Name
Abstract | ||
|---|---|---|
We consider the problem to identify the most likely flow in phase space, of (inertial) particles under stochastic forcing, that is in agreement with spatial (marginal) distributions that are specified at a set of points in time. The question raised generalizes the classical Schrodinger Bridge Problem (SBP) which seeks to interpolate two specified end-point marginal distributions of overdamped particles driven by stochastic excitation. While we restrict our analysis to second-order dynamics for the particles, the data represents partial (i.e., only positional) information on the flow at multiple time-points. The solution sought, as in SBP, represents a probability law on the space of paths that is closest to a uniform prior while consistent with the given marginals. We approach this problem as an optimal control problem to minimize an action integral a la Benamou-Brenier, and derive a time-symmetric formulation that includes a Fisher information term on the velocity field. We underscore the relation of our problem to recent measure-valued splines in Wasserstein space, which is akin to that between SBP and Optimal Mass Transport (OMT). The connection between the two provides a Sinkhorn-like approach to computing measure-valued splines. We envision that interpolation between measures as sought herein will have a wide range of applications in signal/images processing as well as in data science in cases where data have a temporal dimension. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/978-3-030-26980-7_75 | GEOMETRIC SCIENCE OF INFORMATION |
Keywords | DocType | Volume |
Schrodinger bridge, Optimal mass transport, Optimal control, Multi-marginal | Conference | 11712 |
ISSN | Citations | PageRank |
0302-9743 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yongxin Chen | 1 | 99 | 31.89 |
| Giovanni Conforti | 2 | 1 | 0.71 |
| Tryphon T. Georgiou | 3 | 211 | 36.71 |
| Luigia Ripani | 4 | 0 | 0.34 |