Learning do discover: machine learning in high-energy physics

B. Kégl / AppStat@LAL Learning to discover
LEARNING TO DISCOVER:
MACHINE LEARNING IN HIGH-ENERGY PHYSICS
Linear Accelerator Laboratory and Computer Science Laboratory

CNRS/IN2P3 & University Paris-S{ud,aclay}
BALÁZS KÉGL
CERN, May 13, 2014
1

OUTLINE
• What is machine learning?

• Three projects to illustrate data science in HEP

• budgeted learning for triggers (LHCb)

• classiﬁcation for discovery and the HiggsML challenge (ATLAS)

• deep learning for imaging calorimeters (ILC)

• Concluding remarks

• interdisciplinarity: HEP, ML, data science
2

WHAT IS MACHINE LEARNING?
• “The science of getting computers to act without being
explicitly programmed” - Andrew Ng (Stanford/Coursera)

• part of standard computer science curriculum since the 90s

• inferring knowledge from data

• generalizing to unseen data

• usually no parametric  
model assumptions

• emphasizing the computational 
challenges
Machine
Learning
Statistics
Optimization
Artiﬁcial
intelligence
Neuroscience
Cognitive
science
Signal
processing
Information
theory
Statistical
physics
3

MACHINE LEARNING TAXONOMY
• Supervised learning: non-parametric (model-free) input - output
functions

• classiﬁcation (Trees, BDT, SVM, NN) - what you call MVA

• regression (Trees, NN, Gaussian Processes)

• Unsupervised learning: non-parametric data representation

• clustering (k-means, spectral clustering, Dirichlet processes)

• dimensionality reduction (PCA, ISOMAP, LLE, auto-associative NN)

• density estimation (kernel density, Gaussian mixtures, the Boltzmann machine)

• Reinforcement learning:

• learning + dynamic control: learn to behave in an environment to maximize cumulative
reward
4

CLASSIFICATION
Character recognition
5

CLASSIFICATION
Emotion recognition
6

CLASSIFICATION
Speech recognition
7

CLASSIFICATION
• Input: a usually high dimensional vector x

• Output: a category (label, class) y

• Usually no parametric model

• the classiﬁcation function y = g(x) is learned using a training set  
D = {(x1,y1), . . . , (xn,yn)}

• Well-tested algorithms:

• neural networks, support vector machines, boosting
8

CLASSIFICATION
The only goal is a low probability of error

P(g(x) = y)

on previously unseen examples (x, y)
9

BUDGETED CLASSIFICATION
Real time face detection
10

Real time web page ranking
11

Real time ad placement
12

Real time signal/background separation
13

The second goal is the fast execution of

g(x)
14

Trade-off between quality and speed
15

• Time constraints

• Memory constraints

• Consumption constraints

• Communication constraints
16

Learning deep decision DAGs in a
{djalel.benbouzid,busarobi,balazs.kegl}@
Original motivation
Before...
•
Stage 1
Stage 2
Stage 3
Stage 4
The common design:

cascade classiﬁcation = trigger with levels
easy background
medium background
hard background
signal/very hard backgroundViola-Jones CVPR 2001 17

THE LHCB TRIGGER
• Collaboration with

• Vava Gligorov (CERN)

• Mike Williams (MIT)

• Djalel Benbouzid (LAL)
18

THE LHCB TRIGGER
• A beautifully complex problem

• varying feature costs

• cost may depend on the value

• events are bags of overlapping candidates
19

THE LHCB TRIGGER
Immediate cost
Bag-dependent cost
Value-dependent cost
D0_VTX_FD
PiS_IP
D0C_1_IP
D0C_2_IP
D0C_2_PTD0C_1_PT PiS_PT
D0C_2_IPC
D0C_2_TFC
D0C_1_IPC
D0C_1_TFC
PiS_IPC
PiS_TFCDstMD0MD0Tau
20

MDDAG: A SIGNAL/BCKG DECISION GRAPH
Easy background
Background-like Signal-like
EVALUATE
Benbouzid et al. ICML 2012
0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
21

QUIT
Benbouzid et al. ICML 2012
Easy background
0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
22

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
Easy background Benbouzid et al. ICML 201223

Hard background Benbouzid et al. ICML 2012
0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
EVALUATE
24

