New Directions in Data Analysis

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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.
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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

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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

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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

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

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Optimal Event Selection
Conventional cuts
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Discriminant Approximation with Neural Networks
Output of a feed forward neural network can
approximate the Bayesian posterior probability
p(sx,y).
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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.
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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.

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Measuring the Top Quark Mass
Discriminant variables
shaded top
The Discriminants
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NN Discriminant(DNN vs mfit )
Background
Signal (170 GeV/c2)
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Measuring the Top Quark Mass DØ Leptonjets
Background-rich
Signal-rich

mt 173.3 5.6(stat.) 6.2 (syst.) GeV/c2
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Strategy for Discovering the Higgs Boson at the
Tevatron
P.C. Bhat, R. Gilmartin, H. Prosper, PRD 62
(2000)
hep-ph/0001152
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Hints from the Analysis of Precision Data
MH GeV/c2 MH lt 225 GeV/c2 at
95 C.L.
LEP Electroweak Group, http//www.cern.ch/LEPEWWG/
plots/summer99
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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)
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WH Results from NN Analysis
MH 100 GeV/c2
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WH (110 GeV/c2) NN Distributions
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WH Results Is it
worth it?
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Combined Results (WHZH)
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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
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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
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Newer ApproachesEnsembles of Networks
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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
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Probabilistic Approach to Data Analysis
(The Wave of the future)

• Bayesian Methods

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Bayesian Analysis
Likelihood
Prior
Posterior
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
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Higgs Mass Fits
S80 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
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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.

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Bayesian Analysis
Modeling the Survival Probability
C. Bhat, P.C. Bhat, M. Paterno, H.B. Prosper,
Phys. Rev. Lett. 81, 5056 (1998)
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Neutrino Survival Probability
C. Bhat et al.
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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

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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