Metric Methods with Open Collider Data Machine Learning and the - PowerPoint PPT Presentation

Metric Methods with Open Collider Data Machine Learning and the Physical Sciences, NeurIPS 2019 Eric M. Metodiev Center for Theoretical Physics Massachusetts Institute of T echnology Patrick Radha Preksha Jesse Komiske Mastandrea Naik Thaler

Collision Course LHC Event recorded by the CMS Experiment at CERN Eric M. Metodiev, MIT Metric Methods with Open Collider Data 2

Collision Course New Unsupervised Optimal Transport Collider Analyses [OTML Workshop, NeurIPS 2019] New Insights into Public Collider Data Quantum Field Theory [opendata.cern.ch] [h/t Jesse Thaler] Eric M. Metodiev, MIT Metric Methods with Open Collider Data 3

opendata.cern.ch Eric M. Metodiev, MIT Metric Methods with Open Collider Data 4

CMS Open Data 𝜚 𝜚 Download a CMS “AOD” file: 2011A Jet Primary Dataset 𝜃 𝜃 A real collision event recorded by CMS! Fifteen lines of code later… Thanks to the uproot package! Eric M. Metodiev, MIT Metric Methods with Open Collider Data 5

When are two collisions similar? 𝜚 𝜚 𝜃 𝜃 Eric M. Metodiev, MIT Metric Methods with Open Collider Data 6

When are two collisions similar? 𝜚 𝜚 The Earth Mover’s (or Wasserstein) Distance 𝜃 𝜃 The “work” required to rearrange one collision event into another! Plus a cost to create or destroy energy. Optimal Transport Problem Here using python optimal transport [Komiske, EMM , Thaler , PRL 2019] Eric M. Metodiev, MIT Metric Methods with Open Collider Data 7

Six Decades of Collider Techniques Taming infinities Event Shapes Jet Algorithms Jet Substructure Pileup 1960 2020 1997-1998 1977 2014-2019 C/A jet clustering Constituent Subtraction Thrust, Sphericity [Wobisch, Wengler, 1998] [Berta, Spousta, Miller, Leitner, JHEP 2014] [Farhi, PRL 1977] [Doskhitzer, Leder, Moretti,Webber, JHEP 1997] 2010-2015 [Berta, Masetti, Miller, Spousta, JHEP 2019] [Georgi, Machacek, PRL 1977] 1993 1962-1964 N-(sub)jettiness, XCone And many more! Infrared Safety 𝑙 𝑈 jet clustering [Stewart, Tackmann, Waalewijn, PRL 2010] [Kinoshita, JMP 1962] [Ellis, Soper, PRD 1993] [Thaler, Van Tilburg, JHEP 2011] [Lee, Nauenberg, PR 1964] [Catani, Dokshitzer, Seymour, Webber, NPB 1993] [Stewart, Tackmann, Thaler, Vermilion, Wilkason, JHEP 2015] Eric M. Metodiev, MIT Metric Methods with Open Collider Data 8

Six Decades of Collider Techniques as Optimal Transport! [Komiske, EMM , Thaler, to appear ] Smooth function of energy Jets are N-particle event Subtract a pileup as a Event shapes as distances distribution are finite in QFT approximations uniform distribution to the 2-particle manifold EMD ℰ , ℰ ’ < 𝜀 ℐ ℰ = argmin EMD(ℰ , ℰ ’ ) 𝑢 ℰ = min ℰ ′ =2 EMD(ℰ , ℰ ’ ) ℰ − 𝒱 ℰ ′ =𝑂 → |𝓟 ℰ) − 𝓟(ℰ ’ | < 𝜗 Taming infinities Event Shapes Jet Algorithms Jet Substructure Pileup 1960 2020 1997-1998 1977 2014-2019 C/A jet clustering Constituent Subtraction Thrust, Sphericity [Wobisch, Wengler, 1998] [Berta, Spousta, Miller, Leitner, JHEP 2014] [Farhi, PRL 1977] [Doskhitzer, Leder, Moretti,Webber, JHEP 1997] 2010-2015 [Berta, Masetti, Miller, Spousta, JHEP 2019] [Georgi, Machacek, PRL 1977] 1993 1962-1964 N-(sub)jettiness, XCone And many more! Infrared Safety 𝑙 𝑈 jet clustering [Stewart, Tackmann, Waalewijn, PRL 2010] [Kinoshita, JMP 1962] [Ellis, Soper, PRD 1993] [Thaler, Van Tilburg, JHEP 2011] [Lee, Nauenberg, PR 1964] [Catani, Dokshitzer, Seymour, Webber, NPB 1993] [Stewart, Tackmann, Thaler, Vermilion, Wilkason, JHEP 2015] Eric M. Metodiev, MIT Metric Methods with Open Collider Data 9

