Fetching the paper…
Reading the bibliography…
Many applications in machine learning involve data represented as probability distributions.
Information-Type Measures of Difference of Probability Distributions and Indirect Observations
Csiszár, I · 1967
Earlier work this paper cites.
Real and Complex Analysis
Rudin, W · 1986
Earlier work this paper cites.
A Database for Handwritten Text Recognition Research
Hull, J. J · 1994
Earlier work this paper cites.
Integral Probability Metrics and Their Generating Classes of Functions
Müller, A · 1997
Earlier work this paper cites.
The Variational Formulation of the Fokker–Planck Equation
Jordan, R., Kinderlehrer, D., and Otto, F · 1998
Earlier work this paper cites.
Polar factorization of maps on Riemannian manifolds
McCann, R. J · 2001
Earlier work this paper cites.
The Geometry of Dissipative Evolution Equations: The Porous Medium Equation
Otto, F · 2001
Earlier work this paper cites.
Topics in Optimal Transportation , volume 58
Villani, C · 2003
Earlier work this paper cites.
On the geometry of the space of probability measures in ℝ n \mathbb{R}^{n} endowed with the quadratic optimal transport distance
Gigli, N · 2004
Earlier work this paper cites.
Riemannian Manifolds: An Introduction to Curvature , volume 176
Lee, J. M · 2006
Earlier work this paper cites.
Existence, Uniqueness, and Regularity of Optimal Transport Maps
Figalli, A · 2007
Earlier work this paper cites.
Gradient Flows: in Metric Spaces and in the Space of Probability Measures
Ambrosio, L., Gigli, N., and Savaré, G · 2008
Earlier work this paper cites.
Learning Multiple Layers of Features from Tiny Images
Krizhevsky, A., Hinton, G., et al · 2009
Earlier work this paper cites.
Optimal Transport: Old and New , volume 338
Villani, C. et al · 2009
Earlier work this paper cites.
Entropic Measure and Wasserstein Diffusion
von Renesse, M.-K. and Sturm, K.-T · 2009
Earlier work this paper cites.
The heat equation on manifolds as a gradient flow in the wasserstein space
Erbar, M · 2010
Earlier work this paper cites.
MNIST handwritten digit database
LeCun, Y. and Cortes, C · 2010
Earlier work this paper cites.
On the inverse implication of Brenier-McCann theorems and the structure of ( P 2 ( M ) , W 2 ) (P_{2}(M),W_{2})
Gigli, N · 2011
Earlier work this paper cites.
Reading Digits in Natural Images with Unsupervised Feature Learning
Netzer, Y., Wang, T., Coates, A., Bissacco, A., Wu, B., Ng, A. Y., et al · 2011
Earlier work this paper cites.
Scikit-learn: Machine Learning in Python
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, E · 2011
Earlier work this paper cites.
A kernel two-sample test
Gretton, A., Borgwardt, K. M., Rasch, M. J., Schölkopf, B., and Smola, A · 2012
Earlier work this paper cites.
Wasserstein Barycenter and its Application to Texture Mixing
Rabin, J., Peyré, G., Delon, J., and Bernot, M · 2012
Earlier work this paper cites.
Stochastic Gradient Descent on Riemannian Manifolds
Bonnabel, S · 2013
Earlier work this paper cites.
Unidimensional and Evolution Methods for Optimal Transportation
Bonnotte, N · 2013
Earlier work this paper cites.
Sinkhorn Distances: Lightspeed Computation of Optimal Transport
Cuturi, M · 2013
Earlier work this paper cites.
Sliced and Radon Wasserstein Barycenters of Measures
Bonneel, N., Rabin, J., Peyré, G., and Pfister, H · 2015
Earlier work this paper cites.
Learning to Represent Knowledge Graphs with Gaussian Embedding
He, S., Liu, K., Ji, G., and Zhao, J · 2015
Earlier work this paper cites.
From Word Embeddings to Document Distances
Kusner, M., Sun, Y., Kolkin, N., and Weinberger, K · 2015
Earlier work this paper cites.
Optimal Transport for Applied Mathematicians
Santambrogio, F · 2015
Earlier work this paper cites.
Word Representations via Gaussian Embedding
Vilnis, L. and McCallum, A · 2015
Earlier work this paper cites.
