Estimating Latent Population Flows from Aggregated Data via Inversing Multi-Marginal Optimal Transport

2022-12-30 · Sikun Yang, Hongyuan Zha

We study the problem of estimating latent population flows from aggregated count data. This problem arises when individual trajectories are not available due to privacy issues or measurement fidelity. Instead, the aggregated observations are measured over discrete-time points, for estimating the population flows among states. Most related studies tackle the problems by learning the transition parameters of a time-homogeneous Markov process. Nonetheless, most real-world population flows can be influenced by various uncertainties such as traffic jam and weather conditions. Thus, in many cases, a time-homogeneous Markov model is a poor approximation of the much more complex population flows. To circumvent this difficulty, we resort to a multi-marginal optimal transport (MOT) formulation that can naturally represent aggregated observations with constrained marginals, and encode time-dependent transition matrices by the cost functions. In particular, we propose to estimate the transition flows from aggregated data by learning the cost functions of the MOT framework, which enables us to capture time-varying dynamic patterns. The experiments demonstrate the improved accuracy of the proposed algorithms than the related methods in estimating several real-world transition flows.

📄 PDF Abstract BibTeX arXiv:2212.14527

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Estimating Unknown Population Sizes Using the Hypergeometric Distribution

2024-02-22 · Liam Hodgson, Danilo Bzdok

The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of …

Collaborative Filtering

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Decision Making reinforcement-learning Reinforcement Learning Reinforcement Learning (RL)+1

Connecting metapopulation heterogeneity to aggregated lifetime statistics

2019-07-18

Aggregated metapopulation lifetime statistics has been used to access stylized facts that might help identify the underlying patch-level dynamics. For instance, the emergence of scaling laws in the aggregated probability…