Geometry of Covariance Matrices, Covariance Operators, and Gaussian Processes
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.
The Mathematical Universe Behind Deep Neural Networks - Rothschild Lecture
Explore the mathematical foundations of deep neural networks, covering functional analysis, harmonic analysis, complex analysis, approximation theory, and more with Professor Helmut Bölcskei.
DeepParticle: Learning Invariant Measure by Deep Neural Network Minimizing Wasserstein Distance
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.
Weak Limits for Entropic Optimal Transport - Part II
Explore weak limits for entropic optimal transport, covering parametric cases, duality, proofs, and connections to improved CLT and convex optimization.
Data-Driven Latent Representations for Time-Dependent Problems - Lecture 3
Explore data-driven latent representations for time-dependent problems, focusing on applications in climate downscaling, superresolution, and optimal transport.
Wasserstein Gradient Flows and Applications to Sampling in Machine Learning - Lecture 1
Explore Wasserstein gradient flows and their applications to sampling in machine learning through an in-depth lecture by Anna Korba.
Wasserstein Gradient Flows and Applications to Sampling in Machine Learning - Lecture 3
Explore Wasserstein gradient flows and their applications to sampling in machine learning with Anna Korba's advanced lecture on this complex mathematical topic.
Trajectory Inference in Wasserstein Space
Explore advanced trajectory inference methods using Wasserstein geometry and B-spline approximation for analyzing dynamic processes in computational biology and point cloud data.