12 citations · 22 across the 9 of their papers we have counts for
10 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 c…
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…
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…
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…
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…
Manifold Learning with Sparse Regularised Optimal Transport
Stephen Zhang, Gilles Mordant, Tetsuya Matsumoto +1
Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high…
Beyond kNN: Adaptive, Sparse Neighborhood Graphs via Optimal Transport
Tetsuya Matsumoto, Stephen Zhang, Geoffrey Schiebinger
Nearest neighbour graphs are widely used to capture the geometry or topology of a dataset. One of the most common strategies to construct such a graph is based on selecting a fixed…
Trajectory Inference via Mean-field Langevin in Path Space
Lénaïc Chizat, Stephen Zhang, Matthieu Heitz +1
Trajectory inference aims at recovering the dynamics of a population from snapshots of its temporal marginals. To solve this task, a min-entropy estimator relative to the Wiener me…
Towards a mathematical theory of trajectory inference
Hugo Lavenant, Stephen Zhang, Young-Heon Kim +1
We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis o…