Optimal Transport for Domain Adaptation
Courty, N., Flamary, R., Tuia, D., and Rakotomamonjy, A · 2016
Earlier work this paper cites.
Sliced Wasserstein Kernels for Probability Distributions
Kolouri, S., Zou, Y., and Rohde, G. K · 2016
Earlier work this paper cites.
Borrowing strengh in hierarchical Bayes: Posterior concentration of the Dirichlet base measure
Nguyen, X · 2016
Earlier work this paper cites.
Sliced Wasserstein Kernel for Persistence Diagrams
Carriere, M., Cuturi, M., and Oudot, S · 2017
Earlier work this paper cites.
A JKO Splitting Scheme for Kantorovich–Fisher–Rao Gradient Flows
Gallouët, T. and Monsaingeon, L · 2017
Earlier work this paper cites.
Multilevel Clustering via Wasserstein Means
Ho, N., Nguyen, X., Yurochkin, M., Bui, H. H., Huynh, V., and Phung, D · 2017
Earlier work this paper cites.
PointNet: Deep learning on Point Sets for 3D Classification and Segmentation
Qi, C. R., Su, H., Mo, K., and Guibas, L. J · 2017
Cited alongside, same era.
{ \{ Euclidean, Metric, and Wasserstein } \} Gradient Flows: an overview
Santambrogio, F · 2017
Cited alongside, same era.
Snowflake universality of Wasserstein spaces
Andoni, A., Naor, A., and Neiman, O · 2018
Cited alongside, same era.
Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking
Bojchevski, A. and Günnemann, S · 2018
Cited alongside, same era.
JAX: composable transformations of Python+NumPy programs, 2018
Bradbury, J., Frostig, R., Hawkins, P., Johnson, M. J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., Wanderman-Milne, S., and Zhang, Q · 2018
Cited alongside, same era.
Optimal Transport for Gaussian Mixture Models
Chen, Y., Georgiou, T. T., and Tannenbaum, A · 2018
Mirror Sinkhorn: Fast Online Optimization on Transport Polytopes
Ballu, M. and Berthet, Q · 2023
Later among the works it cites.
Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals
Bonet, C., Malézieux, B., Rakotomamonjy, A., Drumetz, L., Moreau, T., Kowalski, M., and Courty, N · 2023
Later among the works it cites.
An Introduction to Optimization on Smooth Manifolds
Boumal, N · 2023
Later among the works it cites.
Forward-Backward Gaussian Variational Inference via JKO in the Bures-Wasserstein Space
Diao, M. Z., Balasubramanian, K., Chewi, S., and Salim, A · 2023
Later among the works it cites.
Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flows
Du, C., Li, T., Pang, T., Yan, S., and Lin, M · 2023
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Deep Learning for Classical Japanese Literature
Clanuwat, T., Bober-Irizar, M., Kitamoto, A., Lamb, A., Yamamoto, K., and Ha, D · 2018
Cited alongside, same era.
Computational Optimal Transport: Complexity by Accelerated Gradient Descent is Better than by Sinkhorn’s Algorithm
Dvurechensky, P., Gasnikov, A., and Kroshnin, A · 2018
Cited alongside, same era.
Wang, T., Zhu, J.-Y., Torralba, A., and Efros, A. A · 2018
Cited alongside, same era.
Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem
Wibisono, A · 2018
Cited alongside, same era.
Maximum Mean Discrepancy Gradient Flow
Arbel, M., Korba, A., Salim, A., and Gretton, A · 2019
Cited alongside, same era.
A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problems
Bonnet, B · 2019
Cited alongside, same era.
Dusson, G., Ehrlacher, V., and Nouaime, N · 2023
Later among the works it cites.
Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces
Fornasier, M., Savaré, G., and Sodini, G. E · 2023
Later among the works it cites.
Dynamic Flows on Curved Space Generated by Labeled Data
Hua, X., Nguyen, T., Le, T., Blanchet, J., and Nguyen, V. A · 2023
Later among the works it cites.
Small Transformers Compute Universal Metric Embeddings
Kratsios, A., Debarnot, V., and Dokmanić, I · 2023
Later among the works it cites.
Birth–death dynamics for sampling: global convergence, approximations and their asymptotics
Lu, Y., Slepčev, D., and Wang, L · 2023
Later among the works it cites.
