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We reframe common tasks in jet physics in probabilistic terms, including jet reconstruction, Monte Carlo tuning, matrix element – parton shower matching for large jet multiplicity, and efficient event generation of jets in complex, signal-like regions of phase space. We also introduce Ginkgo, a simplified, generative model for jets, that facilitates research into these tasks with techniques from statistics, machine learning, and combinatorial optimization. We also review some of the recent research in this direction that has been enabled with Ginkgo. We show how probabilistic programming can be used to efficiently sample the showering process, how a novel trellis algorithm can be used to efficiently marginalize over the enormous number of clustering histories for the same observed particles, and how the dynamic programming and reinforcement learning can be used to find the maximum likelihood clusterinng in this enormous search space. This work builds bridges with work in hierarchical clustering, statistics, combinatorial optmization, and reinforcement learning. 

Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function that can be used to characterize the quality of the clustering. In those cases, hierarchical clustering can be seen as a combinatorial optimization problem. To that end, we introduce a new approach based on A* search. We overcome the prohibitively large search space by combining A* with a novel \emph{trellis} data structure. This combination results in an exact algorithm that scales beyond previous state of the art, from a search space with 10^12 trees to 10^15 trees, and an approximate algorithm that improves over baselines, even in enormous search spaces that contain more than 10^1000 trees. We empirically demonstrate that our method achieves substantially higher quality results than baselines for a particle physics use case and other clustering benchmarks. We describe how our method provides significantly improved theoretical bounds on the time and space complexity of A* for clustering. 

Based on the established task of identifying boosted, hadronicallydecaying top quarks, we compare a wide range of modern machine learningapproaches. Unlike most established methods they rely on low-levelinput, for instance calorimeter output. While their networkarchitectures are vastly different, their performance is comparativelysimilar. In general, we find that these new approaches are extremelypowerful and great fun.