Measure theory | Statistical distance | Theory of probability distributions | Metric geometry
In mathematics, the Wasserstein distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given metric space . It is named after Leonid Vaseršteĭn. Intuitively, if each distribution is viewed as a unit amount of earth (soil) piled on , the metric is the minimum "cost" of turning one pile into the other, which is assumed to be the amount of earth that needs to be moved times the mean distance it has to be moved. This problem was first formalised by Gaspard Monge in 1781. Because of this analogy, the metric is known in computer science as the earth mover's distance. The name "Wasserstein distance" was coined by R. L. Dobrushin in 1970, after learning of it in the work of Leonid Vaseršteĭn on Markov processes describing large systems of automata (Russian, 1969). However the metric was first defined by Leonid Kantorovich in The Mathematical Method of Production Planning and Organization (Russian original 1939) in the context of optimal transport planning of goods and materials. Some scholars thus encourage use of the terms "Kantorovich metric" and "Kantorovich distance". Most English-language publications use the German spelling "Wasserstein" (attributed to the name "Vaseršteĭn" being of German origin). (Wikipedia).
This video is about the measures of center, including the mean, median, and mode.
From playlist Statistical Measures
More Standard Deviation and Variance
Further explanations and examples of standard deviation and variance
From playlist Unit 1: Descriptive Statistics
Percentiles, Deciles, Quartiles
Understanding percentiles, quartiles, and deciles through definitions and examples
From playlist Unit 1: Descriptive Statistics
This video explains how to convert to different metric units of measure for length, capacity, and mass. http://mathispower4u.wordpress.com/
From playlist Unit Conversions: Metric Units
Micrometer/diameter of daily used objects.
What was the diameter? music: https://www.bensound.com/
From playlist Fine Measurements
Micrometer / diameter of daily used objects
What was the diameter? music: https://www.bensound.com/
From playlist Fine Measurements
Compare Metric Units using Metric Conversions (Unit Fractions)
This video explains how to compare quantities in metric units by perform conversions using unit fractions. http://mathispower4u.com
From playlist Unit Conversions: Metric Units
Introduction to the Wasserstein distance
Title: Introduction to the Wasserstein distance Abstract: I give an introduction to the Wasserstein distance, which is also called the Kantorovich-Rubinstein, optimal transport, or earth mover's distance. In particular, I describe how the 1-Wasserstein distance is defined between probabil
From playlist Tutorials
From playlist Contributed talks One World Symposium 2020
Physics CH 0.5: Standard Units (5 of 41) Standard Units in Mechanics
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and derive standard units in mechanics of area, volume, force, pressure, work, power, momentum, impulse. Next video in this series can be found at: https://youtu.be/FNs_-Z1gHxU
From playlist Michel van Biezen: Physics Mechanics 1: Introduction, Standard Units, and Vectors
Third Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk
Date: Wednesday, November 4, 10:00am EDT Speaker: Daniela Calvetti, Case Western Reserve University Title: Bayesian reimaging of sparsity in inverse problems. Abstract: The recovery of sparse generative models from few noisy measurements is a challenging inverse problem with application
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series
Generative Adversarial Networks - FUTURISTIC & FUN AI !
I talk about Generative Adversarial Networks, how it works, fun applications and it’s types. If you liked the video, click that like button and SUBSCIBE for more content on Data Sciences, Machine Learning & Deep Learning. Follow me on QUORA for my answers to interesting questions on Data
From playlist Algorithms and Concepts
Jeremiah Birrell (U Mass) -- Interpolating Between f-Divergences and Wasserstein Metrics
I will present a general framework for constructing new information-theoretic divergences that interpolate between and combine crucial properties of both Wasserstein metrics and f-divergences. Specifically, these divergences are nontrivial in the presence of heavy tails and when there is a
From playlist Northeastern Probability Seminar 2020
Ex: Metric Conversions Using Unit Fractions - Length
This video provides three examples of how to perform metric conversions involving length using unit fractions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Unit Conversions: Metric Units
Giacomo De Palma: "The quantum Wasserstein distance of order 1"
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "The quantum Wasserstein distance of order 1" Giacomo De Palma - Massachusetts Institute of Technology, Research Laboratory of Electronics Abstract: We propose a generalization of the Wasserstein distance of order 1 to th
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021
What are Graph Kernels? Graph Kernels explained, Python + Graph Neural Networks
The abundance of graph-structured data and need to perform machine learning ML tasks on this data led to development of graph kernels. Machine Learning, Deep Learning. Graph kernels, this means kernel functions between graphs, have been proposed in the 2010s to solve the problem of assess
From playlist Learn Graph Neural Networks: code, examples and theory
Franca Hoffmann: Covariance-modulated optimal transport
HYBRID EVENT Recorded during the meeting " Probability/PDE Interactions: Interface Models and Particle Systems " the April 25, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by world
From playlist Dynamical Systems and Ordinary Differential Equations
Jan Maas: Optimal transport methods for discrete and quantum systems (part 1)
Optimal transport has become a powerful tool to attack non-smooth problems in analysis and geometry. A key role is played by the 2-Wasserstein metric, which induces a rich geometric structure on the space of probability measures. This structure allows to obtain gradient flow structures for
From playlist HIM Lectures 2015
Mokshay Madiman : Minicourse on information-theoretic geometry of metric measure
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Geometry
Determining values of a variable at a particular percentile in a normal distribution
From playlist Unit 2: Normal Distributions