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
SKIP
25

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPCEVALUATE
26

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
EVALUATE
27

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
EVALUATE
28

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
EVALUATE
29

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
SKIP
30

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
EVALUATE
31

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
SKIP
32

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
SKIP
SKIP
SKIP
SKIP
33

Easy signal Benbouzid et al. ICML 2012
0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
EVALUATE
34

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
QUIT
35

0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
36

Hard signal Benbouzid et al. ICML 2012
0ms
1.5ms
4ms
D0C_2_IP
D0_VTX_FD
PiS_IP
D0C_1_IP
PiS_PT
D0C_1_PT
D0C_2_PT
∞
D0Tau
D0M
DstM
D0C_1_TFC
PiS_TFC2
D0C_1_IPC
PiS_IPC2
D0C_2_TFC
D0C_2_IPC
EVAL
EVAL EVAL
EVAL
EVAL EVAL
EVAL EVAL
SKIP
SKIP
SKIP
SKIP
SKIP
37

• Classiﬁcation with test-time constraints

• An active research area due to IT applications

• To be exploited for trigger design
38

CLASSIFICATION FOR DISCOVERY
Challenge 1: estimation la plus précise et en un temps CPU minimal de
la masse du candidat boson de Higgs en fonction des observables de
l’événement, et malgré les particules non mesurées. Précision actuelle
(intégration avec chaine de Markov en dimension 5) ~20% en 0.1s par
événement
The HiggsML challenge
39

• In a nutshell

• A vector x of variables is extracted from each event

• A classiﬁer g(x) is trained to separate signal from background

• The background b is estimated in the selection region  
G = {x : g(x) = s}

• Discovery is made when the number of real events n is signiﬁcantly
higher than b
40

• Exciting physics

• The Higgs to tau-tau excess is not yet at ﬁve sigma 
Tech. Rep.ATLAS-CONF-2013-108

• Exciting data science (statistics and machine learning)

• What is the theoretical relationship between classiﬁcation and test
sensitivity?

• What is the quantitative criteria to optimize?

• How to formally include systematic uncertainties?

• Can we redesign classical algorithms (boosting, SVM, neural nets) for
optimizing this criteria? 41

We are organizing a  
data challenge  
to answer some of these
questions
Center for Data Science
Paris-Saclay
the HiggsML challenge
May to September 2014
When High Energy Physics meets Machine Learning
Joerg Stelzer - Atlas-CERN
Marc Schoenauer - INRIA
Balázs Kégl - Appstat-LAL
Cécile Germain - TAO-LRI
David Rousseau - Atlas-LAL
Glen Cowan - Atlas-RHUL
Isabelle Guyon - Chalearn
Claire Adam-Bourdarios - Atlas-LAL
Thorsten Wengler - Atlas-CERN
Andreas Hoecker - Atlas-CERN
Organization committee Advisory committee
info to participate and compete : https://www.kaggle.com/c/higgs-boson
42

The formal setup
• We simulate data: D = (x1, y1, w1), . . . , (xn, yn, wn)
• xi 2 Rd
is the feature vector
• yi 2 {background, signal} is the label
• wi 2 R+
is a non-negative weight (importance sampling)
• let S = {i : yi = s} and B = {i : yi = b} be the index sets of signal
and background events, respectively
• Maximize the Approximate Median Signiﬁcance
G. Cowan, K. Cranmer, E. Gross, and O. Vitells. EPJ C, 71:1554, 2011.
AMS =
r
2
⇣
(s + b) ln
⇣
1 +
s
b
⌘
s
⌘
⇡
s
p
b
• bG = i : g(xi) = s
• s =
P
i2S bG wi
• b =
P
i2B bG wi 43

How to design g to maximize the sensitivity?
• A two-stage approach
1. optimize a discriminant (score) function f : Rd
! R using a classical
learning algorithm (BDT, NN)
Signal
Background
44

Signal
Background
45

Signal
Background
46

• A two-stage approach (make ﬁgure with score)
2. deﬁne g(x) = sign f(x) ✓ and optimize ✓ for maximizing the AMS
θ
3.5σ
47

