Accelerated cross-section predictions with XSEC
Jeriek Van den Abeele
Tools 2020
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@JeriekVda
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Based on arXiv:2006.16273 with A. Buckley, A. Kvellestad, A. Raklev, P. Scott, J. V. Sparre, and I. A. Vazquez-Holm
IP2I, Lyon
Global fits address the need for a consistent comparison of BSM theories to all relevant experimental data
Challenge:
Scanning increasingly high-dimensional parameter spaces with varying phenomenology
Exploration of a combined likelihood function:
L=Lcollider× LHiggs× LDM× LEWPO× Lflavour×…
See GAMBIT talk Friday!
Global fits address the need for a consistent comparison of BSM theories to all relevant experimental data
Challenge:
Scanning increasingly high-dimensional parameter spaces with varying phenomenology
Exploration of a combined likelihood function:
L=Lcollider× LHiggs× LDM× LEWPO× Lflavour×…
Global fits need quick, but sufficiently accurate theory predictions
BSM scans today easily require ∼107 samples or more
Higher-order BSM production cross-sections and theoretical uncertainties make a significant difference!
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[GAMBIT, 1705.07919]
CMSSM
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[hep-ph/9610490]
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Existing higher-order evaluation tools are insufficient for large MSSM scans
- Prospino/MadGraph: full calculation, minutes/hours per point
- N(N)LL-fast: fast grid interpolation, but only degenerate squark masses
pp→g~g~, g~q~i, q~iq~j,
q~iq~j∗, b~ib~i∗, t~it~i∗
at s=13 TeV
xsec 1.0 performs smart regression for strong SUSY processes at the LHC
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- New Python tool for NLO cross-section predictions within seconds
A. Buckley, A. Kvellestad, A. Raklev, P. Scott, J. V. Sparre, JVDA, I. A. Vazquez-Holm
- Pointwise estimates of PDF, αs and scale uncertainties, in addition to the subdominant regression uncertainty
- Future expansions: other processes, more CoM energies, higher-order corrections, ...
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$$$
A quick sketch
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Interpolation ...
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Interpolation ... doesn't give prediction uncertainty!
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Correlation length-scale
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Correlation length-scale
Estimate from data!
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Correlation length-scale
Estimate from data!
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Correlation length-scale
Gaussian process prediction with uncertainty
Estimate from data!
prior distribution over all functions
with the estimated smoothness
The Bayesian Way: quantify beliefs with probability
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prior distribution over all functions
with the estimated smoothness
posterior distribution over functions
with updated m(x)
data
The Bayesian Way: quantify beliefs with probability
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Let's make some draws from this prior distribution
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Let's make some draws from this prior distribution
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Let's make some draws from this prior distribution
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Let's make some draws from this prior distribution
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Let's make some draws from this prior distribution
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Let's make some draws from this prior distribution
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Let's make some draws from this prior distribution
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Let's make some draws from this prior distribution
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At each input point, we obtain a distribution of possible function values (prior to looking at data)
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At each input point, we obtain a distribution of possible function values (prior to looking at data)
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At each input point, we obtain a distribution of possible function values (prior to looking at data)
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A Gaussian process sets up an infinite number of correlated Gaussians, one at each parameter point
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We obtain a posterior by conditioning on known data
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target function
We obtain a posterior by conditioning on known data
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target function
We obtain a posterior by conditioning on known data
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We obtain a posterior by conditioning on known data
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Make posterior predictions at new points by computing correlations to known points
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Make posterior predictions at new points by computing correlations to known points
Posterior predictive distributions are Gaussian too
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Squared Exponential kernel
Matérn-3/2 kernel
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Different kernels lead to different function spaces to marginalise over
Workflow
Generating data
Random sampling
SUSY spectrum
Cross-sections
Optimise kernel hyperparameters
Training GPs
GP predictions
Input parameters
Linear algebra
Cross-section
estimates
Compute covariances between training points
Workflow
Generating data
Random sampling
SUSY spectrum
Cross-sections
Optimise kernel hyperparameters
Training GPs
GP predictions
Input parameters
Linear algebra
Cross-section
estimates
XSEC
Compute covariances between training points
Training scales as O(n3), prediction as O(n2)
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A balancing act
Random sampling with different priors, directly in mass space
Evaluation speed
Sample coverage
Need to cover a large parameter space
Distributed Gaussian processes
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[Liu+, 1806.00720]
Distributed Gaussian Processes
Divide-and-conquer approach for dealing with large datasets
- Make local predictions with smaller data subsets
- Compute a weighted average of these predictions
The exact weighting procedure is important, to ensure
- Smooth final predictions
- Valid regression uncertainties
"Generalized Robust Bayesian Committee Machine"
Validation results
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Gluino-gluino
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Gluino-squark
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Squark-squark
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Squark-antisquark
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Fast estimate of SUSY (strong) production cross- sections at NLO, and uncertainties from
- regression itself
- renormalisation scale
- PDF variation
- αs variation
Goal
pp→g~g~, g~q~i, q~iq~j,
q~iq~j∗, b~ib~i∗, t~it~i∗
Interface
Method
Pre-trained, distributed Gaussian processes
Python tool with command-line interface
Processes
at s=13 TeV
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Tutorial on Friday!
Thank you!
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Backup slides
Some linear algebra
Regression problem, with 'measurement' noise:
y=f(x)+ε, ε∼N(0,σn2)→ infer f, given data D={X,y}
Assume covariance structure expressed by a kernel function, like
Consider the data as a sample from a multivariate Gaussian distribution
[x1,x2,…]
[y1,y2,…]
signal kernel
white-noise kernel
Some linear algebra
Regression problem, with 'measurement' noise:
y=f(x)+ε, ε∼N(0,σn2)→ infer f, given data D={X,y}
Training: optimise kernel hyperparameters by maximising the marginal likelihood
Posterior predictive distribution at a new point x∗ :
with
Implicit integration over points not in X
[
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Scale-dependence of LO/NLO
[Beenakker+, hep-ph/9610490]
Accelerating cross-section predictions with XSEC
By jeriek
Accelerating cross-section predictions with XSEC
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