  Reconstructing jets, which provide vital insights into the properties and
histories of subatomic particles produced in high-energy collisions, is a main
problem in data analyses in collider physics. This intricate task deals with
estimating the latent structure of a jet (binary tree) and involves parameters
such as particle energy, momentum, and types. While Bayesian methods offer a
natural approach for handling uncertainty and leveraging prior knowledge, they
face significant challenges due to the super-exponential growth of potential
jet topologies as the number of observed particles increases. To address this,
we introduce a Combinatorial Sequential Monte Carlo approach for inferring jet
latent structures. As a second contribution, we leverage the resulting
estimator to develop a variational inference algorithm for parameter learning.
Building on this, we introduce a variational family using a pseudo-marginal
framework for a fully Bayesian treatment of all variables, unifying the
generative model with the inference process. We illustrate our method's
effectiveness through experiments using data generated with a collider physics
generative model, highlighting superior speed and accuracy across a range of
tasks.
