Main Web>TWikiUsers>KamalBenslama>ElectronBDT (2009-03-18, YaoMing)

-- KamalBenslama - 20 Aug 2005

Electron Identification Using Boosted Decision Trees

Electron Identification Using Boosted Decision Trees

Introduction

We present a boosted decision trees (BDT) method to discriminate between clusters in the electromagnetic calorimeter originating from electrons and those from other processes. The performance of the method is evaluated using release 14.2.20 of the ATLAS reconstruction software. The reference figures and tables for efficiencies and rejections against jets are described, based on the MC08 simulated data samples.

Discriminating variables

The variables used as input to the BDT method are described below and have been evaluated for both signal electrons from $Z\rightarrow ee$ decay and fake electrons selected from a QCD di-jets sample.

$F^{0}$ Energy fraction deposited in the presampler.
$F^{1}$ Energy fraction deposited in the first sampling of EM.
$F^{2} :$ Energy fraction deposited in the second sampling of EM.
$F^{3} :$ Energy fraction deposited in the third sampling of EM.

$\frac{E_{t}Cone40}{E_{T}} :$ Ratio of transverse energy in a cone of size $\Delta$ R = 0.4 to the total cluster transverse energy.

$\frac{E237}{E277} :$ Ratio in $\eta$ of cell energies in 3X7 versus 7X7 in the second sampling.

$\frac{E233}{E277} :$ Ratio in $\phi$ of cell energies in 3X7 versus 7X7 in the second sampling.

$\frac{E_{T}}{E_{T}+E_{T}^{had1}} :$ transverse electromagnetic fraction.

$\frac{E_{T}}{P_{T}} :$ Ratio of the cluster's measured transverse energy to the track's measured transverse momentum.

$\Delta \eta :$ Distance in $\eta$ between the cluster and its extrapolated track.
$\Delta \phi :$ Distance in $\phi$ between the cluster and its extrapolated track.
$\frac{Z_{vertex}}{\sigma Z} :$ Ratio of Z position of the vertex reconstructed from the cluster to its standard deviation.
$W_{\eta 1} :$ Shower width using three strips around the one with the maximal energy deposit.
$W_{\eta 2} :$ Corrected width using three strips around the one with the maximal energy deposit.
Number of TRT high threshold hits
$\Delta E_{s 1} :$ difference between the energy of the cell corresponding to second energy maximum in the first sampling and energy reconstructed in the strip with the minimal value between the first and second maximum.
$\sum P_{T}^{Smallcone} :$ sum $P_{T}$ of tracks in a small cone of size 0.05.
$\sum P_{T}^{Largecone} :$ sum $P_{T}$ of tracks in a large cone of size 0.5.

Boosted Decision Trees Description

A detailed description of the method is given in the ATLAS note. Here we just would to remind the reader that we used the Adaboost algorithm and that the parameter $\beta$ has been set to its default value of 0.5

Reference plots

In this section, we show the likelihood output for signal electrons (from Z boson) and for fake electrons (from QCD jets), in several ${\eta}$ bins and in the full ${\eta}$ range

${\eta}$ range	likelihood	${\eta}$ range	likelihood
${\mid\eta\mid&lt;2.47}$		${\mid\eta\mid&lt;0.8}$
${0.8&lt; \mid\eta\mid &lt;1.35}$		${1.35&lt; \mid\eta\mid &lt;1.5}$
${1.5&lt; \mid\eta\mid &lt;1.8}$		${1.8&lt; \mid\eta\mid &lt;2.0}$
${2.0&lt; \mid\eta\mid &lt;2.3}$		${2.3&lt; \mid\eta\mid &lt;2.47}$

Performance Studies using $Z\rightarrow ee$ events and QCD dijets events (JF17)

These plots show the rejection versus efficiency obtained using the likelihood method, compared to the results obtained using the two set of cuts (tight and tight (NoIsol))

${\eta}$ range	rejection vs efficiency	${\eta}$ range	rejection vs efficiency
${\mid\eta\mid &lt;2.47}$		${\mid\eta\mid &lt;0.8}$
${0.8&lt; \mid\eta\mid &lt;1.35}$		${1.35&lt;\mid\eta\mid&lt;1.5}$
${1.5&lt;\mid\eta\mid&lt;1.8}$		${1.8&lt;\mid\eta\mid&lt;2.0}$
${2.0&lt;\mid\eta\mid&lt;2.3}$		${2.3&lt;\mid\eta\mid&lt;2.47}$