Comparing with Atlas analysis
• Atlas does a manual pre-selection (category), the ﬁrst maximum of
the AMS is completely eliminated. Why?
s = 250

b = 5000 ± 500!
Systematics!
48

How to handle systematic (model) uncertainties?
• OK, so let’s design an objective function that can take background
systematics into consideration
• Likelihood with unknown background b ⇠ N(µb, b)
L(µs, µb) = P(n, b|µs, µb, b) =
(µs + µb)n
n!
e (µs+µb) 1
p
2⇡ b
e (b µb)2
/2 b
2
• Proﬁle likelihood ratio (0) =
L(0, ˆˆµb)
L(ˆµs, ˆµb)
• The new Approximate Median Signiﬁcance (by Glen Cowan)
AMS =
s
2
✓
(s + b) ln
s + b
b0
s b + b0
◆
+
(b b0)2
b
2
where
b0 =
1
2
⇣
b b
2
+
p
(b b
2)2 + 4(s + b) b
2
⌘
49

How to handle systematic (model) uncertainties?
• The new Approximate Median Signiﬁcance
AMS =
s
2
✓
(s + b) ln
s + b
b0
s b + b0
◆
+
(b b0)2
b
2
where
b0 =
1
2
⇣
b b
2
+
p
(b b
2)2 + 4(s + b) b
2
⌘
New AMS
ATLAS
Old AMS
50

Paris-Saclay
A tool for getting  
the ML community excited
about your problem
OPEN
since yesterday
51

Paris-Saclay
• Organizing committee

• David Rousseau (ATLAS / LAL)

• Balázs Kégl (AppStat / LAL)

• Cécile Germain (LRI / UPSud)

• Glen Cowan (ATLAS / Royal Holloway)

• Claire Adam Bourdarios (ATLAS / LAL)

• Isabelle Guyon (ChaLearn)
52

Paris-Saclay
• Ofﬁcial ATLAS GEANT4 simulations

• 30 features (variables)

• 250K training: input, label, weight

• 100K public test (AMS displayed real-time),
only input

• 450K private test (to determine the winner
after the closing of the challenge), only input

• public and private tests set are shufﬂed,
participants submit a vector of 550K labels

• Using the “old” AMS

• cannot compare participants  
if the metric varies a lot 
53

Paris-Saclay
• 16K$ prize pool

• 7-4-2K$ for the three top
participants

• HEP meets ML award for the most
useful model, decided by the ATLAS
members of the organizing
committee
54

LEADERBOARD AS OF THIS MORNING
55

LEARNING FROM SCRATCH:
THE DEEP LEARNING REVOLUTION
Why don’t we train a neural network on the

raw ~105-108 dimensional signal of ATLAS? 
56

• Because it is notoriously difﬁcult to automatically build a model  
= learn particle physics just by looking at the event browser

• Again, you are not alone: it is also notoriously difﬁcult to
automatically build the model of natural scenes 
= learn a model of our surroundings by just looking at
images

• In the last 5-10 years, we are getting close

• May be interesting if you do not know what you are looking
for  
57

WHAT IS THIS?
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58

WHAT IS THIS?
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59

WHAT IS THIS?
60

WHAT IS THIS?
61

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PE
WHAT IS THIS?
62

WHAT IS THIS?
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MODELS
• Inference

• if you want to be able to answer questions about observed
phenomena, you need a model

• if you want quantitative answers, you need a formal model

• Formal setup

• x: observation vector, Θ: parameter vector to infer

• likelihood: p(x | Θ)

• simulator: given Θ, generate a random x
64

A FORMAL MODEL
Balázs Kégl/LAL 3
The observatory
Balázs Kégl / LAL 4
energy, direction, mass
X0, HEP
XMax, NMuMax, NMuTotal, LEP
LDF, asymmetry, S1000, S38, NMu1000
S, t0, risetime, jumps
Balázs Kégl/LAL
Cherenkov light
PEs given ideal response
name notation unit
expected number of PEs in bin i ¯ni unitless
number of PEs in bin i ni unitless
0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475
0
2
4
6
8
10
12
14
16
18
20
22
24
26
t ns⇥
PE
AL 11
Ideal muon response
name notation unit
signal decay time ⇤ ns
signal risetime td ns
muon arrival time tµ ns
muon tracklength Lµ m
muon energy factor µ unitless
avg number of PEs per 1 m tracklength ⇥ m 1
L⌅⇤⌅⇧t⇥
1⌥
td
⌃
td
L⌅ ⇤⌅ ⇧
⌃td
t⌅
0 25 50 75 100 125 150 175 200
0
2
4
6
8
10
12
14
16
18
20
22
24
26
t ns⇥
PE
p(x | t)
0 100 200 300 400 500 600 700 800
0
5
10
15
20
25
30
35
40
t @nsD
PE
p(x | t1,...t4) p(t | Θ)
65

