In statistics, sufficient dimension reduction (SDR) is a paradigm for analyzing data that combines the ideas of dimension reduction with the concept of sufficiency. Dimension reduction has long been a primary goal of regression analysis. Given a response variable y and a p-dimensional predictor vector , regression analysis aims to study the distribution of , the conditional distribution of given . A dimension reduction is a function that maps to a subset of , k < p, thereby reducing the dimension of . For example, may be one or more linear combinations of . A dimension reduction is said to be sufficient if the distribution of is the same as that of . In other words, no information about the regression is lost in reducing the dimension of if the reduction is sufficient. (Wikipedia).
The concept of “dimension” in measured signals
This is part of an online course on covariance-based dimension-reduction and source-separation methods for multivariate data. The course is appropriate as an intermediate applied linear algebra course, or as a practical tutorial on multivariate neuroscience data analysis. More info here:
From playlist Dimension reduction and source separation
Drawing the 4th, 5th, 6th, and 7th dimension
How to draw 4, 5, 6, and 7 dimensional objects.
From playlist Physics
Volume and Capacity (Converting between units of volume)
More resources available at www.misterwootube.com
From playlist Applications of Measurement
Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Dimensions (1 of 3: The Traditional Definition - Directions)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Bernd Schulze: Characterizing Minimally Flat Symmetric Hypergraphs
Scene analysis is concerned with the reconstruction of d-dimensional objects, such as polyhedral surfaces, from (d-1)-dimensional pictures (i.e., projections of the objects onto a hyperplane). This theory is closely connected to rigidity theory and other areas of discrete applied geometry,
From playlist HIM Lectures 2015
Proper Actions and Representation Theory Part 2
Professor Toshiyuki Kobayashi, University of Tokyo, Japan
From playlist Distinguished Visitors Lecture Series
Chapter 4 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Limit of functions of two variables. We show how to prove a limit does not exist. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
The Shafarevich Conjecture for Hypersurfaces in Abelian Varieties - Will Sawin
Joint IAS/Princeton University Number Theory Seminar Topic: The Shafarevich Conjecture for Hypersurfaces in Abelian Varieties Speaker: Will Sawin Affiliation: Columbia University Date: March 18, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Lattice Studies of Three-Dimensional Super-Yang--Mills by David Schaich
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
From playlist NUMSTRING 2022
Kęstutis Česnavičius - Purity for Flat Cohomology
The absolute cohomological purity conjecture of Grothendieck proved by Gabber ensures that on regular schemes étale cohomology classes of fixed cohomological degree extend uniquely over closed subschemes of large codimension. I will discuss the corresponding phenomenon for flat cohomology.
From playlist Journée Gretchen & Barry Mazur
Andrei Teleman - Instantons and holomorphic curves on surfaces of class VII (Part 4)
This series of lectures is dedicated to recent results concerning the existence of holomorphic curves on the surfaces of class VII. The first lecture will be an introduction to the Donaldson theory. We will present the fundamental notions and some important results in the theory, explainin
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
DDPS | Deep learning for reduced order modeling
Description: Reduced order modeling (ROM) techniques, such as the reduced basis method, provide nowadays an essential toolbox for the efficient approximation of parametrized differential problems, whenever they must be solved either in real-time, or in several different scenarios. These ta
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Geometric Deep Learning II: Georg Gottwald
Machine Learning for the Working Mathematician: Week Six 31 March 2022 Georg Gottwald, Geometric Deep Learning II: Learning the Manifold Seminar series homepage (includes Zoom link): https://sites.google.com/view/mlwm-seminar-2022 Week Six part two lecture: https://youtu.be/q5gvsmF474k
From playlist Machine Learning for the Working Mathematician
Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Reducibility for the Quasi-Periodic Liner Schrodinger and Wave Equations - Lars Hakan Eliasson
Lars Hakan Eliasson University of Paris VI; Institute for Advanced Study February 21, 2012 We shall discuss reducibility of these equations on the torus with a small potential that depends quasi-periodically on time. Reducibility amounts to "reduce” the equation to a time-independent linea
From playlist Mathematics