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Page 1: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Constraining Effective FieldTheories with Machine Learning

ATLAS ML workshop, October 15-17 2018

Gilles Louppe [email protected]

with Johann Brehmer, Kyle Cranmer and Juan Pavez.

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Page 2: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

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Refs: GaltonBoard.com 1 / 24

Page 3: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

The probability of ending in bin corresponds to the total probability of all the

paths from start to .

x

z x

p(x∣θ) = p(x, z∣θ)dz = θ (1 − θ)∫ (n

x) x n−x

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Page 4: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

What if we shift or remove some of the pins?

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Page 5: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

The probability of ending in bin still corresponds to the total probability of all the

paths from start to :

But this integral can no longer be simpli�ed analytically!

As grows larger, evaluating becomes intractable since the number of

paths grows combinatorially.

Generating observations remains easy: drop balls.

x

z x

p(x∣θ) = p(x, z∣θ)dz∫

n p(x∣θ)

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Page 6: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

The Galton board is a metaphore for the simulator-based scienti�c method:

the Galton board device is the equivalent of the scienti�c simulator

are parameters of interest

are stochastic execution traces through the simulator

are observables

Inference in this context requires likelihood-free algorithms.

θ

z

x

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Page 7: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

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Credits: Johann Brehmer 6 / 24

Page 8: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

The Galton board of particle physics

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Page 9: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Treat the simulator as a black box

Histograms of observables,Approximate Bayesiancomputation.

Rely on summary statistics.

Machine learning algorithms

Density estimation, Cᴀʀʟ,autoregressive models, normalizing�ows, etc.

Use latent structure

Matrix Element Method, OptimalObservables, Showerdeconstruction, EventDeconstruction.

Neglect or approximate shower +detector, explicitly calculate integral.

*new* Mining gold from thesimulator.

Leverage matrix-element information +Machine Learning.

Likelihood-free inference methods

z

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Page 10: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Mining gold from simulators

is usually intractable.

What about ?

p(x∣θ)

p(x, z∣θ)

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Page 11: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

This can be computed as the ball falls down the board!

p(x, z∣θ) = p(z ∣θ)p(z ∣z , θ) … p(z ∣z , θ)p(x∣z , θ)1 2 1 T <T ≤T

= p(z ∣θ)p(z ∣θ) … p(z ∣θ)p(x∣z )1 2 T T

= p(x∣z ) θ (1 − θ)T

t

∏ z t 1−z t

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Page 12: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

As the trajectory and the observable are emitted, it is often

possible:

to calculate the joint likelihood ;

to calculate the joint likelihood ratio ;

to calculate the joint score .

We call this process mining gold from your simulator!

z = z , ..., z 1 T x

p(x, z∣θ)

r(x, z∣θ , θ )0 1

t(x, z∣θ ) = ∇ log p(x, z∣θ)0 θ ∣∣θ 0

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Page 13: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Rᴀsᴄᴀʟ

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Refs: Brehmer et al, 2018 (arXiv:1805.12244) 12 / 24

Page 14: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Constraining Effective FieldTheories, effectively

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Page 15: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

LHC processes

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Credits: Johann Brehmer 14 / 24

Page 16: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

LHC processes

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Credits: Johann Brehmer 14 / 24

Page 17: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

LHC processes

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Credits: Johann Brehmer 14 / 24

Page 18: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

LHC processes

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Credits: Johann Brehmer 14 / 24

Page 19: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

p(x∣θ) = p(z ∣θ)p(z ∣z )p(z ∣z )p(x∣z )dz dz dz

intractable

∭ p s p d s d p s d

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Page 20: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Key insights:

The distribution of parton-level momenta

where and are the total and differential cross sections, is tractable.

Downstream processes , and do not depend on .

This implies that both and can be mined. E.g.,

p(z ∣θ) = ,pσ(θ)

1dz p

dσ(θ)

σ(θ) dz p

dσ(θ)

p(z ∣z )s p p(z ∣z )d s p(x∣z )d θ

⇒ r(x, z∣θ , θ )0 1 t(x, z∣θ )0

r(x, z∣θ , θ )0 1 = =

p(z ∣θ )p 1

p(z ∣θ )p 0

p(z ∣z )s p

p(z ∣z )s p

p(z ∣z )d s

p(z ∣z )d s

p(x∣z )d

p(x∣z )d

p(z ∣θ )p 1

p(z ∣θ )p 0

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Page 21: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Proof of concept

Higgs production in weak boson fusion

Goal: Constraints on two theory parameters:

L = L + (D ϕ) σ D ϕ W − (ϕ ϕ) W WSM

Λ2

f W

2ig μ † a ν

μνa

Λ2

f WW

4g2

†μνa μν a

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Credits: Johann Brehmer 17 / 24

Page 22: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Precise likelihood ratio estimates

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Credits: Johann Brehmer 18 / 24

Page 23: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Increased data ef�ciency

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Credits: Johann Brehmer 19 / 24

Page 24: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Better sensitivity

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Credits: Johann Brehmer 20 / 24

Page 25: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Stronger bounds

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Credits: Johann Brehmer 21 / 24

Page 26: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

SummaryMany LHC analysis (and much of modern science) are based on "likelihood-free" simulations.

New inference algorithms:

Leverage more information from the simulator

Combine with the power of machine learning

First application to LHC physics: stronger EFT constraints with lesssimulations.

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Page 27: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

Collaborators

   

Johann Brehmer, Kyle Cranmer and Juan Pavez

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Page 28: Constraining Effective Field Theories with Machine Learning · Constraining Effective Field Theories with Machine Learning ATLAS ML workshop, October 15-17 2018 Gilles Louppe g.louppe@uliege.be

ReferencesStoye, M., Brehmer, J., Louppe, G., Pavez, J., & Cranmer, K. (2018). Likelihood-free inference with an improved cross-entropy estimator. arXiv preprintarXiv:1808.00973.

Brehmer, J., Louppe, G., Pavez, J., & Cranmer, K. (2018). Mining gold fromimplicit models to improve likelihood-free inference. arXiv preprintarXiv:1805.12244.

Brehmer, J., Cranmer, K., Louppe, G., & Pavez, J. (2018). Constraining EffectiveField Theories with Machine Learning. arXiv preprint arXiv:1805.00013.

Brehmer, J., Cranmer, K., Louppe, G., & Pavez, J. (2018). A Guide to ConstrainingEffective Field Theories with Machine Learning. arXiv preprintarXiv:1805.00020.

Cranmer, K., Pavez, J., & Louppe, G. (2015). Approximating likelihood ratioswith calibrated discriminative classi�ers. arXiv preprint arXiv:1506.02169.

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The end.

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