# Presentation: 160428

## Advanced Analysis Techniques in HEP

- Pushpa Bhat
- Fermilab

- ACAT2000
- Fermilab, IL
- October 2000

*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*

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## 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

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Data Collection

- Data Transformation

- Feature Extraction

- Global Decision

- Data Interpretation

- Data
- Organization
- Reduction
- Analysis

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## 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**

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Data Analysis Tasks

- Particle Identification
-  e-ID, -ID, b-ID, e/, 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

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## 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

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Why Multivariate Methods?

-   **Because they are optimal!**

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Also, they need to have optimal flexibility/complexity

- Simple

- Flexible

- Highly flexible

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## The Golden Rule

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

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Optimal Event Selection 

- defines decision boundaries
- that minimize the probability
- of misclassification

**So, the problem mathematically reduces to that of calculating **
***r(x),***** the Bayes Discriminant Function or probability densities**

- Posterior probability

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Slide 11

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Slide 12

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## 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**

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## 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*** x******n****** *** in the hypercube
-          = 0 otherwise

***h***=smoothing
- parameter

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## 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

**If our data set contains *****N******k***** points in class *****C******k***** and *****N***** points in total, then**

*K nearest-neighbor Method*

- N = Number of data points

- Kk = # of points in volume
-          V for class Ck

- ACAT2000  Oct. 16-20, 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)***
**Directly without estimating class-conditional probabilities**

- ACAT2000  Oct. 16-20, 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.

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Neural Networks

**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.**

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Measuring the Top Quark Mass

**The Discriminants**

***Discriminant variables***

**shaded = top**

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Measuring the Top Quark Mass

- Background-rich

- Signal-rich

***Measuring the Top Quark Mass***

**m****t **** = 173.3 ± 5.6(stat.) ± 6.2 (syst.) GeV/c****2**

***DØ Lepton+jets***

- ACAT2000  Oct. 16-20, 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

- ACAT2000  Oct. 16-20, 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)

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## WH Results from NN Analysis

***WH Results from NN Analysis***

- MH = 100 GeV/c2

**WH **

**WH vs Wbb**

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## WH (110 GeV/c2) NN Distributions

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Results, Standard vs. NN

**A good chance of discovery up to M****H****= 130 GeV/c****2 ****with 20-30fb****-****1**** **

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Improving the Higgs Mass Resolution

-  13.8%

- 12.2%

- 13.1%

- 11..3%

- 13%

- 11%

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

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Newer ApproachesEnsembles 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

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## 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

- ACAT2000  Oct. 16-20, 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

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat

## Optimal Event Selection 

*S* =

*B* =

- Conventional cuts

- ACAT2000  Oct. 16-20, 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, H. Prosper, S. Snyder,  Phys. Lett. B 407(1997) 73

- ACAT2000  Oct. 16-20, 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

- ACAT2000  Oct. 16-20, 2000       Pushpa Bhat