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We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals.
On the transfer of masses: Doklady akademii nauk ussr
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The strategy of the genes
Conrad Hal Waddington · 1957
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On the probability of large deviations of random variables
I.N. Sanov · 1958
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I-divergence geometry of probability distributions and minimization problems
Imre Csiszár · 1975
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On the parabolic kernel of the Schrödinger operator
Peter Li and Shing Tung Yau · 1986
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Random fields and diffusion processes
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Minimization of the kullback information of diffusion processes
Patrick Cattiaux and Christian Léonard · 1994
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Estimates of logarithmic sobolev constant: An improvement of bakry–emery criterion
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The variational formulation of the fokker–planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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An introduction to superprocesses
Alison Etheridge · 2000
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An algorithmic introduction to numerical simulation of stochastic differential equations
Desmond J Higham · 2001
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Stochastic analysis on manifolds
Elton P Hsu · 2002
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Numerical resolution of an “unbalanced” mass transport problem
Jean-David Benamou · 2003
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Parametric inference for diffusion processes observed at discrete points in time: a survey
Helle Sørensen · 2004
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Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion)
Alexandros Beskos, Omiros Papaspiliopoulos, Gareth O Roberts, and Paul Fearnhead · 2006
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Reversibility and entropy production of inhomogeneous markov chains
Hao Ge, Da-Quan Jiang, and Min Qian · 2006
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Parameter estimation in stochastic differential equations
Jaya PN Bishwal · 2007
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Gradient flows: in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
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A brief introduction to brownian motion on a riemannian manifold
Elton P Hsu · 2008
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Dna methylation landscapes: provocative insights from epigenomics
M. Suzuki and A. Bird · 2008
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Optimal transport: old and new
Cédric Villani · 2008
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Functional analysis, Sobolev spaces and partial differential equations
Haim Brezis · 2010
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The heat equation on manifolds as a gradient flow in the Wasserstein space
Matthias Erbar · 2010
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An analysis of the convergence of graph laplacians
Daniel Ting, Ling Huang, and Michael Jordan · 2011
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Hi-c: a comprehensive technique to capture the conformation of genomes
J. M. Belton, J. H. McCord, R. P.and Gibcus, Y. Naumova, N.and Zhan, and J. Dekker · 2012
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Girsanov theory under a finite entropy condition
Christian Léonard · 2012
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Analysis and geometry of Markov diffusion operators
Dominique Bakry, Ivan Gentil, and Michel Ledoux · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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A survey of the schrödinger problem and some of its connections with optimal transport
Christian Léonard · 2013
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The dynamics and regulators of cell fate decisions are revealed by pseudotemporal ordering of single cells
Cole Trapnell, Davide Cacchiarelli, Jonna Grimsby, Prapti Pokharel, Shuqiang Li, Michael Morse, Niall J Lennon, Kenneth J Livak, Tarjei S Mikkelsen, and John L Rinn · 2014
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Learning with a wasserstein loss
Charlie Frogner, Chiyuan Zhang, Hossein Mobahi, Mauricio Araya, and Tomaso A Poggio · 2015
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Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells
Allon M. Klein, Linas Mazutis, Ilke Akartuna, Naren Tallapragada, Adrian Veres, Victor Li, Leonid Peshkin, David A. Weitz, and Marc W. Kirschner · 2015
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On the extremal points of the ball of the benamou-brenier energy
Kristian Bredies, Marcello Carioni, Silvio Fanzon, and Francisco Romero · 2019
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Inferring population dynamics from single-cell rna-sequencing time series data
David S Fischer, Anna K Fiedler, Eric M Kernfeld, Ryan MJ Genga, Aimée Bastidas-Ponce, Mostafa Bakhti, Heiko Lickert, Jan Hasenauer, Rene Maehr, and Fabian J Theis · 2019
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Dna barcodes evolve for high-resolution cell lineage tracing
Nanami Masuyama, Hideto Mori, and Nozomu Yachie · 2019
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A lineage-resolved molecular atlas of c. elegans embryogenesis at single-cell resolution
Jonathan S Packer, Qin Zhu, Chau Huynh, Priya Sivaramakrishnan, Elicia Preston, Hannah Dueck, Derek Stefanik, Kai Tan, Cole Trapnell, Junhyong Kim, et al · 2019
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Computational optimal transport: With applications to data science
Gabriel Peyré and Marco Cuturi · 2019
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Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets
