Approximating Functions in a Metric Space
Approximations are common in many areas of mathematics from Taylor series to machine learning. In this video, we will define what is meant by a best approximation and prove that a best approximation exists in a metric space. Chapters 0:00 - Examples of Approximation 0:46 - Best Aproximati
From playlist Approximation Theory
Polynomial approximations -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Daniel Spielman - Sparsification of Graphs and Matrices
March 21, 2016 - This talk was part of the Minerva Lecture Series Random graphs and expander graphs can be viewed as sparse approximations of complete graphs, with Ramanujan expanders providing the best possible approximations. We formalize this notion of approximation and ask how well an
From playlist Minerva Lectures - Daniel Spielman
Matthias Mnich: Approximating Sparsest Cut in Low-Treewidth Graphs
The fundamental sparsest cut problem takes as input a graph G together with the edge costs and demands, and seeks a cut that minimizes the ratio between the costs and demands across the cuts. For n-node graphs G of treewidth k, Chlamtáč, Krauthgamer, and Raghavendra (APPROX 2010) presented
From playlist Workshop: Approximation and Relaxation
Linear Approximations and Differentials
Linear Approximation In this video, I explain the concept of a linear approximation, which is just a way of approximating a function of several variables by its tangent planes, and I illustrate this by approximating complicated numbers f without using a calculator. Enjoy! Subscribe to my
From playlist Partial Derivatives
Polynomial approximation of functions (part 1)
Using a polynomial to approximate a function at f(0). More free lessons at: http://www.khanacademy.org/video?v=sy132cgqaiU
From playlist Calculus
Sparsification of graphs and matrices - Daniel Spielman
Daniel Spielman Yale University November 3, 2014 Random graphs and expander graphs can be viewed as sparse approximations of complete graphs, with Ramanujan expanders providing the best possible approximations. We formalize this notion of approximation and ask how well an arbitrary graph
From playlist Mathematics
Robert Seiringer: The local density approximation in density functional theory
We present a mathematically rigorous justification of the Local Density Approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density (the lowest possible energy of all quantum st
From playlist Mathematical Physics
Kai Yu: "Image Classification Using Sparse Coding, Pt. 2"
Graduate Summer School 2012: Deep Learning, Feature Learning "Image Classification Using Sparse Coding, Pt. 2" Kai Yu, Baidu Inc. Institute for Pure and Applied Mathematics, UCLA July 18, 2012 For more information: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summer-school
From playlist GSS2012: Deep Learning, Feature Learning
James Maynard: Large gaps between primes in subsets
Abstract: All previous methods of showing the existence of large gaps between primes have relied on the fact that smooth numbers are unusually sparse. This feature of the argument does not seem to generalise to showing large gaps between primes in subsets, such as values of a polynomial. W
From playlist Number Theory
Approximation with deep networks - Remi Gribonval, Inria
This workshop - organised under the auspices of the Isaac Newton Institute on “Approximation, sampling and compression in data science” — brings together leading researchers in the general fields of mathematics, statistics, computer science and engineering. About the event The workshop ai
From playlist Mathematics of data: Structured representations for sensing, approximation and learning
Testing Sparsity over Known and Unknown Bases by Arnab Bhattacharyya
Statistical Physics Methods in Machine Learning DATE:26 December 2017 to 30 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The theme of this Discussion Meeting is the analysis of distributed/networked algorithms in machine learning and theoretical computer science in the "th
From playlist Statistical Physics Methods in Machine Learning
Factors of sparse polynomials: structural results and some algorithms - Shubhangi Saraf
Computer Science/Discrete Mathematics Seminar II Topic: Factors of sparse polynomials: structural results and some algorithms Speaker: Shubhangi Saraf Affiliation: Member, School of Mathematics Date: March 26, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Joan Bruna: "On Sparse Linear Programming and (simple) neural networks"
Deep Learning and Combinatorial Optimization 2021 "On Sparse Linear Programming and (simple) neural networks" Joan Bruna - New York University Abstract: Linear programming and sparse inference constraints are amongst the most well-studied optimization and estimation problems, where geome
From playlist Deep Learning and Combinatorial Optimization 2021
Twice-Ramanujan Sparsifiers - Nikhil Srivastava
Nikhil Srivastava Yake University September 21, 2009 We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs can be viewed as gen
From playlist Mathematics
Graph Sparsification by Edge-Connectivity and Random Spanning Trees - Nick Harvey
Nick Harvey University of Waterloo April 11, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Factorization-based Sparse Solvers and Preconditions, Lecture 5
Xiaoye Sherry Li's (from Lawrence Berkeley National Laboratory) lecture number five on Factorization-based sparse solves and preconditioners
From playlist Gene Golub SIAM Summer School Videos
Yann LeCun: "A Few (More) Approaches to Unsupervised Learning"
New Deep Learning Techniques 2018 "A Few (More) Approaches to Unsupervised Learning" Yann LeCun, New York University & Facebook DIrector of AI Research Institute for Pure and Applied Mathematics, UCLA February 7, 2018 For more information: http://www.ipam.ucla.edu/programs/workshops/new
From playlist New Deep Learning Techniques 2018
Approximating the edit distance to within a constant factor in truly subquadratic time - Mike Saks
Computer Science/Discrete Mathematics Seminar I Topic: Approximating the edit distance to within a constant factor in truly subquadratic time. Speaker: Mike Saks Affiliation: Rutgers University Date: October 22, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Shmuel Onn: Sparse integer programming is FPT
We show that sparse integer programming, in variable dimension, with linear or separable convex objective, is fixed-parameter tractable. This is a culmination of a long line of research with many colleagues. We also discuss some of the many consequences of this result, which provides a new
From playlist Workshop: Tropical geometry and the geometry of linear programming