Geometric algorithms | Statistical distance
In mathematics, specifically statistics and information geometry, a Bregman divergence or Bregman distance is a measure of difference between two points, defined in terms of a strictly convex function; they form an important class of divergences. When the points are interpreted as probability distributions – notably as either values of the parameter of a parametric model or as a data set of observed values – the resulting distance is a statistical distance. The most basic Bregman divergence is the squared Euclidean distance. Bregman divergences are similar to metrics, but satisfy neither the triangle inequality (ever) nor symmetry (in general). However, they satisfy a generalization of the Pythagorean theorem, and in information geometry the corresponding statistical manifold is interpreted as a (dually) flat manifold. This allows many techniques of optimization theory to be generalized to Bregman divergences, geometrically as generalizations of least squares. Bregman divergences are named after Russian mathematician Lev M. Bregman, who introduced the concept in 1967. (Wikipedia).
Bregman persistence homology [Hana Dal Poz Kouřimská]
In this tutorial you will learn about what Bregman Divergences are and how to use them to generalize persistence homology. There are few formulas and lots of pictures :) !!! There is a mistake in the video in the definition of the Bregman divergence (minute 2:08). As the last condition, i
From playlist Tutorial-a-thon 2021 Spring
From playlist Divergence
Calculus 3: Divergence and Curl (4 of 32) What is the Divergence? Part 2
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the divergence using a conceptual approach. Next video in the series can be seen at: https://youtu.be/8qsxlUIrdd0
From playlist CALCULUS 3 CH 8 DIVERGENCE AND CURL
24: Divergence - Valuable Vector Calculus
In-depth explanation of divergence formula: https://youtu.be/W--29EqUSl0 Explanation of the definition of divergence of a vector field. What does divergence mean? How do we calculate divergence? We'll also talk about some geometric meaning to the formula for divergence. Full Valuable Vec
From playlist Valuable Vector Calculus
Babak Hassibi: "Implicit and Explicit Regularization in Deep Neural Networks"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop IV: Efficient Tensor Representations for Learning and Computational Complexity "Implicit and Explicit Regularization in Deep Neural Networks" Babak Hassibi - California Institute of Technology Abstra
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Deep Learning and the “Blessing” of Dimensionality - Babak Hassibi - 6/7/2019
Changing Directions & Changing the World: Celebrating the Carver Mead New Adventures Fund. June 7, 2019 in Beckman Institute Auditorium at Caltech. The symposium features technical talks from Carver Mead New Adventures Fund recipients, alumni, and Carver Mead himself! Since 2014, this Fu
From playlist Carver Mead New Adventures Fund Symposium
Stanley Osher: "Linearized Bregman Algorithm for L1-regularized Logistic Regression"
Graduate Summer School 2012: Deep Learning, Feature Learning "Linearized Bregman Algorithm for L1-regularized Logistic Regression" Stanley Osher, UCLA Institute for Pure and Applied Mathematics, UCLA July 20, 2012 For more information: https://www.ipam.ucla.edu/programs/summer-schools/g
From playlist GSS2012: Deep Learning, Feature Learning
From playlist Divergence
Dominique Spehner : Measuring quantum correlations with relative Rényi entropie
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 31, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Free ebook http://tinyurl.com/EngMathYT A basic introduction to the divergence of a vector field - one of the basic operations of vector calculus. I discuss how to calculate the divergence and its physical connection with flux density. Plenty of examples are discussed.
From playlist Engineering Mathematics
Dynamical, symplectic and stochastic perspectives on optimization – Michael Jordan – ICM2018
Plenary Lecture 20 Dynamical, symplectic and stochastic perspectives on gradient-based optimization Michael Jordan Abstract: Our topic is the relationship between dynamical systems and optimization. This is a venerable, vast area in mathematics, counting among its many historical threads
From playlist Plenary Lectures
Free ebook http://tinyurl.com/EngMath A short tutorial on how to apply Gauss' Divergence Theorem, which is one of the fundamental results of vector calculus. The theorem is stated and we apply it to a simple example.
From playlist Several Variable Calculus / Vector Calculus
Set Chasing, with an application to online shortest path - Sébastien Bubeck
Computer Science/Discrete Mathematics Seminar I Topic: Set Chasing, with an application to online shortest path Speaker: Sébastien Bubeck Affiliation: Microsoft Research Lab - Redmond Date: April 18, 2022 Since the late 19th century, mathematicians have realized the importance and genera
From playlist Mathematics
30th Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk
Date: Wednesday, June 30, 2021, 10:00am Eastern Time Zone (US & Canada) Speaker: Leon Bungert Title: A Bregman Learning Framework for Sparse Neural Networks Abstract: I will present a novel learning framework based on stochastic Bregman iterations. It allows to train sparse neural netwo
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series
Hubert Wagner (8/17/22): Topological data analysis in non-Euclidean spaces
Many types of data are best modelled with non-Euclidean spaces -- or even non-metric ones. In this talk I will focus on techniques that enable usage of existing TDA tools in the above contexts. I will also highlight some important caveats. Finally, as an example I will discuss a recent suc
From playlist AATRN 2022
26: Divergence Theorem - Valuable Vector Calculus
Video explaining the definition of divergence: https://youtu.be/UEU9dLgmBH4 Video on surface integrals: https://youtu.be/hVBoEEJlNuI The divergence theorem, also called Gauss's theorem, is a natural consequence of the definition of divergence. In this video, we'll see an intuitive explana
From playlist Valuable Vector Calculus
Simple positive divergence example
From playlist Divergence
Calculus 3: Divergence and Curl (6 of 32) What is the Divergence? Part 4
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the divergence using a non-linear example where F=(x^2)i. Next video in the series can be seen at: https://youtu.be/dyWeTKHFlg8
From playlist CALCULUS 3 CH 8 DIVERGENCE AND CURL
8ECM Invited Lecture: Martin Burger
From playlist 8ECM Invited Lectures