Advanced Analysis Techniques in HEP

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Advanced Analysis Techniques in HEP
A reasonable man adapts himself to the world. An
unreasonable man persists to adapts the world to
himself. So, all progress depends on the
unreasonable one. - Bernard Shaw

• Pushpa Bhat
• Fermilab

ACAT2000 Fermilab, IL October 2000
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Outline

• Introduction
• Intelligent Detectors
• Moving intelligence closer to action
• Optimal Analysis Methods
• The Neural Network Revolution
• New Searches Precision Measurements
• Discovery reach for the Higgs Boson
• Measuring Top quark mass, Higgs mass
• Sophisticated Approaches
• Probabilistic Approach to Data Analysis
• Summary

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Data Collection
Data Transformation
Data Interpretation
Feature Extraction
Global Decision
Data Collection
Data Organization Reduction Analysis
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Intelligent Detectors

• Data analysis starts when a high energy event
  occurs
• Transform electronic data into useful physics
  information in real-time
• Move intelligence closer to action!
• Algorithm-specific hardware
• Neural Networks in Silicon
• Configurable hardware
• FPGAs, DSPs Implement smart algorithms in
  hardware
• Innovative data management on-line smart
  algorithms in hardware
• Data in RAM disk AI algorithms in FPGAs
• Expert Systems for Control Monitoring

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Data Analysis Tasks

• Particle Identification
• e-ID, t-ID, b-ID, e/g, q/g
• Signal/Background Event Classification
• 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
• Correction functions, tag rates, fake rates
• Data Exploration
• Knowledge Discovery via data-mining
• Data-driven extraction of information, latent
  structure analysis

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Optimal Analysis Methods

• The measurements being multivariate, the optimal
  methods of analyses are necessarily multivariate
• Discriminant Analysis Partition multidimensional
  variable space, identify boundaries
  
• Cluster Analysis Assign objects to groups based
  on similarity
• Examples
• Fisher linear discriminant, Gaussian classifier
• Kernel-based methods, K-nearest neighbor
  (clustering) methods
• Adaptive/AI methods

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Why Multivariate Methods?

• Because they are optimal!

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• Also, they need to have optimal
  flexibility/complexity

Flexible
Simple
Highly flexible
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The Golden Rule

• Keep it simple
• As simple as possible
• Not any simpler
• - Einstein

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Optimal Event Selection
defines decision boundaries that minimize the
probability of misclassification
Posterior probability
So, the problem mathematically reduces to that of
calculating r(x), the Bayes Discriminant
Function or probability densities
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Probability Density Estimators

• Histogramming
• The basic problem of non-parametric density
  estimation is very simple!
• Histogram data in M bins in each of the d feature
  variables
• Md bins ? Curse Of Dimensionality
• In high dimensions, we would either require a
  huge number of data points or most of the bins
  would be empty leading to an estimated density of
  zero.
• But, the variables are generally correlated and
  hence tend to be restricted to a sub-space
  ? Intrinsic
  Dimensionality

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Kernel-Based Methods

• Akin to Histogramming but adopts importance
  sampling
• Place in d-dimensional space a hypercube of side
  h centered on each data point x,
• The estimate will have discontinuities
• Can be smoothed out using different forms for
  kernel functions H(u). A common choice is a
  multivariate kernel
• 
  
• 
  

• N Number of data points
• H(u) 1 if xn in the hypercube
• 0 otherwise

hsmoothing parameter
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K nearest-neighbor Method

• Place a hyper-sphere centered at each data point
  x and allow the radius to grow to a volume V
  until it contains K data points. Then, density
  at x
• If our data set contains Nk points in class Ck
  and N points in total, then

N Number of data points
Kk of points in volume V for class
Ck
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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) Directly without estimating
class-conditional probabilities
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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

• NN estimates a mapping function without requiring
  a mathematical description of how the output
  formally depends on the input.
• 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.

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Measuring the Top Quark Mass
Discriminant variables
shaded top
The Discriminants
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Measuring the Top Quark Mass
Background-rich
DØ Leptonjets
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
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
WH vs Wbb
WH
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WH (110 GeV/c2) NN Distributions
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Results, Standard vs. NN
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 NNs to
predict the Higgs boson mass
13.8
12.2
13.1
11..3
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Newer ApproachesEnsembles of Networks

• Committees of Networks
• Performance can be better than the best single
  network
• Stacks of Networks
• Control both bias and variance
• Mixture of Experts
• Decompose complex problems

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Exploring Models 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. It also 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

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Optimal Event Selection
S
B
Conventional cuts
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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,
H. Prosper, S. Snyder, 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