Searching for Single Top Using Decision Trees

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Searching for Single Top Using Decision Trees

• G. Watts (UW)
• For the DØ Collaboration
• 5/13/2005 APSNW Particles I

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SingleTop Challenges
Overwhelming Background!
Straight Cuts
(and counting experiments)
Difficulty taking advantage of correlations
Multivariate Cuts
(and shape fitting)
Designed to take advantage of correlations and
irreducible backgrounds
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Asymmetries in t-Channel Production
Lots of variables give small separation
Pair Production
(Use ME, phase space, etc.)
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Combine Variables!
Multivariate Likelihood Fit
7 variables means 7 dimensions
Neural Network
Many inputs and a single output Trained on signal
and background sample Well understood and mostly
accepted in HEP
Decision Tree
Many inputs and a single output Trained on signal
and background sample Used mostly in life
sciences business (MiniBOONE - physics/0408124).
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Decision Tree
Trained Decision Tree
(Binned Likelihood Fit)
(Limit)
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Internals of a Trained Tree
You can see a decision tree
Rooted Binary Tree
Every Event belongs to a single leaf node!
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Training
Determine a branch point
Calculate Gini Improvement
As a function of a interesting variable (HT in
this case)
Choose the largest improvement as the cut point
Repeat for all interesting variables
HT, Jet pT, Angular Variables, etc.
Best improvement is this nodes decision.
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Gini
Process Requires a Variable to optimize
separation.
Purity
Ws Weight of Signal Events
Wb Weight of Background Events
Gini
G is zero for pure background or signal!
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Gini Improvement
For each node
GI G(S) G(S1) G(S2)
Repeat the process for each subdivision of data
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And Cut
Stop process and generate a leaf.
We used statistical sample error ( of events)
Determine the Purity of each leaf
Use Tree as Estimator of Purity
Each event belongs to a unique leaf The leafs
purity is the estimator of the event
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DT in the Single Top Search
DØ
Backgrounds WJets, QCD, top Pair Production
Fake Leptons
DT tt ljets
Two DTs
Trained on signal and Wbb as background
Trained on signal and tt ? lepton jets as
background
DT Wbb
This part is identical to a NN based
analysis Separate DT for muon electron
2d Histogram used in binned likelihood fit
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Results
Expected Limits
s-channel 4.5 pb (NN 4.5) t-channel 6.4 pb
(NN 5.8)
Actual Limits
s-channel 8.3 pb (NN 6.4) t-channel 8.1 pb
(NN 5.0)
Expected Results Close to NN
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Future of the Analysis
Use a Single Decision Tree
Train it against all backgrounds
Pruning
Train until each leaf has only a single
event Recombine leaves (pruning) using
statistical estimator
Boosting
Combine multiple trees, each weighted Train trees
on event samples that have mis-classified event
weights enhanced
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References Introduction
MiniBooNE Paper hep-ex/0408124
Recent Advances in Predictive (Machine) Learning
Jerome H. Friedman, Conf. Proceedings
I have then linked and other on my web page
http//d0.phys.washington.edu/gwatts/research/con
ferences
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Conclusions

• Decision Trees are good
• Model is obvious in form of 2d binary tree.
• Not as sensitive to outliers in input data as
  other methods
• Easily accommodate integer inputs (NJets) or
  missing variable inputs.
• Easy to implement (several months to go from
  scratch to working code)
• Decision Trees arent so good
• Well understood input variables are a must
• Similar for Neural Networks, of course.
• Minor changes in the input events can make for
  major changes in tree layout and results.
• Estimator is not a continuous function
• Dont have to deal with hidden nodes
• Separate training of background or other issues