Evan Z. Macosko, Anindita Basu, Rahul Satija, James Nemesh, Karthik Shekhar, Melissa Goldman, Itay Tirosh, Allison R. Bialas, Nolan Kamitaki, Emily M. Martersteck, John J. Trombetta, David A. Weitz, Joshua R. Sanes, Alex K. Shalek, Aviv Regev, and Steven A. McCarroll · 2015
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Statistical inference for dynamical systems: A review
Kevin McGoff, Sayan Mukherjee, Natesh Pillai, et al · 2015
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A smoothed dual approach for variational wasserstein problems
Marco Cuturi and Gabriel Peyré · 2016
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Learning population-level diffusions with generative rnns
Tatsunori Hashimoto, David Gifford, and Tommi Jaakkola · 2016
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A new optimal transport distance on the space of finite radon measures
Stanislav Kondratyev, Léonard Monsaingeon, and Dmitry Vorotnikov · 2016
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Brownian motion, martingales, and stochastic calculus
Jean-François Le Gall · 2016
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An entropic interpolation problem for incompressible viscid fluids
Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard, and Jean-Claude Zambrini · 2017
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Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution
Samuel G. Rodriques, Robert R. Stickels, Aleksandrina Goeva, Carly A. Martin, Evan Murray, Charles R. Vanderburg, Joshua Welch, Linlin M. Chen, Fei Chen, and Evan Z. Macosko · 2019
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Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming
Geoffrey Schiebinger, Jian Shu, Marcin Tabaka, Brian Cleary, Vidya Subramanian, Aryeh Solomon, Joshua Gould, Siyan Liu, Stacie Lin, Peter Berube, Lia Lee, Jenny Chen, Justin Brumbaugh, Philippe Rigollet, Konrad Hochedlinger, Rudolf Jaenisch, Aviv Regev, and Eric S. Lander · 2019
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Dynamic cell imaging in PET with optimal transport regularization
Bernhard Schmitzer, Klaus P Schäfers, and Benedikt Wirth · 2019
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Paga: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells
F Alexander Wolf, Fiona K Hamey, Mireya Plass, Jordi Solana, Joakim S Dahlin, Berthold Göttgens, Nikolaus Rajewsky, Lukas Simon, and Fabian J Theis · 2019
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Minimizing relative entropy of path measures under marginal constraints
Aymeric Baradat and Christian Léonard · 2020
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Small noise limit and convexity for generalized incompressible flows, schrödinger problems, and optimal transport
Aymeric Baradat and Léonard Monsaingeon · 2020
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Kristian Bredies, Marcello Carioni, Silvio Fanzon, and Francisco Romero · 2020
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An optimal transport approach for solving dynamic inverse problems in spaces of measures
Kristian Bredies and Silvio Fanzon · 2020
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Uncovering axes of variation among single-cell cancer specimens
S William Chen, Nevena Zivanovic, van David Dijk, Guy Wolf, Bernd Bodenmiller, and Smita Krishnaswamy · 2020
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Xiaoli Chen, Liu Yang, Jinqiao Duan, and George Em Karniadakis · 2020
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Fast and smooth interpolation on wasserstein space
Sinho Chewi, Julien Clancy, Thibaut Le Gouic, Philippe Rigollet, George Stepaniants, and Austin J Stromme · 2020
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A unified framework for lineage tracing and trajectory inference
Aden Forrow and Geoffrey Schiebinger · 2020
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Benamou–Brenier and duality formulas for the entropic cost on RCD ∗ ( K , N ) \mathrm{RCD}^{*}(K,N) spaces
Nicola Gigli and Luca Tamanini · 2020
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Multiscale phate exploration of sars-cov-2 data reveals multimodal signatures of disease
Manik Kuchroo, Jessie Huang, Patrick Wong, Jean-Christophe Grenier, Dennis Shung, Alexander Tong, Carolina Lucas, Jon Klein, Daniel Burkhardt, Scott Gigante, Abhinav Godavarthi, Benjamin Israelow, Tianyang Mao, Ji Eun Oh, Julio Silva, Takehiro Takahashi, Camila D. Odio, Arnau Casanovas-Massana, John Fournier, Shelli Farhadian, Charles S. Dela Cruz, Albert I. Ko, F. Perry Wilson, Julie Hussin, Guy Wolf, Akiko Iwasaki, and Smita Krishnaswamy · 2020
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Gradient flows and Evolution Variational Inequalities in metric spaces. I: Structural properties
Matteo Muratori and Giuseppe Savaré · 2020
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An invitation to statistics in Wasserstein space
Victor M Panaretos and Yoav Zemel · 2020
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Trajectorynet: A dynamic optimal transport network for modeling cellular dynamics
Alexander Tong, Jessie Huang, Guy Wolf, David van Dijk, and Smita Krishnaswamy · 2020
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A benchmark of batch-effect correction methods for single-cell rna sequencing data
Hoa Thi Nhu Tran, Kok Siong Ang, Marion Chevrier, Xiaomeng Zhang, Nicole Yee Shin Lee, Michelle Goh, and Jinmiao Chen · 2020
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Generative modeling of single-cell population time series for inferring cell differentiation landscapes
Grace Hui Ting Yeo, Sachit Dinesh Saksena, and David K Gifford · 2020
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Aymeric Baradat and Hugo Lavenant · 2021
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Kernel operations on the gpu, with autodiff, without memory overflows
Benjamin Charlier, Jean Feydy, Joan Alexis Glaunais, Francois-David Collin, and Ghislain Durif · 2021
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