Performance Studies in $Z\rightarrow ee$ , $W\rightarrow e\nu$ , Top, $Z'\rightarrow ee$ , $W'\rightarrow e/\mu/\tau \nu$ , and SU1

name	reference	name	reference
SU1		T1
Wenu		W'
Zee		Z'

BDT Thresholds and their corresponding efficiencies and fake rates


${{\footnotesize \begin{singlespace} \begin{longtable} \begin{center} \hline Cut value & Efficiency ($\%$) & Rejection (\small $\times 10^{5}$) \\ \hline\hline 0.3 & $ 82.5 \pm 0.08 $ & 0.05 $\pm 0.0004$ \\ 0.66 & $ 80.3 \pm 0.08 $ & 0.86 $\pm 0.03$ \\ 0.74 & $ 75.8 \pm 0.09 $ & 1.76 $\pm 0.09$ \\ 0.78 & $ 70.7 \pm 0.09 $ & 2.70 $\pm 0.2$ \\ 0.81 & $ 64.5 \pm 0.10 $ & 3.90 $\pm 0.3$ \\ 0.82 & $ 61.7 \pm 0.10 $ & 4.30 $\pm 0.4$ \\ \hline \caption{Electron efficiency and rejection factor for several values of the BDT threshold, in the region $\abseta < 2.47$} \label{tab:effrejcut} \end{center} \end{longtable} \end{singlespace} } % end footnotesize}$	${{\footnotesize \begin{longtable} \begin{center} \hline Cut value & Efficiency ($\%$) & Rejection (\small $\times 10^{5}$) \\ \hline\hline 0.6 & $ 90.20 \pm 0.10 $ & 1.54 $\pm$ 0.13 \\ 0.7 & $ 85.30 \pm 0.13$ & 5.30 $\pm$ 0.84 \\ 0.74 & $ 80.50 \pm 0.14 $ & 8.50 $\pm$ 1.70 \\ 0.76 & $ 76.70 \pm 0.15 $ & 12.5 $\pm$ 3.00 \\ 0.79 & $ 68.80 \pm 0.17 $ & 16.3 $\pm$ 4.50 \\ \hline \end{center} \caption{Electron efficiency and rejection factor for several values of the BDT threshold, for $0< \mid \eta \mid < 0.8$} \label{tab:effrej0} \end{longtable} } % end footnotesize}$
${{\footnotesize \begin{longtable} \begin{center} \hline Cut value & Efficiency ($\%$) & Rejection (\small $\times 10^{5}$)\\\hline\hline 0.46 & $ 86.00 \pm 0.15 $ & 1.14 $\pm 0.05$ \\ 0.76 & $ 80.20 \pm 0.18 $ & 2.20 $\pm 0.3$ \\ 0.81 & $ 74.80 \pm 0.19 $ & 2.98 $\pm 0.44$ \\ 0.84 & $ 68.40 \pm 0.20 $ & 4.30 $\pm 0.80$ \\ 0.86 & $ 61.20 \pm 0.21 $ & 5.20 $\pm 1.00$ \\ \hline \end{center} \caption{Electron efficiency and rejection factor for several values of the BDT threshold, for $0.8<\mid \eta \mid < 1.35$} \label{tab:effrej1} \end{longtable} } % end footnotesize}$	${{\footnotesize \begin{longtable} \begin{center} \hline Cut value & Efficiency ($\%$) & Rejection (\small $\times 10^{5}$)\\\hline\hline 0.56 & $ 81.07 \pm 0.32 $ & 0.11 $\pm 0.007$ \\ 0.73 & $ 75.05 \pm 0.36 $ & 0.52 $\pm 0.07$ \\ 0.77 & $ 69.50 \pm 0.40 $ & 1.20 $\pm 0.20$ \\ 0.79 & $ 65.20 \pm 0.40 $ & 1.70 $\pm 0.40$ \\ \hline \end{center} \caption{Electron efficiency and rejection factor for several values of the BDT threshold, for $1.35 < \mid \eta \mid < 1.5$} \label{tab:effrej2} \end{longtable} } % end footnotesize}$
${{\footnotesize \begin{longtable} \begin{center} \hline Cut value & Efficiency ($\%$) & Rejection (\small $\times 10^{5}$)\\\hline\hline 0.58 & $ 73.05 \pm 0.30 $ & 0.4 $\pm 0.03$ \\ 0.78 & $ 65.90 \pm 0.30 $ & 1.60 $\pm 0.3$ \\ 0.81 & $ 61.20 \pm 0.30 $ & 2.30 $\pm 0.44$ \\ 0.83 & $ 55.80 \pm 0.30 $ & 2.85 $\pm 0.60$ \\ 0.84 & $ 52.50 \pm 0.30 $ & 3.40 $\pm 0.80$ \\ \hline \end{center} \caption{Electron efficiency and rejection factor for several values of the BDT threshold, for $1.5 < \mid \eta \mid < 1.8$} \label{tab:effrej3} \end{longtable} } % end footnotesize}$	${{\footnotesize \begin{longtable} \begin{center} \hline Cut value & Efficiency & Rejection (\small $\times 10^{5}$) \\ \hline\hline 0.58 & $ 68.03 \pm 0.30 $ & $0.30 \pm 0.03$ \\ 0.73 & $ 65.30 \pm 0.40 $ & $1.09 \pm 0.20$ \\ 0.79 & $ 61.05 \pm 0.40 $ & $2.03 \pm 0.45$ \\ 0.83 & $ 54.60 \pm 0.40 $ & $3.70 \pm 1.10$ \\ \hline %\end{center} \caption{Electron efficiency and rejection factor for several values of the BDT threshold, for $1.8<\mid \eta \mid < 2.0$} \label{tab:effrej4} \end{center} \end{longtable} } % end footnotesize}$
${{\footnotesize \begin{longtable} \begin{center} \hline Cut value & Efficiency & Rejection (\small $\times 10^{5}$) \\ \hline\hline 0.52 & $ 73.02 \pm 0.30 $ & 0.3 $\pm 0.02$ \\ 0.73 & $ 70.50 \pm 0.30 $ & 1.08 $\pm 0.13$ \\ 0.80 & $ 65.55 \pm 0.30 $ & 1.90 $\pm 0.30$ \\ 0.83 & $ 60.60 \pm 0.30 $ & 2.70 $\pm 0.53$ \\ \hline \end{center} \caption{Electron efficiency and rejection factor for several values of the BDT threshold, for $2.0<\mid \eta \mid < 2.35$} \label{tab:effrej5} \end{longtable} } % end footnotesize}$	${{\footnotesize \begin{table} \begin{center} \hline Cut value & Efficiency ($\%$) & Rejection (\small $\times 10^{5}$)\\\hline\hline 0.60 & $ 70.03 \pm 0.50 $ & 0.40 $\pm 0.05$ \\ 0.78 & $ 65.09 \pm 0.50 $ & 1.50 $\pm 0.40$ \\ 0.80 & $ 60.50 \pm 0.50 $ & 2.35 $\pm 0.80$ \\ 0.84 & $ 56.60 \pm 0.50 $ & 2.64 $\pm 0.90$ \\ \hline \end{center} \caption{Electron efficiency and rejection factor for several values of the BDT threshold, for $2.35<\mid \eta \mid < 2.47$} \label{tab:effrej6} \end{table} } % end footnotesize}$