INFERENCE BY SAMPLING
66

HOW TO BUILD MODELS FOR THESE?
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π
67

• Training multi-layer neural networks

• biological inspiration: we know the brain is multi-layer

• appealing from a modeling point of view: abstraction increases with
depth

• notoriously difﬁcult to train until Hinton et al. (stacked RBMs) and
Bengio et al. (stacked autoencoders), around 2006

• the key principle is (was?) unsupervised pre-training

• they remain computationally very expensive, but they learn high-
level (abstract) features and they scale: with more data they learn
more
68

• Google passes the “purring
test” (ICML’12)

• 16K cores watching 10M
youtube stills for 3 days

• completely unsupervised: the
cat has just appeared as a
useful concept to represent
69

• Can we also learn physics by observing natural
phenomena?
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DEEP LEARNING FOR IMAGING
CALORIMETERS
• Collaboration with

• Roman Poeschl (ILC / LAL)

• Naomi van der Kolk (ILC / LAL)

• Sviatoslav Bilokin (ILC / LAL)

• Mehdi Cherti (AppStat / LAL)

• Trong Hieu Tran (ILC / LLR)

• Vincent Boudry (ILC / LLR)
71

FOOD FOR THOUGHT 1:
CERN ACCELERATING SCIENCE
Data Science

!
Design of automated methods

to analyze massive and complex data

in order to extract useful information from them

72

Data science
statistics 
machine learning 
signal processing 
data visualization 
databases
Tool building
software engineering 
clouds/grids 
high-performance computing 
optimization
Domain science
life brain earth 
universe human society
FOOD FOR THOUGHT 1:
73

You have been doing data science for a long time
Consider transferring knowledge  
to other sciences on  
how to organize large scientiﬁc projects around data
FOOD FOR THOUGHT 1:
74

• What is a data challenge:

• outreach to public?

• peer-to-peer communication?
FOOD FOR THOUGHT II:
75

• What is a data challenge:

• between the two: communicating (translating!) your technical
problems to another scientiﬁc community which might have solutions
(and know-how to design solutions) for you

• think about building formal channels (as you did for outreach and
“classical” publications)
FOOD FOR THOUGHT II:
76

THANK YOU!
77

BACKUP
78

1. optimize a discriminant function f : Rd
! R for balanced AUC or
balanced classiﬁcation error: N0
s = N0
b = 0.5
Tree, N = 2., T = 100000
1 10 100 1000 104
0.00
0.05
0.10
0.15
0.20
0.25
T
balancederror
AdaBoost learning curves
79

Comparing with the ofﬁcial Atlas analysis
• Atlas does a manual pre-selection, the ﬁrst maximum of the AMS is
completely eliminated. Why? Have we found something, or they have
an implicit reason?
• No we haven’t, yes they have
• µb has a ⇠ 10% relative systematic uncertainty: the 300 signals are
completely submerged by the = 600 background systematics
AMS = 1s
AMS = 2s
AMS = 3s
AMS = 4s
AMS = 5s
0 2000 4000 6000 8000 10000 12000
0
100
200
300
400
500
b HFPL
sHTPL
Unnormalized ROC
1 / 1
80

The Higgs boson ML challenge
• Dilemma: the physically relevant AMS is optimized in a tiny region
• the AMS has a high variance: a bad measure to compare the
participants
• in the Atlas analysis, there was 1 between the expected and
measured signiﬁcances
1 / 1
81

The Higgs boson ML challenge
• We are even nervous about the original AMS (red), so we regularize it
AMS =
s
2
✓
(s + b + breg) ln
✓
1 +
s
b + breg
◆
s
◆
with breg = 10
1 / 1
82

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Learning do discover: machine learning in high-energy physics