# Presentation: 160426

## 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

- 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

## Slide 3

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## 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

## Smart Triggers

***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

## Multivariate Methods

*Keep it simple*
*As simple as possible*
*Not any simpler*
*	**	**Einstein*

## Multivariate Methods

- The measurements being multivariate, the optimal methods of analyses are necessarily multivariate
- Many Applications:
- Particle Identification
- e-ID, ID, b-ID, e/ , 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

## Optimal Event Selection 

- Conventional cuts

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## 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

## 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

## Neural Networks The “New” Paradigm

- 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.

***Neural Networks ******The “New” Paradigm***

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## Measuring the Top Quark Mass

**The Discriminants**

***Discriminant variables***

- shaded = top

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## NN Discriminant(DNN vs mfit )

- Signal (170 GeV/c2)

- Background

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## Measuring the Top Quark Mass

- Background-rich

- Signal-rich

***DØ Lepton+jets***

- mt  = 173.3 ± 5.6(stat.) ± 6.2 (syst.) GeV/c2

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## Strategy for Discovering the Higgs Boson at the Tevatron

- P.C. Bhat, R. Gilmartin, H. Prosper,  PRD 62 (2000)
-                                                          hep-ph/0001152

## Hints from the Analysis of Precision Data

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

- MH =               GeV/c2 MH < 225 GeV/c2  at 95% C.L.

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## 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

## WH Results from NN Analysis

*WH Results from NN Analysis*

- MH = 100 GeV/c2

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## WH (110 GeV/c2) NN Distributions

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

##   WH Results                             Is it worth it?

**  *****WH Results                             Is it worth it?***

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## Combined Results (WH+ZH)

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## 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

## Improving the Higgs Mass Resolution

- Network-improved Higgs Mass

-  13.8%

- 12.2%

- 13.1%

- 11.3%

- 13%

- 11%

-  Use mjj and HT (= Etjets ) to train a neural networks to predict the Higgs boson mass

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## Newer ApproachesEnsembles of Networks

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## Committees of Networks

- NN1

- NN2

- NN3

- NNM

**X**

- y1

- y2

- y3

- 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

## Slide 26

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## Probabilistic Approach to Data Analysis

- Bayesian Methods

- (The Wave of the future)

##    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

## 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

## 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

## Bayesian Analysis

- <footer>

***Bayesian Analysis***

**C. Bhat, P.C. Bhat, M. Paterno, H.B. Prosper, **
**Phys. Rev. Lett. 81, 5056 (1998)**

- Modeling the Survival Probability

## Neutrino Survival Probability

- C. Bhat et al.

- DPF2000  Aug. 9-12, 2000               Pushpa Bhat

## 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

## 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