7 papers
Quantitative Stability of Many-Marginal Schrodinger Bridge
Rentian Yao, Young-Heon Kim, Geoffrey Schiebinger
In this paper, we explore quantitative stability of multi-marginal Schrödinger bridges with respect to the marginal constraints. We focus on the case where the number of marginal…
Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots
Vincent Guan, Joseph Janssen, Hossein Rahmani +4
Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets…
STARK denoises spatial transcriptomics images via adaptive regularization
Sharvaj Kubal, Naomi Graham, Matthieu Heitz +4
We present an approach to denoising spatial transcriptomics images that is particularly effective for uncovering cell identities in the regime of ultra-low sequencing depths, and a…
Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm
Nabarun Deb, Young-Heon Kim, Soumik Pal +1
We prove that the sequence of marginals obtained from the iterations of the Sinkhorn algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges…
Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs
Rentian Yao, Young--Heon Kim, Geoffrey Schiebinger
In this paper, we investigate the multi-marginal Schrodinger bridge (MSB) problem whose marginal constraints are marginal distributions of a stochastic differential equation (SDE)…
Principal Curves In Metric Spaces And The Space Of Probability Measures
Andrew Warren, Anton Afanassiev, Forest Kobayashi +2
We introduce principal curves in Wasserstein space, and in general compact metric spaces. Our motivation for the Wasserstein case comes from optimal-transport-based trajectory infe…