Learning tractable multidimensional Bayesian network classifiers

Multidimensional classification has become one of the most relevant topics in view of the many domains that require a vector of class values to be assigned to a vector of given features. The popularity of multidimensional Bayesian network classifiers has increased in the last few years due to their expressive power and the existence of methods for learning different families of these models. The problem with this approach is that the computational cost of using the learned models is usually high, especially if there are a lot of class variables. Class-bridge decomposability means that the multidimensional classification problem can be divided into multiple subproblems for these models. In this paper, we prove that class-bridge decomposability can also be used to guarantee the tractability of the models. We also propose a strategy for efficiently bounding their inference complexity, providing a simple learning method with an order-based search that obtains tractable multidimensional Bayesian network classifiers. Experimental results show that our approach is competitive with other methods in the state of the art and ensures the tractability of the learned models

Energy flow polynomials: A complete linear basis for jet substructure

We introduce the energy flow polynomials: a complete set of jet substructure observables which form a discrete linear basis for all infrared- and collinear-safe observables. Energy flow polynomials are multiparticle energy correlators with specific angular structures that are a direct consequence of infrared and collinear safety. We establish a powerful graph-theoretic representation of the energy flow polynomials which allows us to design efficient algorithms for their computation. Many common jet observables are exact linear combinations of energy flow polynomials, and we demonstrate the linear spanning nature of the energy flow basis by performing regression for several common jet observables. Using linear classification with energy flow polynomials, we achieve excellent performance on three representative jet tagging problems: quark/gluon discrimination, boosted W tagging, and boosted top tagging. The energy flow basis provides a systematic framework for complete investigations of jet substructure using linear methods.Comment: 41+15 pages, 13 figures, 5 tables; v2: updated to match JHEP versio