New Directions in Data Analysis

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29 Οκτ 2013 (πριν από 3 χρόνια και 11 μήνες)

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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.”

DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

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 before

Experiment/

Analysis

World After

Experiment/

Analysis

Data
Interpretation

Data

Collection

Data

Organization

Reduction

Analysis

Transformation

Feature Extraction

Global Decision

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

e
-

920 GeV

p
+

Neural Nets

hardwired logic

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


Multivariate Methods

Keep it simple

As simple as possible

Not any simpler



Einstein

DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

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

Optimal Event Selection


r(x,y)

=
constant


defines an optimal

decision boundary

Feature space

S

=

B

=

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


d
i


=
1

for signal



=
0

for background




=v散t潲潦灡牡p整敲e

T桥h

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


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.

x
1

x
2

x
3

x
4

D
NN

Neural Networks

The “New” Paradigm

DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

12

Measuring the Top Quark Mass

The Discriminants

Discriminant variables

shaded = top


DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

13

NN Discriminant

(
D
NN

vs m
fit
)

Signal (170 GeV/c
2
)

Background

DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

14

Background
-
rich

Signal
-
rich

Measuring the Top Quark Mass

DØ Lepton+jets



m
t

= 173.3
±

5.6(stat.)
±

6.2 (syst.) GeV/c
2

Strategy for Discovering the
Higgs Boson at the Tevatron

P.C. Bhat, R. Gilmartin, H. Prosper, PRD 62 (2000)


hep
-
ph/0001152


DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

16

Hints from the Analysis of
Precision Data

LEP Electroweak Group, http://www.cern.ch/LEPEWWG/plots/summer99

M
H

= GeV/c
2


M
H
< 225 GeV/c
2

at 95% C.L.

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

M
H

= 100 GeV/c
2

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 M
H
= 130 GeV/c
2
with 20
-
30fb
-
1


DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

23

Improving the Higgs Mass
Resolution

Network
-
improved Higgs Mass


13.8%

12.2%

13.1%

11.3%

13%

11%



Use m
jj

and H
T
(=


E
t
jets
) to train a neural networks to
predict the Higgs boson mass


DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

24

Newer Approaches

Ensembles of Networks

DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

25

Committees of Networks

NN
1

NN
2

NN
3

NN
M

X

y
1

y
2

y
3

y
M

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

Probabilistic Approach to
Data Analysis

Bayesian Methods

(The Wave of the future)

DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

28


Bayesian Analysis


M model

A uninteresting parameters

p interesting parameters

d data

Likelihood

Prior

Posterior

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 M
fit
= 114 +/
-

11GeV/c
2


S/B = 1/5 M
fit
= 114 +/
-

7GeV/c
2



DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

30

Solar Neutrino Problem


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.


Solar Neutrino Data 1998

DPF2000 Aug. 9
-
12, 2000 Pushpa Bhat

31

Bayesian Analysis

C. Bhat, P.C. Bhat, M. Paterno, H.B. Prosper,

Phys. Rev. Lett. 81, 5056 (1998)

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

Modeling the Survival Probability

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