How to use the electron BDT in your analysis

Starting release 15, in order to use the BDT, one needs to access egammaPID::AdaBoot . In order to have the output between 0 and 1, you will need to rescale it as follows: ${\begin{center} \begin{displaymath} BDT Score = \frac{BDT Score - BDTLow}{BDTHigh + BDTLow} \end{displaymath} \end{center}}$

The values of BDTLow and BDTHigh are shown below for each ${\eta}$ bin separately.

${{\footnotesize \begin{longtable} \begin{center} \begin{tabular}{|c|c|c|} \hline $\mid \eta \mid $ & BDTLow & BDTHigh \\ \hline\hline 0.0 - 0.8 & -34.84 & 34.84 \\ 0.8 - 1.35 & -26.23 & 24.28 \\ 1.35 - 1.5 & -183.12 & 170.78\\ 1.5 - 1.8 & -98.80 & 94.93\\ 1.8 - 2.0 & -160.08 & 161.18 \\ 2.0 - 2.35 & -35.95 & 397.54\\ 2.35 - 2.47 & -348.94 & 356.23\\ \hline \end{tabular} \end{center} \caption{Values for BDTLow and BDTHigh in several $\eta$ bins} \label{tab:bdtscore} \end{longtable} } % end footnotesize}$

Documentation

ATLAS Note

Major updates:
-- KamalBenslama - 26 Feb 2009

%RESPONSIBLE% kamalbenslama
%REVIEW% Never reviewed

-- KamalBenslama - 17 Mar 2009
Latex rendering error!! dvi file was not created.

Topic revision: r5 - 2009-03-18 - YaoMing

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