Variational Inference for Interacting Particle Systems with Discrete Latent States

We present a novel Bayesian learning framework for interacting particle systems with discrete latent states, addressing the challenge of inferring dynamics from partial, noisy observations. Our approach learns a variational posterior path measure by parameterizing the generator of the underlying continuous-time Markov chain. We formulate the problem as a multi-marginal Schrödinger bridge with aligned samples, employing a two-stage learning procedure. Our method incorporates an emission distribution for decoding latent states and uses a scalable variational approximation.