Toward a mathematical theory of trajectory inference

DOI10.1214/23-aap1969arXiv2102.09204MaRDI QIDQ6126110

Young-Heon Kim, Geoffrey Schiebinger, Hugo Lavenant, Stephen Zhang

Publication date: 9 April 2024

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.09204

zbMATH Keywords

convex optimizationstochastic processesoptimal transportdevelopmental biologysingle-cell RNA-sequencingtrajectory inference

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Numerical methods involving duality (49M29) Developmental biology, pattern formation (92C15) Nonparametric inference (62G99) Optimal transportation (49Q22)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A survey of the Schrödinger problem and some of its connections with optimal transport
• Estimates of logarithmic Sobolev constant: An improvement of Bakry-Emery criterion
• Statistical inference for dynamical systems: a review
• The heat equation on manifolds as a gradient flow in the Wasserstein space
• Functional analysis, Sobolev spaces and partial differential equations
• On the parabolic kernel of the Schrödinger operator
• I-divergence geometry of probability distributions and minimization problems
• Minimization of the Kullback information of diffusion processes
• Entropic optimal transport is maximum-likelihood deconvolution
• A new optimal transport distance on the space of finite Radon measures
• Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures
• Unbalanced optimal transport: dynamic and Kantorovich formulations
• Dynamical aspects of the generalized Schrödinger problem via Otto calculus -- a heuristic point of view
• An entropic interpolation problem for incompressible viscous fluids
• Gradient flows and evolution variational inequalities in metric spaces. I: structural properties
• Benamou-Brenier and duality formulas for the entropic cost on \(\mathsf{RCD}^*(K,N)\) spaces
• Small noise limit and convexity for generalized incompressible flows, Schrödinger problems, and optimal transport
• Second-order models for optimal transport and cubic splines on the Wasserstein Space
• Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions
• Parameter estimation in stochastic differential equations.
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Brownian Motion, Martingales, and Stochastic Calculus
• Girsanov Theory Under a Finite Entropy Condition
• Finite Difference Computing with PDEs
• Scaling algorithms for unbalanced optimal transport problems
• Exact and Computationally Efficient Likelihood-Based Estimation for Discretely Observed Diffusion Processes (with Discussion)
• The Variational Formulation of the Fokker--Planck Equation
• Numerical resolution of an “unbalanced” mass transport problem
• Measure-Valued Spline Curves: An Optimal Transport Viewpoint
• Analysis and Geometry of Markov Diffusion Operators
• An entropy minimization approach to second-order variational mean-field games
• An optimal transport approach for solving dynamic inverse problems in spaces of measures
• Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks
• On the extremal points of the ball of the Benamou–Brenier energy
• An Invitation to Statistics in Wasserstein Space
• A Smoothed Dual Approach for Variational Wasserstein Problems
• Reversibility and entropy production of inhomogeneous Markov chains
• Optimal Transport
• A generalized conditional gradient method for dynamic inverse problems with optimal transport regularization

This page was built for publication: Toward a mathematical theory of trajectory inference