SEACells infers transcriptional and epigenomic cellular states from single-cell genomics data
Persad, S., Choo, Z.-N., Dien, C., Sohail, N., Masilionis, I., Chaligné, R., Nawy, T., Brown, C. C., Sharma, R., Pe’er, I., et al · 2023
Later among the works it cites.
Unbalanced Optimal Transport, from Theory to Numerics
Séjourné, T., Peyré, G., and Vialard, F.-X · 2023
Later among the works it cites.
Dataset Condensation with Distribution Matching
Zhao, B. and Bilen, H · 2023
Later among the works it cites.
Mirror and Preconditioned Gradient Descent in Wasserstein Space
Bonet, C., Uscidda, T., David, A., Aubin-Frankowski, P.-C., and Korba, A · 2024
Later among the works it cites.
Catalano, M. and Lavenant, H · 2024
Later among the works it cites.
Statistical and Geometrical properties of the Kernel Kullback-Leibler divergence
Chazal, C., Bach, F., and Korba, A · 2024
Later among the works it cites.
Optimal Transport for Mixtures of Radial Functions
Chen, K. and Zhang, Y · 2024
Later among the works it cites.
(De)-regularized Maximum Mean Discrepancy Gradient Flow
Chen, Z., Mustafi, A., Glaser, P., Korba, A., Gretton, A., and Sriperumbudur, B. K · 2024
Later among the works it cites.
Scalable Wasserstein Gradient Flow for Generative Modeling through Unbalanced Optimal Transport
Choi, J., Choi, J., and Kang, M · 2024
Later among the works it cites.
Theoretical Guarantees for Variational Inference with Fixed-Variance Mixture of Gaussians
Huix, T., Korba, A., Durmus, A. O., and Moulines, E · 2024
Later among the works it cites.
Learning to Embed Distributions via Maximum Kernel Entropy
Kachaiev, O. and Recanatesi, S · 2024
Later among the works it cites.
Particle Semi-Implicit Variational Inference
Lim, J. N. and Johansen, A · 2024
Later among the works it cites.
MMD-Regularized Unbalanced Optimal Transport
Manupriya, P., Jagarlapudi, S., and Jawanpuria, P · 2024
Later among the works it cites.
Neumayer, S., Stein, V., Steidl, G., and Rux, N · 2024
Later among the works it cites.
Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributions
Nguyen, K. and Ho, N · 2024
Later among the works it cites.
Wasserstein Diffusion on Multidimensional Spaces
Sturm, K.-T · 2024
Later among the works it cites.
A Wasserstein-Type Distance for Gaussian Mixtures on Vector Bundles with Applications to Shape Analysis
Wilson, M., Needham, T., Park, C., Kundu, S., and Srivastava, A · 2024
Later among the works it cites.
Learning Gaussian Mixtures Using the Wasserstein–Fisher–Rao Gradient Flow
Yan, Y., Wang, K., and Rigollet, P · 2024
Later among the works it cites.
Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds
Bonet, C., Drumetz, L., and Courty, N · 2025
Closest in time.
Optimal transport with optimal transport cost: the Monge–Kantorovich problem on Wasserstein spaces
Emami, P. and Pass, B · 2025
Closest in time.
DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flows
Geuter, J., Bonet, C., Korba, A., and Alvarez-Melis, D · 2025
Closest in time.
First-Order Conditions for Optimization in the Wasserstein Space
Lanzetti, N., Bolognani, S., and Dörfler, F · 2025
Closest in time.
Wasserstein Task Embedding for Measuring Task Similarities
Liu, X., Bai, Y., Lu, Y., Soltoggio, A., and Kolouri, S · 2025
Closest in time.
Lightspeed Geometric Dataset Distance via Sliced Optimal Transport
Nguyen, K., Nguyen, H., Pham, T., and Ho, N · 2025
Closest in time.
ELBOing Stein: Variational Bayes with Stein Mixture Inference
Rønning, O., Nalisnick, E., Ley, C., Smyth, P., and Hamelryck, T · 2025
Closest in time.
Approximation Theory, Computing, and Deep Learning on the Wasserstein Space
Sodini, G. E., Fornasier, M., and Heid, P · 2025
Closest in time.