Computing the Bayes-optimal classifier and exact maximum likelihood estimator with a semi-realistic generative model for jet physics

Deep learning techniques have proven to be extremely effective in studying complicated, collimated sprays of particles found in high energy particle collisions known as jets. As with most realistic classification tasks, the Bayes-optimal classifier is unknown or intractable, even when trained with simulated data. Here we consider Ginkgo, a semi-realistic simulator for jets that captures the essential physics and produces data with similar features and format. By using a recently-developed hierarchical trellis data structure and dynamic programming algorithm, we are able to exactly marginalize over the combinatorically large space of latent variables associated to this generative model. This allows us to compute the Bayes-optimal classifier and the exact maximum likelihood estimator for this model, which can serve as a powerful benchmarking tool for studying the performance of machine learning approaches to these problems.