We are doing a reading course on optimal transport in the context of graphs and its ties with information geometry. A list of possible papers can be found here or for the summer, here. What follows are a list of relevant papers beyond these. When it is your week to present, please add any relevant papers to the list. To add your references, edit here.
April 12th, and 19th: Optimal Mass Transport: Signal processing and machine-learning applications
Presenter: Yiqun Shao
38, Otto, 2001: the paper that presented the 2-Wasserstein space as a Riemannian metric derived from a Variational problem.
40, Park et al, 2018(Arxiv: The paper that transforms optimal transport into a Euclidian space in 1D via preserving distances to a reference distribution. It makes density functions separable after the transform.
Santambrogio 2015: Optimal transport for the applied mathematician. Good reference book for further reading.
50, W. Wang, D. Slepcev, S. Basu, J. A. Ozolek, and G. K. Rohde “A linear opti- mal transportation framework for quantifying and visualizing variations in sets of images,” The original LOT.
14, M. Cuturi “Sinkhorn distances: Lightspeed computation of optimal trans- port” Using the entropy penalty term to compute optimal transport map fast.
26, S. Kolouri and G. K. Rohde “Transport-based single frame super resolution of very low resolution face images”. Single frame superresolution using PCA on transport map.
April 26th: Quadratically-Regularized Optimal Transport on Graphs
Presenter: Shaofeng Deng
D. Knowles Lagrangian Duality for Dummies!
Davis, T.A., 2011 This paper shows how to update the pseudo inverse of a graph Laplacian given a rank-1 change via Cholesky factorization.
Graph Laplacian A good tutorial on graph laplacian.
May 3rd: Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances
Presenter: Dong Min Roh
T. Cover, J. Thomas; CH.2 Introduction to Entropy
P. Knight Sinkhorn-Knopp Algorithm
May 17th: Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem
Presenter: Haolin Chen
Amari 2016: Information geometry and its applications
Cuturi 2013: Sinkhorn distances: Lightspeed computation of optimal transport
May 24th: Information Geometry for Regularized Optimal Transport and Barycenters of Patterns
Presenter: David Weber
Amari 2016 Recent reference on information geometry for machine learning by Amari.
Determinant of Block Matrices used in the proof of convexity of
Sherman-Morrison formula used in the proof of convexity of
Agueh & CarlieEnr, 2011 (preprint): Demonstration that the Barycenters of the Wasserstein metric are translation invariant.
Cuturi & Doucet, 2014: uses the C-function to compute Barycenters.
May 31st: The data-driven Schroedinger bridge
Presenter: Haotian Li
June 19th: Application of the Wasserstein metric to seismic signals
Presenter: Bohan Zhou
Engquist_2018_Seismic_Inversion: Data normalization techs for pre-processing seismic data.
Engquist_2018_Seismic_Imaging: A review for seismic inversion problem and the application of optimal transport.
Plessix_2006_Review: A review of the adjoint-state method for computing the gradient of a functional with geophysical applications.
Yang_2017_Analysis: Analysis of misfit functions.
Engquist_2013_Application: Basic property to be satisfied before applying Wasserstein distance.
Bradley_2013_adjoint method: A manual for PDE-constrained optimization and the adjoint method from the beginning.
August 2nd and 9th: {Euclidean, metric, and Wasserstein} gradient flows:an overview
Presenter: Bohan Zhou
Santambrogio_2017_Review: Gradient flow in Euclidean, metric, Waaserstein space giving three generic functionals including the heat equation, porous medium equation, Fokker-Planck equation and etc.
Ambrosio_2008_Gradient_Flow: The Bible in gradient flow.
Otto_2001_Geometry: Gradient flow strcture of porous medium equation. Compare the traditional approach to gradient flow of density with respect to L^2 norm of metric derivatives, with the new approach to gradient flow of density with repsect to Wasserstein distance, or equivalently the gradient flow of Lagrangian velocity with respect to L^2 norm.
Jordan_1998_JKO: JKO scheme is a discrete scheme, rising from Backwards Euler method, to show the weak solution exists systematically. Morevoer, the interpolated solution converges and it satisfies Fokker-Planck Equations in distributional sense.
August 16th and 23rd: Optimal Spectral transportation with application to music transcription
Presenter: Naoki Saito
August 23rd and September 6th: A Parallel Method for Earth Mover’s Distance
Presenter: Haotian Li
September 6th: Logarithmic divergences from optimal transport and Rényi geometry
Presenter: David Weber