Exploring the Space of Jets ℇ′ ℇ ′′ ℇ EMD(ℇ , ℇ′) + EMD ℇ ′ , ℇ ′′ ≥ EMD(ℇ , ℇ′′) Eric M. Metodiev, MIT Metric Methods with Open Collider Data 10

Most Representative Jets Jet Mass Histogram 𝜈 2 𝑁 𝑞 𝑗 Jet Mass: 𝑛 = σ 𝑗=1 Measures how “wide” the jet is. [Komiske, Mastandrea, EMM , Naik, Thaler, 1908.08542] Eric M. Metodiev, MIT Metric Methods with Open Collider Data 11

T owards Anomaly Detection Mean EMD to Dataset: 𝑂 ത 𝑅(ℇ) = ෍ EMD (ℇ, ℇ 𝑗 ) 𝑗=1 More Typical More Anomalous [Collins, Howe, Nachman, 1805.02664] Complements recent [Heimel, Kasieczka, Plehn, Thompson, 1808.08979] developments in anomaly [Farina, Nakai, Shih, 1808.08992] detection for collider physics. [Cerri, Nguyen, Pierini, Spiropulu, Vlimant, 1811.10276] Eric M. Metodiev, MIT Metric Methods with Open Collider Data 12

Visualizing the Manifold What does the space of jets look like? [van der Maaten, Hinton, JMLR 2008] t-SNE embedding Eric M. Metodiev, MIT Metric Methods with Open Collider Data 13

Visualizing the Manifold What does the space of jets look like? [van der Maaten, Hinton, JMLR 2008] t-SNE embedding: 25-medoid jets shown [Komiske, Mastandrea, EMM , Naik, Thaler, 1908.08542] Eric M. Metodiev, MIT Metric Methods with Open Collider Data 14

Visualizing the Manifold 𝜄 What does the space of jets look like? 𝐹 [van der Maaten, Hinton, JMLR 2008] t-SNE embedding: 25-medoid jets shown [Komiske, Mastandrea, EMM , Naik, Thaler, 1908.08542] Eric M. Metodiev, MIT Metric Methods with Open Collider Data 15

Correlation Dimension Experimental Data Conceptual Idea Theoretical Calculation 𝑂 neighbors 𝑠 ∝ 𝑠 dim 𝑂 𝑂 dim 𝑅 = 𝑅 𝜖 𝜖𝑅 ln ෍ ෍ Θ[EMD ℇ 𝑗 , ℇ 𝑘 < 𝑅] Dimension blows up at low energies. 𝑗=1 𝑘=1 [Komiske, Mastandrea, EMM , Naik, Thaler, 1908.08542] [Grassberger, Procaccia, PRL 1983] [Kegl, NeurIPS 2002] Eric M. Metodiev, MIT Metric Methods with Open Collider Data 16

Thank You! New Unsupervised Optimal Transport Collider Analyses [OTML Workshop, NeurIPS 2019] Publicly released New Insights into Public Collider Data jet dataset Quantum Field Theory [opendata.cern.ch] Eric M. Metodiev, MIT Metric Methods with Open Collider Data 17

