  We consider incremental inference problems from aggregate data for collective
dynamics. In particular, we address the problem of estimating the aggregate
marginals of a Markov chain from noisy aggregate observations in an incremental
(online) fashion. We propose a sliding window Sinkhorn belief propagation
(SW-SBP) algorithm that utilizes a sliding window filter of the most recent
noisy aggregate observations along with encoded information from discarded
observations. Our algorithm is built upon the recently proposed multi-marginal
optimal transport based SBP algorithm that leverages standard belief
propagation and Sinkhorn algorithm to solve inference problems from aggregate
data. We demonstrate the performance of our algorithm on applications such as
inferring population flow from aggregate observations.
