Recovering Stochastic Dynamics via Gaussian Schrödinger Bridges

02/11/2022
by   Charlotte Bunne, et al.
0

We propose a new framework to reconstruct a stochastic process {ℙ_t: t ∈[0, T]} using only samples from its marginal distributions, observed at start and end times 0 and T. This reconstruction is useful to infer population dynamics, a crucial challenge, e.g., when modeling the time-evolution of cell populations from single-cell sequencing data. Our general framework encompasses the more specific Schrödinger bridge (SB) problem, where ℙ_t represents the evolution of a thermodynamic system at almost equilibrium. Estimating such bridges is notoriously difficult, motivating our proposal for a novel adaptive scheme called the GSBflow. Our goal is to rely on Gaussian approximations of the data to provide the reference stochastic process needed to estimate SB. To that end, we solve the SB problem with Gaussian marginals, for which we provide, as a central contribution, a closed-form solution and SDE-representation. We use these formulas to define the reference process used to estimate more complex SBs, and show that this does indeed help with its numerical solution. We obtain notable improvements when reconstructing both synthetic processes and single-cell genomics experiments.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/13/2020

The Elliptical Processes: a New Family of Flexible Stochastic Processes

We present the elliptical processes-a new family of stochastic processes...
research
03/03/2023

Deep Momentum Multi-Marginal Schrödinger Bridge

Reconstructing population dynamics using only samples from distributions...
research
08/27/2019

Multi-Task Gaussian Processes and Dilated Convolutional Networks for Reconstruction of Reproductive Hormonal Dynamics

We present an end-to-end statistical framework for personalized, accurat...
research
06/15/2023

Unbalanced Diffusion Schrödinger Bridge

Schrödinger bridges (SBs) provide an elegant framework for modeling the ...
research
04/23/2023

Stochastic Cell Transmission Models of Traffic Networks

We introduce a rigorous framework for stochastic cell transmission model...
research
08/17/2018

Statistical modeling for adaptive trait evolution in randomly evolving environment

In past decades, Gaussian processes has been widely applied in studying ...
research
06/05/2023

Branching model with state dependent offspring distribution for Chlamydia spread

Chlamydiae are bacteria with an interesting unusual developmental cycle....

Please sign up or login with your details

Forgot password? Click here to reset