A0821
Title: Beyond Schrodinger bridges: A least-squares approach for learning stochastic dynamics with unknown volatility
Authors: Renato Berlinghieri - Massachusetts Institute of Technology (United States) [presenting]
Abstract: Scientists often need to learn the underlying stochastic dynamics of systems from population-level snapshot data, where individual trajectories are unavailable. For example, in time course single-cell mRNA profiling, cellular transcriptional state measurement is performed on different biological replicates because the measurement process destroys the cells. Existing methods based on Schrodinger bridge techniques rely on Kullback-Leibler divergence and assume known, constant volatility, limiting their applicability in realistic settings where volatility may be unknown or varying. A new framework that directly matches the joint distribution of the state (e.g., mRNA expression levels) is proposed, and the time of observation using maximum mean discrepancy. This approach reduces to a least-squares formulation in distributional space and motivates an $R^2$-type goodness-of-fit measure for model inspection and comparison. It is shown in the experiments that the proposed method outperforms existing Schrodinger bridge-based baselines in forecasting and is robust to unknown volatility and missing observations.
