{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/deep-momentum-multi-marginal-schrodinger","title":"Deep Momentum Multi-Marginal Schrödinger Bridge","arxiv_id":"2303.01751","date":"2023-03-03","proceeding":"NeurIPS 2023 11","authors":[],"abstract":"It is a crucial challenge to reconstruct population dynamics using unlabeled samples from distributions at coarse time intervals. Recent approaches such as flow-based models or Schr\\\"odinger Bridge (SB) models have demonstrated appealing performance, yet the inferred sample trajectories either fail to account for the underlying stochasticity or are $\\underline{D}$eep $\\underline{M}$omentum Multi-Marginal $\\underline{S}$chr\\\"odinger $\\underline{B}$ridge(DMSB), a novel computational framework that learns the smooth measure-valued spline for stochastic systems that satisfy position marginal constraints across time. By tailoring the celebrated Bregman Iteration and extending the Iteration Proportional Fitting to phase space, we manage to handle high-dimensional multi-marginal trajectory inference tasks efficiently. Our algorithm outperforms baselines significantly, as evidenced by experiments for synthetic datasets and a real-world single-cell RNA sequence dataset. 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