Extra Slides Eric M. Metodiev, MIT Metric Methods with Open Collider Data 18

Exploring the Space of Jets ℇ′ ℇ ′′ ℇ EMD(ℇ , ℇ′) + EMD ℇ ′ , ℇ ′′ ≥ EMD(ℇ , ℇ′′) Eric M. Metodiev, MIT Metric Methods with Open Collider Data 19

When are two events similar? These two jets “look” similar, but have different numbers of particles, flavors, and locations. How do we quantify this? Jet 1 Jet 2 “Space of Jets” 400 GeV 𝑆 = 0.5 anti- 𝑙 𝑈 Jets from CMS Open Data Eric M. Metodiev, MIT Metric Methods with Open Collider Data 20

When are two events similar? How a jet gets its shape Detection 𝑞 Hadronization hadrons 𝜌 ± 𝐿 ± … Fragmentation partons 𝑕 𝑣 𝑒 … 𝑞 Collision Eric M. Metodiev, MIT Metric Methods with Open Collider Data 21

When are two events similar? An event is… Theoretically: very complicated Experimentally: very complicated However: The energy flow (distribution of energy) is the information that is robust to: fragmentation, hadronization, detector effects, … [N.A. Sveshnikov, F.V. Tkachov, 9512370] [F.V. Tkachov, 9601308] [P.S. Cherzor, N.A. Sveshnikov, 9710349] Energy flow  Infrared and Collinear (IRC) Safe information Eric M. Metodiev, MIT Metric Methods with Open Collider Data 22

When are two jets similar? Energy flow is robust information Detection 𝑞 Hadronization hadrons 𝜌 ± 𝐿 ± … Fragmentation partons 𝑕 𝑣 𝑒 … 𝑞 Collision 𝑁 Treat events as distributions of energy: ℇ(ො 𝑜) = ෍ 𝐹 𝑗 𝜀(ො 𝑜 − ො 𝑜 𝑗 ) 𝑗=1 Ignoring particle flavor, charge… energy direction Eric M. Metodiev, MIT Metric Methods with Open Collider Data 23

The Energy Mover’s Distance Review: The Earth Mover’s Distance Earth Mover’s Distance : the minimum “work” (stuff x distance) to rearrange one pile of dirt into another [Peleg, Werman, Rom] [Rubner, Tomasi, Guibas] Metric on the space of (normalized) distributions: symmetric, non-negative, triangle inequality Distributions are close in EMD  their expectation values are close. Also known as the 1- Wasserstein metric. Eric M. Metodiev, MIT Metric Methods with Open Collider Data 24

The Energy Mover’s Distance From Earth to Energy Energy Mover’s Distance : the minimum “work” ( energy x angle) to rearrange one jet (pile of energy) into another [Komiske, EMM , Thaler, 1902.02346] 𝑁 ′ 𝑁 ′ 𝑁 𝑁 𝐹 𝑗 𝜄 𝑗𝑘 𝜄 𝑗𝑘 EMD ℇ, ℇ ′ = min ′ 𝑔 𝑆 + ෍ 𝐹 𝑗 − ෍ 𝐹 {𝑔} ෍ ෍ ′ 𝐹 𝑗𝑘 𝑘 𝑘 𝑔 𝑗𝑘 𝑗=1 𝑘=1 𝑗=1 𝑘=1 Difference in Difference in radiation pattern total energy Eric M. Metodiev, MIT Metric Methods with Open Collider Data 25

The Energy Mover’s Distance From Earth to Energy Energy Mover’s Distance : the minimum “work” ( energy x angle) to rearrange one event (pile of energy) into another [Komiske, EMM , Thaler, 1902.02346] ℇ′ ℇ ′′ ℇ EMD(ℇ , ℇ′) + EMD ℇ ′ , ℇ ′′ ≥ EMD(ℇ , ℇ′′) EMD has dimensions of energy 1 True metric as long as 𝑆 ≥ 2 𝜄 max 𝑆 ≥ the jet radius, for conical jets Solvable via Optimal Transport problem. ~ 1 ms to compute EMD for two jets with 100 particles. Eric M. Metodiev, MIT Metric Methods with Open Collider Data 26