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#Wasserstein Distances

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Hausdorff Center for Mathematics

Entropy and Curvature of Markov Chains on Metric Spaces

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Explore the Peres-Tetali conjecture and its implications for Markov chains in this 57-minute lecture by Justin Salez from the Hausdorff Center for Mathematics. Delve into the relationship between contraction in Wasserstein distance and relative entropy f…
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1 Lesons
57 minutes
On-Demand
Free-Video
Institut Henri Poincaré

Some Bounds for the Wasserstein Distance Between the Empirical Measure

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Explorez les limites de la distance de Wasserstein entre la mesure empirique, en approfondissant les concepts mathématiques avancés et leurs applications statistiques.
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1 Lesons
35 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Analysis of Mean-Field Games - Lecture 1

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Explore static mean-field games, Nash equilibria, and convergence theorems in large symmetric systems. Learn key concepts and proofs in this advanced applied probability lecture.
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19 Lesons
1 hour
On-Demand
Free-Video
Google TechTalks

Private Convex Optimization via Exponential Mechanism - Differential Privacy for Machine Learning

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Explore private convex optimization using the exponential mechanism. Learn differential privacy, noisy SGD, and isoperimetric inequality for ML applications.
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21 Lesons
53 minutes
On-Demand
Free-Video
Cambridge University Press

Uniform Propagation of Chaos for a Dollar Exchange Model

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Explore a mathematical model for money exchange, focusing on agent-based dynamics and the convergence to a Poisson distribution as time and agent numbers increase.
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1 Lesons
11 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Why Should Q=P in the Wasserstein Distance Between Persistence Diagrams?

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Explore Wasserstein distance in persistence diagrams, focusing on q=p choice. Covers geometric implications, stability results, algebraic versions, and computational advantages for central tendencies.
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21 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Detecting Spoofing Strategies in High Frequency Trading

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Exploring detection methods for spoofing strategies in high-frequency trading, focusing on volume imbalance impact and optimization models to identify manipulative behaviors in limit order books.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Topological Data Analysis on Dynamic Brain Networks

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Explore topological data analysis for dynamic brain networks, learning to cluster networks into states and analyze temporal changes using Wasserstein distance. Gain insights into state space estimation and heritability of network changes.
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1 Lesons
51 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Washington Mio - Stable Homology of Metric Measure Spaces

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Explore stable homology in metric measure spaces, covering Wasserstein distance, local homology stability, and applications in data analysis and taxonomic classification.
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24 Lesons
58 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Universality of Persistence Diagrams and Bottleneck & Wasserstein Distances

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Explore the mathematical foundations of persistence diagrams and their associated metrics, focusing on universality properties and distance calculations in topological data analysis.
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1 Lesons
28 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Wasserstein Distances, Geodesics and Barycenters of Merge Trees

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Explore computational frameworks for merge trees, including Wasserstein distances, geodesics, and barycenters. Learn efficient algorithms and applications in visualization, feature tracking, and ensemble clustering.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Barycenters and a Law of Large Numbers in Gromov Hyperbolic Spaces

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Explore barycenters in Gromov hyperbolic spaces, examining contraction properties and a law of large numbers for convex optimization applications in metric spaces.
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1 Lesons
51 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Optimal Transport for Inverse Problems and Implicit Regularization

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Exploring optimal transport theory for inverse problems, addressing nonconvexity and noise sensitivity in least-squares methods, with applications in industry and broader data-fitting challenges.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Dual of the Dual Formula for Distance in Noncommutative Geometry

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Explore Connes's spectral distance and its dual formula in noncommutative geometry, extending Kantorovich's and Beckmann's concepts from optimal transport theory.
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1 Lesons
46 minutes
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Free-Video
BIMSA

Regressing Multivariate Gaussian Distribution on Vector Covariates for Co-expression Network Analysis

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Explore Fréchet regression for analyzing gene co-expression networks using population-level single-cell data. Learn to test associations between covariance matrices and covariates.
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1 Lesons
54 minutes
On-Demand
Free-Video
Finnish Center for Artificial Intelligence FCAI

Functional Priors for Bayesian Deep Learning

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Explore functional priors for Bayesian deep learning, focusing on imposing Gaussian process priors on neural networks through Wasserstein distance minimization.
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1 Lesons
58 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Quantitative Uniform Propagation of Chaos for Maxwell Molecules

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Explores propagation of chaos in Kac's N-particle system for Maxwell molecules, using probabilistic coupling techniques and recent stabilization results to establish uniform-in-time estimates.
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1 Lesons
47 minutes
On-Demand
Free-Video
Alan Turing Institute

Regularization for Optimal Transport and Dynamic Time Warping Distances - Marco Cuturi

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Explore regularization techniques for optimal transport and dynamic time warping distances, focusing on smoothing strategies to enhance machine learning applications and Fréchet mean computation.
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29 Lesons
44 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Wasserstein Distributionally Robust Optimization - Theory and Applications in Machine Learning

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Explore Wasserstein distributionally robust optimization theory and its applications in machine learning, focusing on data-driven decision-making under uncertainty and statistical learning.
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20 Lesons
1 hour 1 minute
On-Demand
Free-Video
Alan Turing Institute

Convergence of Denoising Diffusion Models Under the Manifold Hypothesis

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Explores theoretical analysis of denoising diffusion models, providing convergence results for data distributions on lower-dimensional manifolds or empirical distributions, with quantitative bounds on Wasserstein distance.
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1 Lesons
46 minutes
On-Demand
Free-Video
Conference GSI

The Total Variation Wasserstein Problem - A New Derivation of the Euler-Lagrange Equations

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Explore a novel derivation of Euler-Lagrange equations for the Total Variation Wasserstein problem, advancing understanding in mathematical optimization and transport theory.
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1 Lesons
22 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Metric Geometry of Spaces of Persistence Diagrams

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Explore metric geometry of persistence diagram spaces, focusing on synthetic curvature bounds and applications in non-smooth, infinite-dimensional contexts.
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1 Lesons
46 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Non-commutative Optimal Transport - Spring 2025

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Explore non-commutative optimal transport's applications in AI, quantum physics, and electronic structure theory. Delve into evolution equations, Wasserstein distances, and computational algorithms for density operators.
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1 Lesons
55 minutes
On-Demand
Free-Video
VinAI

Supervised Quantile Normalization for Matrix Factorization Using Optimal Transport

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Explore advanced matrix factorization techniques using optimal transport for quantile normalization. Learn applications in dimensionality reduction and genomics from expert Marco Cuturi.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
VinAI

Geometry of Covariance Matrices, Covariance Operators, and Gaussian Processes

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Explore geometric approaches to covariance matrices, operators, and Gaussian processes. Gain insights into non-Euclidean distances, Fisher-Rao distance, and Wasserstein distance in infinite-dimensional settings.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Inside Livermore Lab

DeepParticle: Learning Invariant Measure by Deep Neural Network Minimizing Wasserstein Distance

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Explore DeepParticle: an integrated approach combining deep learning, optimal transport, and interacting particles to solve high-dimensional PDEs, demonstrated through Fisher-Kolmogorov-Petrovsky-Piskunov front speeds in incompressible flows.
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1 Lesons
1 hour
On-Demand
Free-Video
Institute for Advanced Study

Challenges and Breakthroughs in the Mathematics of Plasmas

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Explore fundamental mathematical concepts in plasma physics, focusing on Vlasov equations, kinetic theory, and new Wasserstein-type distances for analyzing charged particle behavior.
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1 Lesons
58 minutes
On-Demand
Free-Video