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We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) that learns stochastic, continuous population dynamics from static snapshot samples taken at sporadic timepoints.
A relationship between arbitrary positive matrices and doubly stochastic matrices
Richard Sinkhorn · 1964
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Handbook of stochastic methods , volume 3
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Sharp explicit lower bounds of heat kernels
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A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
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Semi-Supervised Learning on Riemannian Manifolds
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Monge’s problem with a quadratic cost by the zero-noise limit of h-path processes
Toshio Mikami · 2004
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Duality theorem for the stochastic optimal control problem
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From graph to manifold Laplacian: The convergence rate
A. Singer · 2006
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Mean field games
Jean-Michel Lasry and Pierre-Louis Lions · 2007
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A kernel method for the two-sample problem
Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf, and Alexander Smola · 2008
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Optimal transport: old and new , volume 338
Cédric Villani · 2009
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Continuity of optimal control costs and its application to weak kam theory
Andrei Agrachev and Paul WY Lee · 2010
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Targeted deletion of hand2 in enteric neural precursor cells affects its functions in neurogenesis, neurotransmitter specification and gangliogenesis, causing functional aganglionosis
Jun Lei and Marthe J Howard · 2011
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Sinkhorn Distances: Lightspeed Computation of Optimal Transport
Marco Cuturi · 2013
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Pseudo-temporal ordering of individual cells reveals dynamics and regulators of cell fate decisions
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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Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
Justin Solomon, Fernando De Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas · 2015
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Diffusion pseudotime robustly reconstructs lineage branching
Laleh Haghverdi, Maren Büttner, F. Alexander Wolf, Florian Buettner, and Fabian J. Theis · 2016
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Learning population-level diffusions with generative rnns
Tatsunori Hashimoto, David Gifford, and Tommi Jaakkola · 2016
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Hölder–Lipschitz Norms and Their Duals on Spaces with Semigroups, with Applications to Earth Mover’s Distance
William Leeb and Ronald Coifman · 2016
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Neural ordinary differential equations
Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 2018
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RNA velocity of single cells
Gioele La Manno, Ruslan Soldatov, Amit Zeisel, Emelie Braun, Hannah Hochgerner, Viktor Petukhov, Katja Lidschreiber, Maria E. Kastriti, Peter Lönnerberg, Alessandro Furlan, Jean Fan, Lars E. Borm, Zehua Liu, David van Bruggen, Jimin Guo, Xiaoling He, Roger Barker, Erik Sundström, Gonçalo Castelo-Branco, Patrick Cramer, Igor Adameyko, Sten Linnarsson, and Peter V. Kharchenko · 2018
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Manifold learning-based methods for analyzing single-cell RNA-sequencing data
Kevin R. Moon, Jay S. Stanley, Daniel Burkhardt, David van Dijk, Guy Wolf, and Smita Krishnaswamy · 2018
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Slingshot: cell lineage and pseudotime inference for single-cell transcriptomics
Kelly Street, Davide Risso, Russell B Fletcher, Diya Das, John Ngai, Nir Yosef, Elizabeth Purdom, and Sandrine Dudoit · 2018
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Decoupled weight decay regularization
Ilya Loshchilov and Frank Hutter · 2018
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Scalable gradients for stochastic differential equations
Xuechen Li, Ting-Kam Leonard Wong, Ricky T. Q. Chen, and David Duvenaud · 2020
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RNA velocity—current challenges and future perspectives
Volker Bergen, Ruslan A. Soldatov, Peter V. Kharchenko, and Fabian J. Theis · 2021
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Spearheading future omics analyses using dyngen, a multi-modal simulator of single cells
Robrecht Cannoodt, Wouter Saelens, Louise Deconinck, and Yvan Saeys · 2021
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Diffusion schrödinger bridge with applications to score-based generative modeling
Valentin De Bortoli, James Thornton, Jeremy Heng, and Arnaud Doucet · 2021
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Pot: Python optimal transport
Rémi Flamary, Nicolas Courty, Alexandre Gramfort, Mokhtar Z. Alaya, Aurélie Boisbunon, Stanislas Chambon, Laetitia Chapel, Adrien Corenflos, Kilian Fatras, Nemo Fournier, Léo Gautheron, Nathalie T.H. Gayraud, Hicham Janati, Alain Rakotomamonjy, Ievgen Redko, Antoine Rolet, Antony Schutz, Vivien Seguy, Danica J. Sutherland, Romain Tavenard, Alexander Tong, and Titouan Vayer · 2021
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FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models
Will Grathwohl, Ricky T. Q. Chen, Jesse Bettencourt, Ilya Sutskever, and David Duvenaud · 2019
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Diffusion nets
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Visualizing structure and transitions in high-dimensional biological data
Kevin R. Moon, David van Dijk, Zheng Wang, Scott Gigante, Daniel B. Burkhardt, William S. Chen, Kristina Yim, Antonia van den Elzen, Matthew J. Hirn, Ronald R. Coifman, Natalia B. Ivanova, Guy Wolf, and Smita Krishnaswamy · 2019
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A comparison of single-cell trajectory inference methods
Wouter Saelens, Robrecht Cannoodt, Helena Todorov, and Yvan Saeys · 2019
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Reconstruction of developmental landscapes by optimal-transport analysis of single-cell gene expression sheds light on cellular reprogramming
Geoffrey Schiebinger, Jian Shu, Marcin Tabaka, Brian Cleary, Vidya Subramanian, Aryeh Solomon, 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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Generative Modeling by Estimating Gradients of the Data Distribution
Yang Song and Stefano Ermon · 2019
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Onecut transcription factors induce neuronal characteristics and remodel chromatin accessibility
Jori van der Raadt, Sebastianus HC van Gestel, Nael Nadif Kasri, and Cornelis A Albers · 2019
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A solution to the monge transport problem for brownian martingales
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The data-driven schrödinger bridge
Michele Pavon, Giulio Trigila, and Esteban G Tabak · 2021
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Diffusion earth mover’s distance and distribution embeddings
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Solving Schrödinger Bridges via Maximum Likelihood
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Deep generative learning via schrödinger bridge
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Optimal transport analysis reveals trajectories in steady-state systems
Stephen Zhang, Anton Afanassiev, Laura Greenstreet, Tetsuya Matsumoto, and Geoffrey Schiebinger · 2021
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Inference of high-resolution trajectories in single-cell RNA-seq data by using RNA velocity
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Neural SDEs as Infinite-Dimensional GANs
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Proximal Optimal Transport Modeling of Population Dynamics
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Eigen-convergence of gaussian kernelized graph laplacian by manifold heat interpolation
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Non-genetic determinants of malignant clonal fitness at single-cell resolution
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Embedding signals on graphs with unbalanced diffusion earth mover’s distance
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