the Analysis of Precision Data • MH = GeV/c2MH < 225 GeV/c2 at 95% C.L. LEP Electroweak Group, http://www.cern.ch/LEPEWWG/plots/summer99 DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  17. Event Simulation • Signal Processes • Backgrounds • Event generation • WH, ZH, ZZ and Top with PYTHIA • Wbb, Zbb with CompHEP, fragmentation with PYTHIA • Detector modeling • SHW (http://www.physics.rutgers.edu/~jconway/soft/shw/shw.html) • Trigger, Tracking, Jet-finding • b-tagging (double b-tag efficiency ~ 45%) • Di-jet mass resolution ~ 14% • (Scaled down to 10% for RunII Higgs Studies) DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  18. WH Results from NN Analysis MH = 100 GeV/c2 DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  19. WH (110 GeV/c2)NN Distributions DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  20. WH Results Is it worth it? DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  21. Combined Results (WH+ZH) DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  22. Results, Standard vs. NN About half the luminosity required in case of NN analyses relative to conventional analyses for the same discovery reach. A good chance of discovery up to MH= 130 GeV/c2 with 20-30fb-1 DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  23. Improving the Higgs Mass Resolution • Use mjj and HT (= Etjets ) to train a neural networks to predict the Higgs boson mass Network-improved Higgs Mass 13.8% 12.2% 13.1% 11.3% 13% 11% DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  24. Newer ApproachesEnsembles of Networks DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  25. Committees of Networks NN1 y1 NN2 y2 X NN3 y3 NNM yM Decision by a committee has lower error than the individuals. The performance of a committee can be better than the performance of the best single network used in isolation DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  26. DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  27. Probabilistic Approach to Data Analysis (The Wave of the future) Bayesian Methods

  28. Bayesian Analysis Posterior Likelihood Prior M model A uninteresting parameters p interesting parameters d data Bayesian Analysis of Multi-source Data P.C. Bhat et al., Phys. Lett. B 407(1997) 73 DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  29. Higgs Mass Fits S=80 WH events, assume background distribution described by Wbb. Results S/B = 1/10 Mfit= 114 +/- 11GeV/c2 S/B = 1/5 Mfit= 114 +/- 7GeV/c2 DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  30. Solar Neutrino Problem Solar Neutrino Data 1998 • Electron neutrinos from the Sun seem to be lost en route to the Earth. That loss is described by the neutrino survival probability, P(E). • We have used solar neutrino data and standard solar model predictions to extract P(E) and its uncertainties. DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  31. The first term models the high frequency components, which occur near the origin, while the second term models the lower frequency components. Take likelihood to be a multivariate Gaussian, I is prior info. Marginalization Bayesian Analysis Modeling the Survival Probability C. Bhat, P.C. Bhat, M. Paterno, H.B. Prosper, Phys. Rev. Lett. 81, 5056 (1998) DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  32. Neutrino Survival Probability C. Bhat et al. DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  33. Advantages of Bayesian Approach • Provides probabilistic information on each parameter of a model (SUSY, for example) via marginalization over other parameters • Bayesian method enables straight-forward and meaningful model comparisons. • Bayesian approach allows treatment of all uncertainties in a consistent manner. • Mathematically linked to adaptive algorithms such as Neural Networks (NN) • Hybrid methods involving NN for probability density estimation and Bayesian treatement can be very powerful DPF2000 Aug. 9-12, 2000 Pushpa Bhat

  34. Summary • We are building very sophisticated equipment and will record unprecedented amounts of data in the coming decade • Use of advanced “optimal” analysis techniques will be crucial to achieve the physics goals • Multivariate methods, particularly Neural Network techniques, have already made impact on discoveries and precision measurements and will be the methods of choice in future analyses • Hybrid methods combining “intelligent” algorithms and probabilistic approach will be the wave of the future DPF2000 Aug. 9-12, 2000 Pushpa Bhat

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